25x25 mega.txt

Order 5: digits 25; houses 75, cells 625.

Grid.grid1: initial copying

pending={a2, a5, a6, a7, a10, a14, a15, a16, a19, a21, a22, b2, b4, b5, b6, b7, b8, b9, b13, b15, b18, b19, b20, b21, b23, b24, c1, c3, c4, c5, c6, c7, c8, c9, c11, c12, c14, c15, c18, c19, c21, c25, d1, d2, d3, d4, d5, d6, d7, d8, d13, d15, d16, d20, d21, e2, e5, e6, e9, e11, e15, e17, e24, e25, f2, f4, f5, f6, f7, f8, f13, f14, f16, f20, f21, f22, g1, g2, g4, g6, g8, g9, g11, g12, g13, g14, g16, g19, g21, g24, h1, h2, h7, h10, h11, h13, h14, h17, h21, h23, h25, i1, i3, i5, i7, i9, i10, i13, i14, i15, i16, i19, i22, j1, j2, j3, j4, j5, j6, j8, j11, j14, j15, j16, j17, j18, j19, j21, j23, j24, k4, k7, k8, k13, k15, k19, k20, k21, k24, k25, l1, l2, l3, l5, l7, l8, l9, l11, l15, l16, l17, l18, l19, l20, m2, m3, m5, m7, m8, m9, m14, m15, m16, m17, m23, m24, m25, n5, n6, n8, n12, n13, n16, n18, n19, n21, n22, n24, n25, o1, o6, o7, o8, o9, o10, o12, o16, o18, o22, o24, p4, p5, p6, p9, p11, p12, p13, p14, p18, p19, p22, p23, p25, q5, q6, q10, q11, q12, q13, q18, q20, q21, q22, q23, q25, r1, r6, r9, r10, r12, r13, r17, r19, r24, r25, s1, s3, s4, s7, s9, s10, s13, s14, s17, s19, s20, s21, s23, s25, t2, t6, t7, t10, t14, t16, t19, t22, u5, u10, u11, u16, u17, u18, u20, u22, v4, v7, v10, v14, v15, v16, v19, v20, v22, v23, v25, w1, w3, w5, w8, w9, w11, w13, w21, w23, x1, x5, x6, x8, x9, x11, x12, x16, x21, x22, x24, x25, y2, y3, y4, y5, y7, y9, y11, y14, y16, y17, y18, y19, y22, y23}

deduce.grid1: naked-singles

deduce.grid1: hidden-singles

deduce.grid1.rowa. a24 is 4 by hidden-single.

pending={a24}

deduce.grid1: naked-singles

deduce.grid1: hidden-singles

deduce.grid1.rowa. a12 is 16 by hidden-single.

pending={a12}

deduce.grid1: naked-singles

deduce.grid1: hidden-singles

deduce.grid1.rowb. b17 is 19 by hidden-single.

pending={b17}

deduce.grid1: naked-singles

deduce.grid1: hidden-singles

deduce.grid1.rowb. b11 is 22 by hidden-single.

deduce.grid1.rowb. b22 is 15 by hidden-single.

pending={b11, b22}

deduce.grid1: naked-singles

deduce.grid1: hidden-singles

deduce.grid1.rowb. b12 is 25 by hidden-single.

pending={b12}

deduce.grid1: naked-singles

deduce.grid1: hidden-singles

deduce.grid1.rowb. b25 is 21 by hidden-single.

pending={b25}

deduce.grid1: naked-singles

deduce.grid1: hidden-singles

deduce.grid1.rowd. d10 is 10 by hidden-single.

pending={d10}

deduce.grid1: naked-singles

deduce.grid1: hidden-singles

deduce.grid1.rowf. f18 is 3 by hidden-single.

pending={f18}

deduce.grid1: naked-singles

deduce.grid1: hidden-singles

deduce.grid1.rowf. f19 is 5 by hidden-single.

pending={f19}

deduce.grid1: naked-singles

deduce.grid1: hidden-singles

deduce.grid1.rowh. h6 is 24 by hidden-single.

pending={h6}

deduce.grid1: naked-singles

deduce.grid1: hidden-singles

deduce.grid1.rowj. j22 is 16 by hidden-single.

pending={j22}

deduce.grid1: naked-singles

deduce.grid1: hidden-singles

deduce.grid1.rowc. c24 is 16 by hidden-single.

pending={c24}

deduce.grid1: naked-singles

deduce.grid1: hidden-singles

deduce.grid1.rowf. f1 is 16 by hidden-single.

pending={f1}

deduce.grid1: naked-singles

deduce.grid1: hidden-singles

deduce.grid1.rowj. j7 is 10 by hidden-single.

pending={j7}

deduce.grid1: naked-singles

deduce.grid1: hidden-singles

deduce.grid1.rowj. j10 is 11 by hidden-single.

pending={j10}

deduce.grid1: naked-singles

deduce.grid1: hidden-singles

deduce.grid1.rowk. k6 is 3 by hidden-single.

pending={k6}

deduce.grid1: naked-singles

deduce.grid1: hidden-singles

deduce.grid1.rowl. l12 is 1 by hidden-single.

pending={l12}

deduce.grid1: naked-singles

deduce.grid1: hidden-singles

deduce.grid1.rowp. p10 is 12 by hidden-single.

pending={p10}

deduce.grid1: naked-singles

deduce.grid1: hidden-singles

deduce.grid1.col6. s6 is 7 by hidden-single.

pending={s6}

deduce.grid1: naked-singles

deduce.grid1: hidden-singles

deduce.grid1.col14. r14 is 17 by hidden-single.

pending={r14}

deduce.grid1: naked-singles

deduce.grid1: hidden-singles

deduce.grid1.col16. w16 is 13 by hidden-single.

pending={w16}

deduce.grid1: naked-singles

deduce.grid1: hidden-singles

deduce.grid1.col18. r18 is 10 by hidden-single.

pending={r18}

deduce.grid1: naked-singles

deduce.grid1: hidden-singles

deduce.grid1.col20. y20 is 17 by hidden-single.

pending={y20}

deduce.grid1: naked-singles

deduce.grid1: hidden-singles

deduce.grid1.col21. i21 is 4 by hidden-single.

pending={i21}

deduce.grid1: naked-singles

deduce.grid1: hidden-singles

deduce.grid1.rowi. i23 is 10 by hidden-single.

pending={i23}

deduce.grid1: naked-singles

deduce.grid1: hidden-singles

deduce.grid1.rowh. h15 is 10 by hidden-single.

pending={h15}

deduce.grid1: naked-singles

deduce.grid1: hidden-singles

deduce.grid1.col24. d24 is 5 by hidden-single.

deduce.grid1.col24. i24 is 20 by hidden-single.

pending={d24, i24}

deduce.grid1: naked-singles

deduce.grid1: hidden-singles

deduce.grid1.rowj. j13 is 20 by hidden-single.

pending={j13}

deduce.grid1: naked-singles

deduce.grid1: hidden-singles

deduce.grid1.col21. m21 is 5 by hidden-single.

pending={m21}

deduce.grid1: naked-singles

deduce.grid1: hidden-singles

deduce.grid1.col24. h24 is 14 by hidden-single.

pending={h24}

deduce.grid1: naked-singles

deduce.grid1: hidden-singles

deduce.grid1.col25. o25 is 20 by hidden-single.

pending={o25}

deduce.grid1: naked-singles

deduce.grid1: hidden-singles

deduce.grid1.box14. n17 is 11 by hidden-single.

pending={n17}

deduce.grid1: naked-singles

deduce.grid1: hidden-singles

deduce.grid1: naked-pairs

two's heap=a13 {7|8}, j25 {7|12}, s24 {3|17}, i6 {6|15}, d9 {7|13}, l6 {6|19}, c2 {13|17}, y13 {3|25}, c13 {5|24}, j9 {12|19}, b14 {2|14}, g5 {18|25}, m18 {8|24}, p21 {8|24}, g7 {18|20}, h5 {18|25}.

Naked-pair {18|25} in cells {g5, h5} contained within {col5, box6}, updating cells {f3, g3, h3, h4, i2, i4, k5, o5, r5, s5, t5, v5}:

grid1
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
a
12   
    10
     
     
     
12
12   
    10
11 1314 
     
     
 2   
    10
  1314 
     
     
22 5 21
1    
   9 
   14 
     
    25
     
 7   
  13  
     
    25
17
 2   
  89 
  1314 
     
     
16
     
 78  
     
     
     
18 23 24
1    
  89 
    15
     
    25
1    
  89 
11  1415
     
    25
3
12   
  8  
   1415
     
    25
20 19
1    
6  9 
  13  
     
     
4
 2   
6  9 
     
     
     
b
12  5
     
     
     
     
3
12  5
     
   14 
     
     
23 7 12 6 24 20
1    
   9 
   14 
     
     
22 25 10
 2   
     
   14 
     
     
17
12  5
   9 
     
     
     
19 13 4 16 11 15 8 18 21
c 4
     
     
  13  
 17   
     
21 8 20 18 2 15 3
     
   9 
  13  
     
  23  
1 11
    5
     
     
     
   24 
12 19
    5
   9 
     
     
  23  
     
   9 
     
     
 2223 25
6 10
    5
     
     
     
 2223 25
7
     
   9 
  13  
 17   
     
     
   9 
  13  
 17   
  2324 
16 14
d 25 9 16 15 24 11 8 19
     
 7   
  13  
     
     
10
 2   
     
  1314 
     
21    
  3  
 7   
  1314 
     
21    
4
 23  
 7   
   14 
     
     
6 17
1    
     
     
     
21 23  
1    
     
 12 14 
    20
     
12   
     
 12   
    20
21    
18 22
123  
     
 1213  
     
     
1    
     
 1213  
     
  23  
5
 2   
     
 12   
     
  23  
e
12  5
     
     
 1718  
     
19
12  5
     
11 1314 
 1718  
     
 2  5
     
  1314 
 1718  
     
6 22 4
1    
   9 
   14 
     
  23  
16
1    
   9 
  1314 
     
  23  
20
  3 5
  89 
  1314 
     
21  24 
  3 5
  8  
     
     
   24 
 23  
     
   14 
     
   24 
15
12  5
   9 
11    
     
  23  
7
1   5
  89 
1112 14 
     
     
12   
  8  
1112   
     
21    
12  5
  8  
   14 
     
21 23  
  3  
   9 
     
 17   
   24 
123  
   9 
 1213  
 17   
     
1    
   9 
 1213  
 17   
  2324 
10 25
f 16 20
     
     
    15
 17   
     
9 10 21 14 2
     
  8  
 12  15
  1819 
     
     
  8  
    15
  18  
     
     
  8  
     
 171819 
     
     
 78  
 12   
  1819 
     
6 4
     
 78  
 12   
  18  
     
25
     
  8  
  13  
  18  
 2223  
3 5 11 1 24
     
 7   
 1213  
 17   
  23  
     
  8  
  13  
 17   
 2223  
     
 78  
 12   
 17   
 2223  
g 11 5
   4 
6    
   14 
     
     
3
     
     
     
  18  
    25
17
     
     
     
  18 20
     
16 23
1    
  8  
     
  18 20
     
24 2 9 22
     
 78  
 12 14 
  18  
    25
10
1  4 
  8  
  13  
  18  
     
1    
 78  
 12 14 
     
     
15
1  4 
 78  
   14 
     
     
21
     
6 8  
 1213  
     
     
     
67   
 1213  
     
     
19
     
678  
 12   
     
     
h 7 23
   4 
6    
     
 17   
     
     
6    
     
 17   
     
     
     
     
  18  
    25
24 13
1    
6 8  
     
     
    25
     
6 8  
 12   
  1819 
    25
3 11
     
  8  
 12   
  1819 
     
16 21 10
1    
   9 
     
  18  
     
20
1    
  89 
 12   
   19 
     
1    
  8  
 12   
     
 22   
1  4 
  8  
     
   19 
 22   
2
     
6 89 
 12   
 17   
     
5 14 15
i 19
     
     
   1415
 17   
21    
12
     
6    
   14 
 17   
21    
2
     
6    
    15
     
     
7
     
6 8  
     
     
    25
5 22
     
  8  
   14 
 1718  
    25
     
  8  
   14 
  18  
     
1 13 3 16
     
  89 
     
  18  
  23  
     
  89 
   14 
     
     
24
     
  8  
   14 
     
  23  
4 11 10 20
     
6 89 
     
 17   
  23  
j 13 22 24 1 8 9 10 4
     
     
 12   
   19 
     
11 23
     
 7   
 12 14 
   19 
     
20 15 5 21 17 2 6
     
 7   
   14 
   19 
     
18 16 3 25
     
 7   
 12   
     
     
k
 2  5
  8  
     
  18  
2122 24 
 2   
  8  
    15
     
21  24 
 2  5
 78  
    15
  1819 
     
12
    5
     
     
   19 
21    
3 25 13
   4 
6 8  
    15
  1819 
 22   
     
  8  
    15
16 18  
     
   45
  8  
     
  1819 
21    
   45
678  
     
  1819 
21  24 
17
     
67   
     
16    
   24 
20
 2   
6    
     
     
  23  
     
6 8  
     
16    
21 2324 
     
 78  
     
     
   24 
9 10 14
 2   
6 8  
     
     
21    
     
67   
     
  1819 
21    
11 1
l 23 4 25
 2   
    10
     
  18  
     
14
     
6    
     
   19 
     
24 12 21
     
  8  
     
16 18  
     
3 1
     
 78  
11    
  1819 
     
     
67  10
11    
16    
     
22 15 5 17 13 20
     
  8910
     
   19 
     
 2   
6 8910
     
     
     
     
67 9 
     
  1819 
     
 2   
6 89 
     
     
     
 2   
6789 
     
     
     
m
 2   
  8 10
     
 1718 20
21  24 
6 9
 2   
    10
     
 1718 20
21  24 
11
   4 
     
    15
   1920
     
23 7 1
     
  8  
    15
  18 20
     
   4 
  8  
     
  1819 
21    
   4 
  8  
     
  1819 
21  24 
     
  8  
     
  1819 
   24 
25 13 3 14
     
  8  
     
     
   24 
 2   
  8  
     
     
21    
 2   
  8  
     
     
21  24 
5
 2   
  8 10
     
 17   
21    
22 12 16
n
1   5
  8 10
     
  18 20
2122   
1    
  8 10
     
     
21    
1   5
 78 10
     
  18  
     
    5
    10
     
  18 20
2122   
16 14
     
     
     
  18 20
 22   
17
     
6 8  
     
  18  
 22   
     
  8  
     
  18 20
     
    5
  89 
     
  18  
21    
15 2
     
67  10
     
     
     
     
 789 
     
  18  
21    
12 11 4 19
1    
678  
     
     
21   25
13 23
     
67 9 
     
  18  
21   25
24 3
o 3
1    
  8  
  13  
 17   
21  24 
1    
 78  
  13  
 17 19 
     
     
     
  13  
 17   
21  24 
1    
     
     
   19 
21    
2 9 11 10 5
     
  8  
   14 
   19 
21    
23
     
 78  
 12   
   19 
   24 
     
67   
   14 
16    
   24 
     
 78  
 12 14 
16    
21    
22
1    
6 8  
     
16    
21  2425
18
1    
  8  
     
16    
21    
1    
678  
     
     
21  2425
     
  8  
     
 17 19 
    25
4
     
67   
     
 17 19 
21   25
15 20
p
12   
  8  
     
     
21  24 
12   
  8  
11 13  
     
21  24 
12   
  8  
11 13  
     
  23  
7 3 25
     
     
11    
  18  
 22   
     
     
     
     
212223  
9 12 6 10 15 19
 2 4 
     
11    
  18  
     
1    
     
11    
  18  
     
1  4 
  8  
     
  18  
21  24 
16 17
1  4 
  8  
     
     
21  24 
     
  8  
     
     
   24 
14 20
1    
  8  
  13  
     
 2223  
5
q
1   5
  8 10
     
     
21  24 
1    
  8 10
11 13  
     
21  24 
1   5
  8 10
11 13  
     
  23  
    5
    10
  13  
     
21  24 
17 16
    5
     
11   15
  18  
     
    5
     
     
     
21 23  
     
     
  13 15
  18  
     
19 12 20 14
     
 7   
11    
     
  2324 
     
 7 9 
11    
  18  
     
1   5
   9 
11    
  18  
     
1    
  89 
    15
  18  
21  24 
22
1    
  8  
11    
     
21    
3 6 25 2
1    
  89 
  13  
     
  23  
4
r 15
1    
     
11  14 
16    
    25
1   5
6    
11  14 
   19 
  23  
    5
6    
   14 
16   20
    25
1   5
     
     
   19 
  23  
8
    5
     
11    
    20
     
  3 5
     
     
    20
  23  
2 24
   45
   9 
     
     
    25
22 13 17
   4 
   9 
11    
16    
    25
1   5
6  9 
11    
    20
     
12 10 7
1  45
6    
     
   19 
     
  3  
   9 
     
   19 
     
1 3  
   9 
     
     
     
1    
   9 
11    
   19 
  23  
21 18
s 9
     
     
11    
     
   2425
22 4
    5
     
 12   
   19 
     
7 1
  3 5
     
     
    20
     
14 6
    5
     
     
  18  
    25
  3 5
     
     
  18  
   24 
21 8
     
     
11    
  18  
    25
    5
     
11    
  18 20
     
2
    5
     
11    
   1920
   24 
23 13 16
  3  
     
 12   
 17   
     
15
  3  
     
     
 17   
     
10
t
 2  5
6 8  
     
    20
21  24 
18
 2  5
6 8  
11 13  
   19 
  23  
 2  5
6    
  13  
16   20
21  24 
    5
     
 12   
   19 
21 23  
10 17
  3 5
     
     
    20
212223  
     
     
  13 15
     
 22   
4
 2  5
   9 
     
     
     
  3 5
   9 
     
     
   24 
  3 5
     
11    
     
  2324 
1
 2   
   9 
11    
16    
     
14
     
6 89 
    15
     
21  24 
    5
  89 
11   15
   1920
   24 
25
    5
6 8  
    15
   19 
21  24 
  3  
  89 
     
   19 
   24 
7
     
   9 
111213  
   19 
  2324 
  3  
  89 
  13  
     
 2223  
     
  89 
1112   
     
 222324 
u
12  5
6 8 10
     
 1718  
   24 
12   
  8 10
     
1617   
   2425
12  5
6 8 10
     
 1718  
  23  
 2  5
6   10
     
161718  
   2425
4
1    
6    
  13  
    20
     
    5
     
     
16   20
     
1   5
6 89 
   14 
    20
     
     
6 8  
  13  
     
     
7 15
     
6 8  
  1314 
  18  
     
     
  8  
11    
  18  
  23 25
 2   
6    
11  14 
    20
  23  
12   
  8  
11  14 
  18  
    25
19 3 21
12   
     
11    
16   20
     
12
     
  8910
     
 17   
   2425
22
1    
6  9 
11    
 17   
   2425
12   
6 89 
     
 17   
     
 2   
6 89 
11    
 17   
   24 
v
12   
6 8 10
     
 17   
2122   
12   
  8 10
     
 17   
21    
12   
6 8 10
     
 17   
  23  
11
1    
     
     
     
21 23  
1  4 
6    
  13 15
    20
     
3
1    
6 8  
     
    20
2122   
   4 
6 8  
  13 15
     
 22   
25
 2 4 
  8  
  13  
     
21    
   4 
6 8  
 1213  
     
21    
     
  8  
 12   
     
  23  
5 24 7
1    
6    
    15
     
 22   
1    
     
    15
    20
     
14 9
     
  8 10
    15
 17   
     
18 16
12   
6 8  
     
 17   
     
19
w 12
12   
  8  
     
16    
21  2425
3
 2  5
6    
     
16 18  
21  2425
9
1  4 
6    
    15
   1920
     
    5
     
    15
16  1920
     
10 17
12   
  8  
    15
16   20
21    
7
   4 
6 8  
     
  1819 
21    
22
 2   
6    
11    
    20
     
12 4 
  8  
11    
  18  
21   25
13
1    
6    
    15
16    
   2425
1   5
     
11   15
    20
   2425
12   
     
11    
16   20
     
12  5
6    
    15
     
   2425
23
12   
6 8  
     
     
21    
14
12   
6 8  
     
     
     
 2   
6 8  
11    
     
   24 
x 14
12   
  8  
     
16    
21   25
12  5
6 8  
     
     
     
 2  5
6    
     
16    
2122  25
15 23
    5
     
     
16  19 
 22   
18 24
12   
  89 
     
16    
21    
10 17
  3  
  8  
11    
   19 
    25
 23  
6    
11    
     
     
12   
  8  
11    
     
21   25
4
1    
6    
     
16    
 22  25
1   5
     
11    
     
    25
12   
     
11    
16    
 22   
12  5
6    
     
     
 22  25
12 20
1    
6  9 
11    
     
21   25
7 13
y
12   
6    
     
     
2122 24 
7 20 19 13
1    
6    
    15
     
     
12
1    
6    
   14 
     
2122   
11
12   
     
   1415
     
21    
16
  3  
6    
   14 
     
21    
  3  
     
     
     
    25
9
12   
     
   14 
     
21   25
8 10 23 18 17
  3  
     
    15
     
   2425
5 4
123  
6    
     
     
     
 2   
6    
     
     
   24 

backtrack.grid1 → grid2: a13 guess 7 ∈ {7|8}

pending={a13}

deduce.grid2: naked-singles

deduce.grid2: hidden-singles

deduce.grid2.rowd. d9 is 7 by hidden-single.

pending={d9}

deduce.grid2: naked-singles

deduce.grid2: hidden-singles

deduce.grid2: naked-pairs

two's heap=j25 {7|12}, i6 {6|15}, b14 {2|14}, s24 {3|17}, h4 {6|17}, c2 {13|17}, g7 {18|20}, f3 {15|17}, h5 {18|25}, c13 {5|24}, j9 {12|19}, g5 {18|25}, l6 {6|19}, m18 {8|24}, p21 {8|24}, a9 {13|25}, y13 {3|25}.

Naked-pair {18|25} in cells {g5, h5} contained within {col5, box6}, updating cells {f3, g3, h3, h4, i2, i4, k5, o5, r5, s5, t5, v5}:

grid2
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
a
12   
    10
     
     
     
12
12   
    10
11 1314 
     
     
 2   
    10
  1314 
     
     
22 5 21
1    
   9 
   14 
     
    25
     
     
  13  
     
    25
17
 2   
  89 
  1314 
     
     
16 7 18 23 24
1    
  89 
    15
     
    25
1    
  89 
11  1415
     
    25
3
12   
  8  
   1415
     
    25
20 19
1    
6  9 
  13  
     
     
4
 2   
6  9 
     
     
     
b
12  5
     
     
     
     
3
12  5
     
   14 
     
     
23 7 12 6 24 20
1    
   9 
   14 
     
     
22 25 10
 2   
     
   14 
     
     
17
12  5
   9 
     
     
     
19 13 4 16 11 15 8 18 21
c 4
     
     
  13  
 17   
     
21 8 20 18 2 15 3
     
   9 
  13  
     
  23  
1 11
    5
     
     
     
   24 
12 19
    5
   9 
     
     
  23  
     
   9 
     
     
 2223 25
6 10
    5
     
     
     
 2223 25
7
     
   9 
  13  
 17   
     
     
   9 
  13  
 17   
  2324 
16 14
d 25 9 16 15 24 11 8 19 7 10
 2   
     
  1314 
     
21    
  3  
     
  1314 
     
21    
4
 23  
     
   14 
     
     
6 17
1    
     
     
     
21 23  
1    
     
 12 14 
    20
     
12   
     
 12   
    20
21    
18 22
123  
     
 1213  
     
     
1    
     
 1213  
     
  23  
5
 2   
     
 12   
     
  23  
e
12  5
     
     
 1718  
     
19
12  5
     
11 1314 
 1718  
     
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 1718  
     
6 22 4
1    
   9 
   14 
     
  23  
16
1    
   9 
  1314 
     
  23  
20
  3 5
  89 
  1314 
     
21  24 
  3 5
  8  
     
     
   24 
 23  
     
   14 
     
   24 
15
12  5
   9 
11    
     
  23  
7
1   5
  89 
1112 14 
     
     
12   
  8  
1112   
     
21    
12  5
  8  
   14 
     
21 23  
  3  
   9 
     
 17   
   24 
123  
   9 
 1213  
 17   
     
1    
   9 
 1213  
 17   
  2324 
10 25
f 16 20
     
     
    15
 17   
     
9 10 21 14 2
     
  8  
 12  15
  1819 
     
     
  8  
    15
  18  
     
     
  8  
     
 171819 
     
     
 78  
 12   
  1819 
     
6 4
     
 78  
 12   
  18  
     
25
     
  8  
  13  
  18  
 2223  
3 5 11 1 24
     
 7   
 1213  
 17   
  23  
     
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  13  
 17   
 2223  
     
 78  
 12   
 17   
 2223  
g 11 5
   4 
6    
   14 
     
     
3
     
     
     
  18  
    25
17
     
     
     
  18 20
     
16 23
1    
  8  
     
  18 20
     
24 2 9 22
     
 78  
 12 14 
  18  
    25
10
1  4 
  8  
  13  
  18  
     
1    
 78  
 12 14 
     
     
15
1  4 
 78  
   14 
     
     
21
     
6 8  
 1213  
     
     
     
67   
 1213  
     
     
19
     
678  
 12   
     
     
h 7 23
   4 
6    
     
 17   
     
     
6    
     
 17   
     
     
     
     
  18  
    25
24 13
1    
6 8  
     
     
    25
     
6 8  
 12   
  1819 
    25
3 11
     
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 12   
  1819 
     
16 21 10
1    
   9 
     
  18  
     
20
1    
  89 
 12   
   19 
     
1    
  8  
 12   
     
 22   
1  4 
  8  
     
   19 
 22   
2
     
6 89 
 12   
 17   
     
5 14 15
i 19
     
     
   1415
 17   
21    
12
     
6    
   14 
 17   
21    
2
     
6    
    15
     
     
7
     
6 8  
     
     
    25
5 22
     
  8  
   14 
 1718  
    25
     
  8  
   14 
  18  
     
1 13 3 16
     
  89 
     
  18  
  23  
     
  89 
   14 
     
     
24
     
  8  
   14 
     
  23  
4 11 10 20
     
6 89 
     
 17   
  23  
j 13 22 24 1 8 9 10 4
     
     
 12   
   19 
     
11 23
     
 7   
 12 14 
   19 
     
20 15 5 21 17 2 6
     
 7   
   14 
   19 
     
18 16 3 25
     
 7   
 12   
     
     
k
 2  5
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  18  
2122 24 
 2   
  8  
    15
     
21  24 
 2  5
 78  
    15
  1819 
     
12
    5
     
     
   19 
21    
3 25 13
   4 
6 8  
    15
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 22   
     
  8  
    15
16 18  
     
   45
  8  
     
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21    
   45
678  
     
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21  24 
17
     
67   
     
16    
   24 
20
 2   
6    
     
     
  23  
     
6 8  
     
16    
21 2324 
     
 78  
     
     
   24 
9 10 14
 2   
6 8  
     
     
21    
     
67   
     
  1819 
21    
11 1
l 23 4 25
 2   
    10
     
  18  
     
14
     
6    
     
   19 
     
24 12 21
     
  8  
     
16 18  
     
3 1
     
  8  
11    
  1819 
     
     
67  10
11    
16    
     
22 15 5 17 13 20
     
  8910
     
   19 
     
 2   
6 8910
     
     
     
     
67 9 
     
  1819 
     
 2   
6 89 
     
     
     
 2   
6789 
     
     
     
m
 2   
  8 10
     
 1718 20
21  24 
6 9
 2   
    10
     
 1718 20
21  24 
11
   4 
     
    15
   1920
     
23 7 1
     
  8  
    15
  18 20
     
   4 
  8  
     
  1819 
21    
   4 
  8  
     
  1819 
21  24 
     
  8  
     
  1819 
   24 
25 13 3 14
     
  8  
     
     
   24 
 2   
  8  
     
     
21    
 2   
  8  
     
     
21  24 
5
 2   
  8 10
     
 17   
21    
22 12 16
n
1   5
  8 10
     
  18 20
2122   
1    
  8 10
     
     
21    
1   5
 78 10
     
  18  
     
    5
    10
     
  18 20
2122   
16 14
     
     
     
  18 20
 22   
17
     
6 8  
     
  18  
 22   
     
  8  
     
  18 20
     
    5
  89 
     
  18  
21    
15 2
     
67  10
     
     
     
     
 789 
     
  18  
21    
12 11 4 19
1    
678  
     
     
21   25
13 23
     
67 9 
     
  18  
21   25
24 3
o 3
1    
  8  
  13  
 17   
21  24 
1    
 78  
  13  
 17 19 
     
     
     
  13  
 17   
21  24 
1    
     
     
   19 
21    
2 9 11 10 5
     
  8  
   14 
   19 
21    
23
     
  8  
 12   
   19 
   24 
     
67   
   14 
16    
   24 
     
 78  
 12 14 
16    
21    
22
1    
6 8  
     
16    
21  2425
18
1    
  8  
     
16    
21    
1    
678  
     
     
21  2425
     
  8  
     
 17 19 
    25
4
     
67   
     
 17 19 
21   25
15 20
p
12   
  8  
     
     
21  24 
12   
  8  
11 13  
     
21  24 
12   
  8  
11 13  
     
  23  
7 3 25
     
     
11    
  18  
 22   
     
     
     
     
212223  
9 12 6 10 15 19
 2 4 
     
11    
  18  
     
1    
     
11    
  18  
     
1  4 
  8  
     
  18  
21  24 
16 17
1  4 
  8  
     
     
21  24 
     
  8  
     
     
   24 
14 20
1    
  8  
  13  
     
 2223  
5
q
1   5
  8 10
     
     
21  24 
1    
  8 10
11 13  
     
21  24 
1   5
  8 10
11 13  
     
  23  
    5
    10
  13  
     
21  24 
17 16
    5
     
11   15
  18  
     
    5
     
     
     
21 23  
     
     
  13 15
  18  
     
19 12 20 14
     
 7   
11    
     
  2324 
     
 7 9 
11    
  18  
     
1   5
   9 
11    
  18  
     
1    
  89 
    15
  18  
21  24 
22
1    
  8  
11    
     
21    
3 6 25 2
1    
  89 
  13  
     
  23  
4
r 15
1    
     
11  14 
16    
    25
1   5
6    
11  14 
   19 
  23  
    5
6    
   14 
16   20
    25
1   5
     
     
   19 
  23  
8
    5
     
11    
    20
     
  3 5
     
     
    20
  23  
2 24
   45
   9 
     
     
    25
22 13 17
   4 
   9 
11    
16    
    25
1   5
6  9 
11    
    20
     
12 10 7
1  45
6    
     
   19 
     
  3  
   9 
     
   19 
     
1 3  
   9 
     
     
     
1    
   9 
11    
   19 
  23  
21 18
s 9
     
     
11    
     
   2425
22 4
    5
     
 12   
   19 
     
7 1
  3 5
     
     
    20
     
14 6
    5
     
     
  18  
    25
  3 5
     
     
  18  
   24 
21 8
     
     
11    
  18  
    25
    5
     
11    
  18 20
     
2
    5
     
11    
   1920
   24 
23 13 16
  3  
     
 12   
 17   
     
15
  3  
     
     
 17   
     
10
t
 2  5
6 8  
     
    20
21  24 
18
 2  5
6 8  
11 13  
   19 
  23  
 2  5
6    
  13  
16   20
21  24 
    5
     
 12   
   19 
21 23  
10 17
  3 5
     
     
    20
212223  
     
     
  13 15
     
 22   
4
 2  5
   9 
     
     
     
  3 5
   9 
     
     
   24 
  3 5
     
11    
     
  2324 
1
 2   
   9 
11    
16    
     
14
     
6 89 
    15
     
21  24 
    5
  89 
11   15
   1920
   24 
25
    5
6 8  
    15
   19 
21  24 
  3  
  89 
     
   19 
   24 
7
     
   9 
111213  
   19 
  2324 
  3  
  89 
  13  
     
 2223  
     
  89 
1112   
     
 222324 
u
12  5
6 8 10
     
 1718  
   24 
12   
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1617   
   2425
12  5
6 8 10
     
 1718  
  23  
 2  5
6   10
     
161718  
   2425
4
1    
6    
  13  
    20
     
    5
     
     
16   20
     
1   5
6 89 
   14 
    20
     
     
6 8  
  13  
     
     
7 15
     
6 8  
  1314 
  18  
     
     
  8  
11    
  18  
  23 25
 2   
6    
11  14 
    20
  23  
12   
  8  
11  14 
  18  
    25
19 3 21
12   
     
11    
16   20
     
12
     
  8910
     
 17   
   2425
22
1    
6  9 
11    
 17   
   2425
12   
6 89 
     
 17   
     
 2   
6 89 
11    
 17   
   24 
v
12   
6 8 10
     
 17   
2122   
12   
  8 10
     
 17   
21    
12   
6 8 10
     
 17   
  23  
11
1    
     
     
     
21 23  
1  4 
6    
  13 15
    20
     
3
1    
6 8  
     
    20
2122   
   4 
6 8  
  13 15
     
 22   
25
 2 4 
  8  
  13  
     
21    
   4 
6 8  
 1213  
     
21    
     
  8  
 12   
     
  23  
5 24 7
1    
6    
    15
     
 22   
1    
     
    15
    20
     
14 9
     
  8 10
    15
 17   
     
18 16
12   
6 8  
     
 17   
     
19
w 12
12   
  8  
     
16    
21  2425
3
 2  5
6    
     
16 18  
21  2425
9
1  4 
6    
    15
   1920
     
    5
     
    15
16  1920
     
10 17
12   
  8  
    15
16   20
21    
7
   4 
6 8  
     
  1819 
21    
22
 2   
6    
11    
    20
     
12 4 
  8  
11    
  18  
21   25
13
1    
6    
    15
16    
   2425
1   5
     
11   15
    20
   2425
12   
     
11    
16   20
     
12  5
6    
    15
     
   2425
23
12   
6 8  
     
     
21    
14
12   
6 8  
     
     
     
 2   
6 8  
11    
     
   24 
x 14
12   
  8  
     
16    
21   25
12  5
6 8  
     
     
     
 2  5
6    
     
16    
2122  25
15 23
    5
     
     
16  19 
 22   
18 24
12   
  89 
     
16    
21    
10 17
  3  
  8  
11    
   19 
    25
 23  
6    
11    
     
     
12   
  8  
11    
     
21   25
4
1    
6    
     
16    
 22  25
1   5
     
11    
     
    25
12   
     
11    
16    
 22   
12  5
6    
     
     
 22  25
12 20
1    
6  9 
11    
     
21   25
7 13
y
12   
6    
     
     
2122 24 
7 20 19 13
1    
6    
    15
     
     
12
1    
6    
   14 
     
2122   
11
12   
     
   1415
     
21    
16
  3  
6    
   14 
     
21    
  3  
     
     
     
    25
9
12   
     
   14 
     
21   25
8 10 23 18 17
  3  
     
    15
     
   2425
5 4
123  
6    
     
     
     
 2   
6    
     
     
   24 

backtrack.grid2 → grid3: a9 guess 13 ∈ {13|25}

…

backtrack.grid9447 → grid9448: c17 guess 22 ∈ {22|25}

pending={c17}

deduce.grid9448: naked-singles

deduce.grid9448: hidden-singles

deduce.grid9448.rown. n23 is 25 by hidden-single.

pending={n23}

deduce.grid9448: naked-singles

deduce.grid9448: hidden-singles

deduce.grid9448.rowo. o17 is 25 by hidden-single.

pending={o17}

deduce.grid9448: naked-singles

deduce.grid9448: hidden-singles

deduce.grid9448.col20. x20 is 22 by hidden-single.

pending={x20}

deduce.grid9448: naked-singles

deduce.grid9448: hidden-singles

deduce.grid9448.col4. n4 is 22 by hidden-single.

pending={n4}

deduce.grid9448: naked-singles

deduce.grid9448: hidden-singles

deduce.grid9448.rowk. k9 is 22 by hidden-single.

pending={k9}

deduce.grid9448: naked-singles

deduce.grid9448: hidden-singles

deduce.grid9448.col7. p7 is 22 by hidden-single.

pending={p7}

deduce.grid9448: naked-singles

deduce.grid9448: hidden-singles

deduce.grid9448.col9. v9 is 4 by hidden-single.

pending={v9}

deduce.grid9448: naked-singles

deduce.grid9448: hidden-singles

deduce.grid9448.col6. m6 is 4 by hidden-single.

pending={m6}

deduce.grid9448: naked-singles

deduce.grid9448: hidden-singles

deduce.grid9448.rowm. m10 is 15 by hidden-single.

pending={m10}

deduce.grid9448: naked-singles

deduce.grid9448: hidden-singles

deduce.grid9448.col10. f10 is 18 by hidden-single.

pending={f10}

deduce.grid9448: naked-singles

deduce.grid9448: hidden-singles

deduce.grid9448.col9. q9 is 18 by hidden-single.

pending={q9}

deduce.grid9448: naked-singles

deduce.grid9448: hidden-singles

deduce.grid9448.rowq. q7 is 15 by hidden-single.

pending={q7}

deduce.grid9448: naked-singles

deduce.grid9448: hidden-singles

deduce.grid9448.col7. r7 is 11 by hidden-single.

pending={r7}

deduce.grid9448: naked-singles

deduce.grid9448: hidden-singles

deduce.grid9448.col9. f9 is 15 by hidden-single.

pending={f9}

deduce.grid9448: naked-singles

deduce.grid9448: hidden-singles

deduce.grid9448.rowk. k3 is 15 by hidden-single.

pending={k3}

deduce.grid9448: naked-singles

deduce.grid9448: hidden-singles

deduce.grid9448.rows. s24 is 17 by hidden-single.

pending={s24}

deduce.grid9448: naked-singles

deduce.grid9448: hidden-singles

deduce.grid9448.col3. u3 is 18 by hidden-single.

pending={u3}

deduce.grid9448: naked-singles

deduce.grid9448: hidden-singles

deduce.grid9448.roww. w15 is 18 by hidden-single.

pending={w15}

deduce.grid9448: naked-singles

deduce.grid9448: hidden-singles

deduce.grid9448.rowp. p16 is 18 by hidden-single.

pending={p16}

deduce.grid9448: naked-singles

deduce.grid9448: hidden-singles

deduce.grid9448.rowp. p2 is 11 by hidden-single.

pending={p2}

deduce.grid9448: naked-singles

deduce.grid9448: hidden-singles

deduce.grid9448.rowp. p24 is 13 by hidden-single.

pending={p24}

deduce.grid9448: naked-singles

deduce.grid9448: hidden-singles

deduce.grid9448.rows. s11 is 18 by hidden-single.

pending={s11}

deduce.grid9448: naked-singles

deduce.grid9448: hidden-singles

deduce.grid9448.rowk. k23 is 18 by hidden-single.

pending={k23}

deduce.grid9448: naked-singles

deduce.grid9448: hidden-singles

deduce.grid9448.rows. s2 is 25 by hidden-single.

pending={s2}

deduce.grid9448: naked-singles

deduce.grid9448: hidden-singles

deduce.grid9448.rowr. r11 is 25 by hidden-single.

pending={r11}

deduce.grid9448: naked-singles

deduce.grid9448: hidden-singles

deduce.grid9448.rows. s12 is 24 by hidden-single.

pending={s12}

deduce.grid9448: naked-singles

deduce.grid9448: hidden-singles

deduce.grid9448.rowu. u13 is 23 by hidden-single.

pending={u13}

deduce.grid9448: naked-singles

deduce.grid9448: hidden-singles

deduce.grid9448.roww. w12 is 4 by hidden-single.

pending={w12}

deduce.grid9448: naked-singles

deduce.grid9448: hidden-singles

deduce.grid9448.rowk. k11 is 4 by hidden-single.

pending={k11}

deduce.grid9448: naked-singles

deduce.grid9448: hidden-singles

deduce.grid9448.roww. w7 is 19 by hidden-single.

pending={w7}

deduce.grid9448: naked-singles

deduce.grid9448: hidden-singles

deduce.grid9448.rowx. x13 is 19 by hidden-single.

deduce.grid9448.rowx. x14 is 3 by hidden-single.

pending={x13, x14}

deduce.grid9448: naked-singles

deduce.grid9448: hidden-singles

deduce.grid9448.rowl. l4 is 18 by hidden-single.

pending={l4}

deduce.grid9448: naked-singles

deduce.grid9448: hidden-singles

deduce.grid9448.rowo. o15 is 12 by hidden-single.

pending={o15}

deduce.grid9448: naked-singles

deduce.grid9448: hidden-singles

deduce.grid9448.rowm. m12 is 19 by hidden-single.

pending={m12}

deduce.grid9448: naked-singles

deduce.grid9448: hidden-singles

deduce.grid9448.rowk. k5 is 19 by hidden-single.

pending={k5}

deduce.grid9448: naked-singles

deduce.grid9448: hidden-singles

deduce.grid9448.rowk. k12 is 5 by hidden-single.

pending={k12}

deduce.grid9448: naked-singles

deduce.grid9448: hidden-singles

deduce.grid9448.rown. n3 is 5 by hidden-single.

pending={n3}

deduce.grid9448: naked-singles

deduce.grid9448: hidden-singles

deduce.grid9448.rown. n14 is 7 by hidden-single.

pending={n14}

deduce.grid9448: naked-singles

deduce.grid9448: hidden-singles

deduce.grid9448.rowo. o11 is 14 by hidden-single.

pending={o11}

deduce.grid9448: naked-singles

deduce.grid9448: hidden-singles

deduce.grid9448.rows. s18 is 19 by hidden-single.

pending={s18}

deduce.grid9448: naked-singles

deduce.grid9448: hidden-singles

deduce.grid9448.col3. o3 is 7 by hidden-single.

pending={o3}

deduce.grid9448: naked-singles

deduce.grid9448: hidden-singles

deduce.grid9448.col11. t11 is 5 by hidden-single.

pending={t11}

deduce.grid9448: naked-singles

deduce.grid9448: hidden-singles

deduce.grid9448.col11. v11 is 2 by hidden-single.

pending={v11}

deduce.grid9448: naked-singles

deduce.grid9448: hidden-singles

deduce.grid9448.col11. d11 is 13 by hidden-single.

pending={d11}

deduce.grid9448: naked-singles

deduce.grid9448: hidden-singles

deduce.grid9448.col14. l14 is 10 by hidden-single.

pending={l14}

deduce.grid9448: naked-singles

deduce.grid9448: hidden-singles

deduce.grid9448.rowl. l10 is 16 by hidden-single.

pending={l10}

deduce.grid9448: naked-singles

deduce.grid9448: hidden-singles

deduce.grid9448.rowk. k14 is 16 by hidden-single.

pending={k14}

deduce.grid9448: naked-singles

deduce.grid9448: hidden-singles

deduce.grid9448.rowo. o19 is 16 by hidden-single.

pending={o19}

deduce.grid9448: naked-singles

deduce.grid9448: hidden-singles

deduce.grid9448.col12. v12 is 8 by hidden-single.

pending={v12}

deduce.grid9448: naked-singles

deduce.grid9448: hidden-singles

deduce.grid9448.rowv. v6 is 13 by hidden-single.

pending={v6}

deduce.grid9448: naked-singles

deduce.grid9448: hidden-singles

deduce.grid9448.rowu. u12 is 13 by hidden-single.

pending={u12}

deduce.grid9448: naked-singles

deduce.grid9448: hidden-singles

deduce.grid9448.col12. y12 is 6 by hidden-single.

pending={y12}

deduce.grid9448: naked-singles

deduce.grid9448: hidden-singles

deduce.grid9448.col21. u21 is 25 by hidden-single.

pending={u21}

deduce.grid9448: naked-singles

deduce.grid9448: hidden-singles

deduce.grid9448.col21. v21 is 10 by hidden-single.

pending={v21}

deduce.grid9448: naked-singles

deduce.grid9448: hidden-singles

deduce.grid9448.rowv. v1 is 17 by hidden-single.

pending={v1}

deduce.grid9448: naked-singles

deduce.grid9448: hidden-singles

deduce.grid9448.rowm. m4 is 17 by hidden-single.

pending={m4}

deduce.grid9448: naked-singles

deduce.grid9448: hidden-singles

deduce.grid9448.rowm. m1 is 20 by hidden-single.

pending={m1}

deduce.grid9448: naked-singles

deduce.grid9448: hidden-singles

deduce.grid9448.rowm. m22 is 10 by hidden-single.

pending={m22}

deduce.grid9448: naked-singles

deduce.grid9448: hidden-singles

deduce.grid9448.rowq. q2 is 13 by hidden-single.

pending={q2}

deduce.grid9448: naked-singles

deduce.grid9448: hidden-singles

deduce.grid9448.rowv. v8 is 22 by hidden-single.

pending={v8}

deduce.grid9448: naked-singles

deduce.grid9448: hidden-singles

deduce.grid9448.rowv. v18 is 20 by hidden-single.

pending={v18}

deduce.grid9448: naked-singles

deduce.grid9448: hidden-singles

deduce.grid9448.rowd. d19 is 20 by hidden-single.

pending={d19}

deduce.grid9448: naked-singles

deduce.grid9448: hidden-singles

deduce.grid9448.rowv. v17 is 15 by hidden-single.

pending={v17}

deduce.grid9448: naked-singles

deduce.grid9448: hidden-singles

deduce.grid9448.rowt. t18 is 15 by hidden-single.

pending={t18}

deduce.grid9448: naked-singles

deduce.grid9448: hidden-singles

deduce.grid9448.roww. w6 is 15 by hidden-single.

pending={w6}

deduce.grid9448: naked-singles

deduce.grid9448: hidden-singles

deduce.grid9448.rowy. y1 is 22 by hidden-single.

deduce.grid9448.rowy. y21 is 15 by hidden-single.

pending={y1, y21}

deduce.grid9448: naked-singles

deduce.grid9448: hidden-singles

deduce.grid9448.rowy. y24 is 3 by hidden-single.

deduce.grid9448.rowy. y25 is 24 by hidden-single.

pending={y24, y25}

deduce.grid9448: naked-singles

deduce.grid9448: hidden-singles

deduce.grid9448.rowy. y10 is 2 by hidden-single.

pending={y10}

deduce.grid9448: naked-singles

deduce.grid9448: hidden-singles

deduce.grid9448.col3. q3 is 10 by hidden-single.

pending={q3}

deduce.grid9448: naked-singles

deduce.grid9448: hidden-singles

deduce.grid9448.col8. u8 is 6 by hidden-single.

pending={u8}

deduce.grid9448: naked-singles

deduce.grid9448: hidden-singles

deduce.grid9448.col1. t1 is 6 by hidden-single.

pending={t1}

deduce.grid9448: naked-singles

deduce.grid9448: hidden-singles

deduce.grid9448.col19. e19 is 12 by hidden-single.

pending={e19}

deduce.grid9448: naked-singles

deduce.grid9448: hidden-singles

deduce.grid9448.col20. w20 is 24 by hidden-single.

pending={w20}

deduce.grid9448: naked-singles

deduce.grid9448: hidden-singles

deduce.grid9448.col20. r20 is 6 by hidden-single.

pending={r20}

deduce.grid9448: naked-singles

deduce.grid9448: hidden-singles

deduce.grid9448.rowr. r15 is 4 by hidden-single.

pending={r15}

deduce.grid9448: naked-singles

deduce.grid9448: hidden-singles

deduce.grid9448.rowp. p20 is 4 by hidden-single.

pending={p20}

deduce.grid9448: naked-singles

deduce.grid9448: hidden-singles

deduce.grid9448.rowr. r4 is 16 by hidden-single.

pending={r4}

deduce.grid9448: naked-singles

deduce.grid9448: hidden-singles

deduce.grid9448.col4. t4 is 20 by hidden-single.

pending={t4}

deduce.grid9448: naked-singles

deduce.grid9448: hidden-singles

deduce.grid9448.rowt. t3 is 2 by hidden-single.

pending={t3}

deduce.grid9448: naked-singles

deduce.grid9448: hidden-singles

deduce.grid9448.col3. r3 is 19 by hidden-single.

pending={r3}

deduce.grid9448: naked-singles

deduce.grid9448: hidden-singles

deduce.grid9448.col16. k16 is 6 by hidden-single.

pending={k16}

deduce.grid9448: naked-singles

deduce.grid9448: hidden-singles

deduce.grid9448.col16. e16 is 2 by hidden-single.

pending={e16}

deduce.grid9448: naked-singles

deduce.grid9448: hidden-singles

deduce.grid9448.col16. q16 is 11 by hidden-single.

pending={q16}

deduce.grid9448: naked-singles

deduce.grid9448: hidden-singles

deduce.grid9448.col20. m20 is 2 by hidden-single.

pending={m20}

deduce.grid9448: naked-singles

deduce.grid9448: hidden-singles

deduce.grid9448.col21. p21 is 24 by hidden-single.

pending={p21}

deduce.grid9448: naked-singles

deduce.grid9448: hidden-singles

deduce.grid9448.col22. k22 is 21 by hidden-single.

pending={k22}

deduce.grid9448: naked-singles

deduce.grid9448: hidden-singles

deduce.grid9448.rowq. q4 is 24 by hidden-single.

pending={q4}

deduce.grid9448: naked-singles

deduce.grid9448: hidden-singles

deduce.grid9448.rowq. q8 is 5 by hidden-single.

pending={q8}

deduce.grid9448: naked-singles

deduce.grid9448: hidden-singles

deduce.grid9448.rowu. u2 is 24 by hidden-single.

pending={u2}

deduce.grid9448: naked-singles

deduce.grid9448: hidden-singles

deduce.grid9448.rowu. u1 is 10 by hidden-single.

deduce.grid9448.rowu. u7 is 16 by hidden-single.

pending={u1, u7}

deduce.grid9448: naked-singles

deduce.grid9448: hidden-singles

deduce.grid9448.rown. n2 is 10 by hidden-single.

pending={n2}

deduce.grid9448: naked-singles

deduce.grid9448: hidden-singles

deduce.grid9448.roww. w25 is 11 by hidden-single.

pending={w25}

deduce.grid9448: naked-singles

deduce.grid9448: hidden-singles

deduce.grid9448.rowt. t23 is 11 by hidden-single.

pending={t23}

deduce.grid9448: naked-singles

deduce.grid9448: hidden-singles

deduce.grid9448.rowt. t21 is 19 by hidden-single.

pending={t21}

deduce.grid9448: naked-singles

deduce.grid9448: hidden-singles

deduce.grid9448.rowo. o23 is 19 by hidden-single.

pending={o23}

deduce.grid9448: naked-singles

deduce.grid9448: hidden-singles

deduce.grid9448.rowo. o21 is 17 by hidden-single.

pending={o21}

deduce.grid9448: naked-singles

deduce.grid9448: hidden-singles

deduce.grid9448.rowr. r8 is 20 by hidden-single.

pending={r8}

deduce.grid9448: naked-singles

deduce.grid9448: hidden-singles

deduce.grid9448.rowt. t5 is 12 by hidden-single.

pending={t5}

deduce.grid9448: naked-singles

deduce.grid9448: hidden-singles

deduce.grid9448.rowu. u25 is 17 by hidden-single.

pending={u25}

deduce.grid9448: naked-singles

deduce.grid9448: hidden-singles

deduce.grid9448.col25. l25 is 2 by hidden-single.

pending={l25}

deduce.grid9448: naked-singles

deduce.grid9448: hidden-singles

deduce.grid9448.rowu. u23 is 9 by hidden-single.

pending={u23}

deduce.grid9448: naked-singles

deduce.grid9448: hidden-singles

deduce.grid9448.col23. r23 is 1 by hidden-single.

pending={r23}

deduce.grid9448: naked-singles

grid9448 didn't work: naked-singles ran out of candidates.

…backtrack.grid9447 again

backtrack.grid9447 → grid9449: c17 guess 25 ∈ {22|25}

pending={c17}

deduce.grid9449: naked-singles

deduce.grid9449: hidden-singles

deduce.grid9449: naked-pairs

two's heap=r22 {1|3}, l25 {2|7}, t11 {2|5}, d14 {3|14}, j25 {7|12}, r7 {5|11}, k16 {2|6}, h4 {6|17}, e21 {3|17}, h22 {12|17}, p16 {11|18}, f3 {15|17}, i6 {6|15}, u7 {5|16}, y25 {2|24}, g15 {18|25}, j9 {12|19}, e14 {3|24}, l4 {2|18}, h5 {18|25}, l6 {6|19}, n7 {18|22}, d17 {1|21}, p21 {8|24}, i2 {15|21}, d18 {1|20}, s24 {3|17}, g5 {18|25}, i8 {6|25}, i11 {17|25}, y13 {3|25}.

Naked-pair {18|25} in cells {g5, g15, h5} contained within {rowg, col5, box6}, updating cells {f3, h4, i2, i4, k5, o5, r5, s5, t5, v5}:

backtrack.grid9449 → grid9450: d14 guess 3 ∈ {3|14}

pending={d14}

deduce.grid9450: naked-singles

deduce.grid9450: hidden-singles

deduce.grid9450.rowx. x13 is 3 by hidden-single.

pending={x13}

deduce.grid9450: naked-singles

deduce.grid9450: hidden-singles

deduce.grid9450.rowl. l13 is 11 by hidden-single.

pending={l13}

deduce.grid9450: naked-singles

deduce.grid9450: hidden-singles

deduce.grid9450.rowx. x7 is 19 by hidden-single.

pending={x7}

deduce.grid9450: naked-singles

deduce.grid9450: hidden-singles

deduce.grid9450.roww. w12 is 19 by hidden-single.

pending={w12}

deduce.grid9450: naked-singles

deduce.grid9450: hidden-singles

deduce.grid9450.rowj. j9 is 19 by hidden-single.

pending={j9}

deduce.grid9450: naked-singles

deduce.grid9450: hidden-singles

deduce.grid9450.rowf. f11 is 19 by hidden-single.

pending={f11}

deduce.grid9450: naked-singles

deduce.grid9450: hidden-singles

deduce.grid9450.col11. i11 is 17 by hidden-single.

deduce.grid9450.col11. v11 is 13 by hidden-single.

pending={i11, v11}

deduce.grid9450: naked-singles

deduce.grid9450: hidden-singles

deduce.grid9450.rowi. i8 is 25 by hidden-single.

pending={i8}

deduce.grid9450: naked-singles

deduce.grid9450: hidden-singles

deduce.grid9450.rowh. h5 is 25 by hidden-single.

pending={h5}

deduce.grid9450: naked-singles

deduce.grid9450: hidden-singles

deduce.grid9450.col6. u6 is 13 by hidden-single.

pending={u6}

deduce.grid9450: naked-singles

deduce.grid9450: hidden-singles

deduce.grid9450.col11. t11 is 2 by hidden-single.

pending={t11}

deduce.grid9450: naked-singles

deduce.grid9450: hidden-singles

deduce.grid9450.col12. s12 is 3 by hidden-single.

pending={s12}

deduce.grid9450: naked-singles

deduce.grid9450: hidden-singles

deduce.grid9450.rowm. m13 is 19 by hidden-single.

pending={m13}

deduce.grid9450: naked-singles

deduce.grid9450: hidden-singles

deduce.grid9450.rows. s2 is 24 by hidden-single.

pending={s2}

deduce.grid9450: naked-singles

deduce.grid9450: hidden-singles

grid9450 didn't work: rowq is not bijective.

…backtrack.grid9449 again

backtrack.grid9449 → grid9451: d14 guess 14 ∈ {3|14}

pending={d14}

deduce.grid9451: naked-singles

deduce.grid9451: hidden-singles

deduce.grid9451.col11. o11 is 14 by hidden-single.

pending={o11}

deduce.grid9451: naked-singles

deduce.grid9451: hidden-singles

deduce.grid9451: naked-pairs

two's heap=r22 {1|3}, l25 {2|7}, t11 {2|5}, i6 {6|15}, j25 {7|12}, r7 {5|11}, k16 {2|6}, j9 {12|19}, h4 {6|17}, h22 {12|17}, p16 {11|18}, f3 {15|17}, e21 {3|17}, u7 {5|16}, y25 {2|24}, g15 {18|25}, d18 {1|20}, e14 {3|24}, l4 {2|18}, h5 {18|25}, l6 {6|19}, n7 {18|22}, d11 {13|21}, p21 {8|24}, i2 {15|21}, d17 {1|21}, s24 {3|17}, g5 {18|25}, i8 {6|25}, i11 {17|25}, y13 {3|25}.

Naked-pair {18|25} in cells {g5, g15, h5} contained within {rowg, col5, box6}, updating cells {f3, h4, i2, i4, k5, o5, r5, s5, t5, v5}:

backtrack.grid9451 → grid9452: d11 guess 13 ∈ {13|21}

pending={d11}

deduce.grid9452: naked-singles

deduce.grid9452: hidden-singles

deduce.grid9452: naked-pairs

two's heap=r22 {1|3}, l25 {2|7}, t11 {2|5}, i6 {6|15}, j25 {7|12}, r7 {5|11}, k16 {2|6}, j9 {12|19}, h4 {6|17}, h22 {12|17}, p16 {11|18}, f3 {15|17}, e21 {3|17}, u7 {5|16}, y25 {2|24}, g15 {18|25}, d18 {1|20}, e14 {3|24}, l4 {2|18}, h5 {18|25}, l6 {6|19}, n7 {18|22}, d12 {3|21}, p21 {8|24}, i2 {15|21}, d17 {1|21}, s24 {3|17}, g5 {18|25}, i8 {6|25}, i11 {17|25}, y13 {3|25}.

Naked-pair {18|25} in cells {g5, g15, h5} contained within {rowg, col5, box6}, updating cells {f3, h4, i2, i4, k5, o5, r5, s5, t5, v5}:

backtrack.grid9452 → grid9453: d12 guess 3 ∈ {3|21}

pending={d12}

deduce.grid9453: naked-singles

deduce.grid9453: hidden-singles

deduce.grid9453.col14. x14 is 3 by hidden-single.

pending={x14}

deduce.grid9453: naked-singles

deduce.grid9453: hidden-singles

deduce.grid9453.col13. t13 is 3 by hidden-single.

pending={t13}

deduce.grid9453: naked-singles

deduce.grid9453: hidden-singles

deduce.grid9453.col13. o13 is 24 by hidden-single.

pending={o13}

deduce.grid9453: naked-singles

deduce.grid9453: hidden-singles

deduce.grid9453.rowo. o15 is 12 by hidden-single.

pending={o15}

deduce.grid9453: naked-singles

deduce.grid9453: hidden-singles

deduce.grid9453.col12. s12 is 24 by hidden-single.

pending={s12}

deduce.grid9453: naked-singles

deduce.grid9453: hidden-singles

deduce.grid9453.col12. k12 is 5 by hidden-single.

pending={k12}

deduce.grid9453: naked-singles

deduce.grid9453: hidden-singles

deduce.grid9453.col13. v13 is 12 by hidden-single.

pending={v13}

deduce.grid9453: naked-singles

deduce.grid9453: hidden-singles

deduce.grid9453.col13. u13 is 23 by hidden-single.

pending={u13}

deduce.grid9453: naked-singles

deduce.grid9453: hidden-singles

deduce.grid9453.col14. q14 is 23 by hidden-single.

pending={q14}

deduce.grid9453: naked-singles

deduce.grid9453: hidden-singles

deduce.grid9453.rowq. q15 is 7 by hidden-single.

pending={q15}

deduce.grid9453: naked-singles

deduce.grid9453: hidden-singles

deduce.grid9453: naked-pairs

two's heap=r22 {1|3}, t11 {2|5}, k16 {2|6}, l25 {2|7}, j25 {7|12}, p16 {11|18}, r7 {5|11}, i6 {6|15}, y6 {1|15}, l4 {2|18}, h22 {12|17}, d18 {1|20}, q8 {5|21}, e21 {3|17}, s24 {3|17}, u7 {5|16}, u14 {11|20}, k14 {6|16}, h4 {6|17}, f15 {8|18}, l6 {6|19}, i2 {15|21}, m13 {18|19}, g5 {18|25}, n7 {18|22}, i8 {6|25}, p21 {8|24}, g15 {18|25}, j9 {12|19}, i11 {17|25}, s2 {11|25}, d17 {1|21}, f3 {15|17}, k5 {19|21}, w14 {11|20}, h5 {18|25}, x13 {11|19}, y25 {2|24}.

Naked-pair {11|20} in cells {u14, w14} contained within {col14, box23}, updating cells {k14, l14, n14, o14, u12, u15, v11, v12, w12, w15, x13, x15, y15}:

Naked-pair {18|25} in cells {g5, g15, h5} contained within {rowg, col5, box6}, updating cells {f3, h4, i2, i4, k5, o5, r5, s5, t5, v5}:

pending={x13}

deduce.grid9453: naked-singles

deduce.grid9453: hidden-singles

deduce.grid9453.col7. w7 is 19 by hidden-single.

pending={w7}

deduce.grid9453: naked-singles

deduce.grid9453: hidden-singles

deduce.grid9453.col7. q7 is 15 by hidden-single.

pending={q7}

deduce.grid9453: naked-singles

deduce.grid9453: hidden-singles

deduce.grid9453: naked-pairs

two's heap=r22 {1|3}, t11 {2|5}, k16 {2|6}, l25 {2|7}, j25 {7|12}, p16 {11|18}, r7 {5|11}, i6 {6|15}, y6 {1|15}, l4 {2|18}, h22 {12|17}, d18 {1|20}, q8 {5|21}, q9 {13|18}, e21 {3|17}, f3 {15|17}, u7 {5|16}, u14 {11|20}, k14 {6|16}, f15 {8|18}, l6 {6|19}, i2 {15|21}, n7 {18|22}, g5 {18|25}, n11 {8|21}, i8 {6|25}, p21 {8|24}, g15 {18|25}, j9 {12|19}, i11 {17|25}, s2 {11|25}, d17 {1|21}, t9 {13|22}, k5 {19|21}, s24 {3|17}, h5 {18|25}, w14 {11|20}, h4 {6|17}, y25 {2|24}.

Naked-pair {11|20} in cells {u14, w14} contained within {col14, box23}, updating cells {k14, l14, n14, o14, u12, u15, v11, v12, w12, w15, x15, y15}:

Naked-pair {18|25} in cells {g5, g15, h5} contained within {rowg, col5, box6}, updating cells {f3, h4, i2, i4, k5, o5, r5, s5, t5, v5}:

backtrack.grid9453 → grid9454: d17 guess 1 ∈ {1|21}

pending={d17}

deduce.grid9454: naked-singles

deduce.grid9454: hidden-singles

deduce.grid9454.rowd. d19 is 21 by hidden-single.

pending={d19}

deduce.grid9454: naked-singles

deduce.grid9454: hidden-singles

deduce.grid9454.col19. e19 is 12 by hidden-single.

pending={e19}

deduce.grid9454: naked-singles

deduce.grid9454: hidden-singles

deduce.grid9454: naked-pairs

two's heap=r22 {1|3}, e20 {2|5}, l25 {2|7}, t11 {2|5}, e18 {5|11}, m19 {2|8}, i6 {6|15}, r7 {5|11}, k16 {2|6}, v18 {1|15}, y6 {1|15}, e23 {1|17}, d22 {2|12}, p16 {11|18}, f3 {15|17}, q8 {5|21}, j25 {7|12}, f15 {8|18}, s24 {3|17}, e21 {3|17}, u7 {5|16}, k14 {6|16}, l4 {2|18}, h5 {18|25}, l6 {6|19}, h22 {12|17}, n7 {18|22}, i2 {15|21}, n11 {8|21}, p17 {21|24}, p21 {8|24}, i8 {6|25}, d23 {12|23}, i11 {17|25}, q9 {13|18}, g5 {18|25}, s2 {11|25}, t9 {13|22}, j9 {12|19}, g15 {18|25}, u14 {11|20}, k5 {19|21}, w14 {11|20}, h4 {6|17}, y25 {2|24}.

Naked-pair {11|20} in cells {u14, w14} contained within {col14, box23}, updating cells {k14, l14, n14, o14, u12, u15, v11, v12, w12, w15, x15, y15}:

Naked-pair {18|25} in cells {g5, g15, h5} contained within {rowg, col5, box6}, updating cells {f3, h4, i2, i4, k5, o5, r5, s5, t5, v5}:

backtrack.grid9454 → grid9455: d22 guess 2 ∈ {2|12}

pending={d22}

deduce.grid9455: naked-singles

deduce.grid9455: hidden-singles

deduce.grid9455: naked-pairs

two's heap=r22 {1|3}, e20 {2|5}, l25 {2|7}, t11 {2|5}, e18 {5|11}, m19 {2|8}, e23 {1|17}, r7 {5|11}, k16 {2|6}, v18 {1|15}, y6 {1|15}, h22 {12|17}, i6 {6|15}, p16 {11|18}, f3 {15|17}, q8 {5|21}, j25 {7|12}, f15 {8|18}, s24 {3|17}, e21 {3|17}, u7 {5|16}, k14 {6|16}, l4 {2|18}, h5 {18|25}, l6 {6|19}, d23 {12|23}, n7 {18|22}, i2 {15|21}, n11 {8|21}, p17 {21|24}, p21 {8|24}, i8 {6|25}, d25 {12|23}, i11 {17|25}, q9 {13|18}, g5 {18|25}, s2 {11|25}, t9 {13|22}, j9 {12|19}, g15 {18|25}, u14 {11|20}, k5 {19|21}, w14 {11|20}, h4 {6|17}, y25 {2|24}.

Naked-pair {11|20} in cells {u14, w14} contained within {col14, box23}, updating cells {k14, l14, n14, o14, u12, u15, v11, v12, w12, w15, x15, y15}:

Naked-pair {12|23} in cells {d23, d25} contained within {rowd, box5}, updating cells {e21, e22, e23}:

Naked-pair {18|25} in cells {g5, g15, h5} contained within {rowg, col5, box6}, updating cells {f3, h4, i2, i4, k5, o5, r5, s5, t5, v5}:

backtrack.grid9455 → grid9456: d23 guess 12 ∈ {12|23}

pending={d23}

deduce.grid9456: naked-singles

deduce.grid9456: hidden-singles

deduce.grid9456: naked-pairs

two's heap=r22 {1|3}, e20 {2|5}, m19 {2|8}, t11 {2|5}, l25 {2|7}, i6 {6|15}, q9 {13|18}, r7 {5|11}, k16 {2|6}, v18 {1|15}, e18 {5|11}, e21 {3|17}, f15 {8|18}, p17 {21|24}, q8 {5|21}, j25 {7|12}, s24 {3|17}, k14 {6|16}, u7 {5|16}, h22 {12|17}, y6 {1|15}, l6 {6|19}, f3 {15|17}, i2 {15|21}, n7 {18|22}, n11 {8|21}, p16 {11|18}, g5 {18|25}, i8 {6|25}, i11 {17|25}, p21 {8|24}, g15 {18|25}, e23 {1|17}, s2 {11|25}, j9 {12|19}, t9 {13|22}, k5 {19|21}, h4 {6|17}, u14 {11|20}, h5 {18|25}, w14 {11|20}, l4 {2|18}, y25 {2|24}.

Naked-pair {11|20} in cells {u14, w14} contained within {col14, box23}, updating cells {k14, l14, n14, o14, u12, u15, v11, v12, w12, w15, x15, y15}:

Naked-pair {18|25} in cells {g5, g15, h5} contained within {rowg, col5, box6}, updating cells {f3, h4, i2, i4, k5, o5, r5, s5, t5, v5}:

backtrack.grid9456 → grid9457: e18 guess 5 ∈ {5|11}

pending={e18}

deduce.grid9457: naked-singles

deduce.grid9457: hidden-singles

deduce.grid9457.rowm. m4 is 2 by hidden-single.

pending={m4}

deduce.grid9457: naked-singles

deduce.grid9457: hidden-singles

deduce.grid9457.rowq. q9 is 18 by hidden-single.

pending={q9}

deduce.grid9457: naked-singles

deduce.grid9457: hidden-singles

deduce.grid9457.col3. u3 is 18 by hidden-single.

pending={u3}

deduce.grid9457: naked-singles

deduce.grid9457: hidden-singles

deduce.grid9457.col7. n7 is 18 by hidden-single.

pending={n7}

deduce.grid9457: naked-singles

deduce.grid9457: hidden-singles

deduce.grid9457.rowk. k23 is 18 by hidden-single.

pending={k23}

deduce.grid9457: naked-singles

deduce.grid9457: hidden-singles

deduce.grid9457.col10. f10 is 18 by hidden-single.

pending={f10}

deduce.grid9457: naked-singles

deduce.grid9457: hidden-singles

deduce.grid9457.col11. s11 is 18 by hidden-single.

pending={s11}

deduce.grid9457: naked-singles

deduce.grid9457: hidden-singles

deduce.grid9457.box17. t9 is 13 by hidden-single.

pending={t9}

deduce.grid9457: naked-singles

deduce.grid9457: hidden-singles

deduce.grid9457: naked-pairs

two's heap=r22 {1|3}, r20 {1|4}, u9 {6|8}, l25 {2|7}, t11 {2|5}, u12 {8|13}, o17 {6|16}, k14 {6|16}, q3 {8|10}, i6 {6|15}, s8 {3|5}, v18 {1|15}, y6 {1|15}, e23 {1|17}, j9 {12|19}, p21 {8|24}, h12 {12|18}, j25 {7|12}, q19 {1|11}, l10 {8|16}, h22 {12|17}, s24 {3|17}, u7 {5|16}, h4 {6|17}, o19 {1|16}, n10 {8|20}, n11 {8|21}, i11 {17|25}, f3 {15|17}, p7 {11|22}, p8 {22|23}, h5 {18|25}, p17 {21|24}, k5 {19|21}, q4 {13|24}, f11 {17|19}, e21 {3|17}, l6 {6|19}, r7 {5|11}, g5 {18|25}, s2 {11|25}, s15 {11|25}, s18 {11|19}, i2 {15|21}, m11 {4|19}, t20 {8|24}, m10 {15|20}, g15 {18|25}, m22 {10|17}, u14 {11|20}, m12 {4|19}, i8 {6|25}, w14 {11|20}, y8 {14|22}, y25 {2|24}.

Naked-pair {4|19} in cells {m11, m12} contained within {rowm, box13}, updating cells {k11, k14, l14, m1, m6, m10, m22, n11, n14, o14}:

Naked-pair {11|20} in cells {u14, w14} contained within {col14, box23}, updating cells {k14, l14, n14, o14, u12, u15, v11, v12, w12, w15, x15, y15}:

Naked-pair {11|25} in cells {s2, s15} contained within {rows}, updating cells {s5, s8, s18, s22, s24}:

Naked-pair {18|25} in cells {g5, g15, h5} contained within {rowg, col5, box6}, updating cells {f3, h4, i2, i4, k5, o5, r5, s5, t5, v5}:

pending={s18}

deduce.grid9457: naked-singles

deduce.grid9457: hidden-singles

deduce.grid9457.rowk. k9 is 4 by hidden-single.

pending={k9}

deduce.grid9457: naked-singles

deduce.grid9457: hidden-singles

deduce.grid9457.rowk. k1 is 22 by hidden-single.

pending={k1}

deduce.grid9457: naked-singles

deduce.grid9457: hidden-singles

deduce.grid9457.rowk. k2 is 24 by hidden-single.

pending={k2}

deduce.grid9457: naked-singles

deduce.grid9457: hidden-singles

deduce.grid9457.rown. n9 is 22 by hidden-single.

pending={n9}

deduce.grid9457: naked-singles

deduce.grid9457: hidden-singles

deduce.grid9457.rowy. y8 is 22 by hidden-single.

pending={y8}

deduce.grid9457: naked-singles

deduce.grid9457: hidden-singles

deduce.grid9457.rowv. v17 is 22 by hidden-single.

pending={v17}

deduce.grid9457: naked-singles

deduce.grid9457: hidden-singles

deduce.grid9457.rowx. x4 is 22 by hidden-single.

pending={x4}

deduce.grid9457: naked-singles

deduce.grid9457: hidden-singles

deduce.grid9457.rowy. y15 is 14 by hidden-single.

pending={y15}

deduce.grid9457: naked-singles

deduce.grid9457: hidden-singles

deduce.grid9457.rowu. u8 is 14 by hidden-single.

pending={u8}

deduce.grid9457: naked-singles

deduce.grid9457: hidden-singles

deduce.grid9457.col2. i2 is 15 by hidden-single.

pending={i2}

deduce.grid9457: naked-singles

deduce.grid9457: hidden-singles

deduce.grid9457.rowl. l14 is 10 by hidden-single.

pending={l14}

deduce.grid9457: naked-singles

deduce.grid9457: hidden-singles

deduce.grid9457.rowl. l10 is 16 by hidden-single.

pending={l10}

deduce.grid9457: naked-singles

deduce.grid9457: hidden-singles

deduce.grid9457.rowk. k14 is 16 by hidden-single.

pending={k14}

deduce.grid9457: naked-singles

deduce.grid9457: hidden-singles

deduce.grid9457.rowk. k22 is 6 by hidden-single.

pending={k22}

deduce.grid9457: naked-singles

grid9457 didn't work: naked-singles ran out of candidates.

…backtrack.grid9456 again

backtrack.grid9456 → grid9458: e18 guess 11 ∈ {5|11}

pending={e18}

deduce.grid9458: naked-singles

deduce.grid9458: hidden-singles

deduce.grid9458: naked-pairs

two's heap=r22 {1|3}, e16 {2|5}, m19 {2|8}, e20 {2|5}, k16 {2|6}, i6 {6|15}, q9 {13|18}, r7 {5|11}, t11 {2|5}, v18 {1|15}, l25 {2|7}, e21 {3|17}, f15 {8|18}, p17 {21|24}, q8 {5|21}, j25 {7|12}, s18 {5|19}, s24 {3|17}, u7 {5|16}, h22 {12|17}, y6 {1|15}, l6 {6|19}, f3 {15|17}, i2 {15|21}, n7 {18|22}, n11 {8|21}, p16 {11|18}, g5 {18|25}, i8 {6|25}, i11 {17|25}, p21 {8|24}, g15 {18|25}, e23 {1|17}, s2 {11|25}, j9 {12|19}, k5 {19|21}, t9 {13|22}, h4 {6|17}, k14 {6|16}, h5 {18|25}, u14 {11|20}, w14 {11|20}, l4 {2|18}, y25 {2|24}.

Naked-pair {2|5} in cells {e16, e20, t11} contained within {rowe, box4}, updating cells {e21, e22, e23}:

Naked-pair {11|20} in cells {u14, w14} contained within {col14, box23}, updating cells {k14, l14, n14, o14, u12, u15, v11, v12, w12, w15, x15, y15}:

Naked-pair {18|25} in cells {g5, g15, h5} contained within {rowg, col5, box6}, updating cells {f3, h4, i2, i4, k5, o5, r5, s5, t5, v5}:

backtrack.grid9458 → grid9459: e16 guess 2 ∈ {2|5}

pending={e16}

deduce.grid9459: naked-singles

deduce.grid9459: hidden-singles

deduce.grid9459.rowl. l10 is 16 by hidden-single.

pending={l10}

deduce.grid9459: naked-singles

deduce.grid9459: hidden-singles

deduce.grid9459.rowo. o14 is 6 by hidden-single.

pending={o14}

deduce.grid9459: naked-singles

deduce.grid9459: hidden-singles

deduce.grid9459.rown. n9 is 6 by hidden-single.

pending={n9}

deduce.grid9459: naked-singles

deduce.grid9459: hidden-singles

deduce.grid9459: naked-pairs

two's heap=r22 {1|3}, t11 {2|5}, n14 {7|10}, l25 {2|7}, l14 {7|10}, i6 {6|15}, r7 {5|11}, e23 {1|17}, m19 {2|8}, j25 {7|12}, n11 {8|21}, o17 {16|21}, p16 {11|18}, j9 {12|19}, h4 {6|17}, k22 {8|21}, s24 {3|17}, h22 {12|17}, u9 {8|13}, v18 {1|15}, y6 {1|15}, n7 {18|22}, i2 {15|21}, g15 {18|25}, i8 {6|25}, i11 {17|25}, p17 {21|24}, p21 {8|24}, q8 {5|21}, q9 {13|18}, f3 {15|17}, h5 {18|25}, s2 {11|25}, k5 {19|21}, s18 {5|19}, t9 {13|22}, f15 {8|18}, l4 {2|18}, u7 {5|16}, g5 {18|25}, u14 {11|20}, w14 {11|20}, e21 {3|17}, y25 {2|24}.

Naked-pair {7|10} in cells {l14, n14} contained within {col14, box13}, updating cells {k11, m11, m12, n11, u14, w14}:

Naked-pair {11|20} in cells {u14, w14} contained within {col14, box23}, updating cells {l14, n14, u12, u15, v11, v12, w12, w15, x15, y15}:

Naked-pair {18|25} in cells {g5, g15, h5} contained within {rowg, col5, box6}, updating cells {f3, h4, i2, i4, k5, o5, r5, s5, t5, v5}:

backtrack.grid9459 → grid9460: e21 guess 3 ∈ {3|17}

pending={e21}

deduce.grid9460: naked-singles

deduce.grid9460: hidden-singles

deduce.grid9460.rowy. y24 is 3 by hidden-single.

pending={y24}

deduce.grid9460: naked-singles

deduce.grid9460: hidden-singles

deduce.grid9460: naked-pairs

two's heap=r22 {1|3}, t11 {2|5}, n14 {7|10}, l25 {2|7}, l14 {7|10}, e22 {1|17}, q9 {13|18}, r7 {5|11}, m19 {2|8}, u9 {8|13}, j25 {7|12}, f3 {15|17}, p16 {11|18}, p21 {8|24}, j9 {12|19}, h4 {6|17}, e23 {1|17}, l4 {2|18}, s22 {3|12}, i6 {6|15}, v18 {1|15}, y6 {1|15}, n7 {18|22}, g5 {18|25}, n11 {8|21}, i8 {6|25}, o17 {16|21}, g15 {18|25}, p17 {21|24}, i11 {17|25}, q8 {5|21}, f15 {8|18}, r21 {9|19}, k5 {19|21}, s2 {11|25}, h5 {18|25}, s18 {5|19}, t9 {13|22}, k22 {8|21}, f24 {22|23}, u7 {5|16}, u14 {11|20}, h22 {12|17}, i2 {15|21}, w14 {11|20}, y21 {15|24}, y25 {2|24}.

Naked-pair {7|10} in cells {l14, n14} contained within {col14, box13}, updating cells {k11, m11, m12, n11, u14, w14}:

Naked-pair {11|20} in cells {u14, w14} contained within {col14, box23}, updating cells {l14, n14, u12, u15, v11, v12, w12, w15, x15, y15}:

Naked-pair {18|25} in cells {g5, g15, h5} contained within {rowg, col5, box6}, updating cells {f3, h4, i2, i4, k5, o5, r5, s5, t5, v5}:

backtrack.grid9460 → grid9461: e22 guess 1 ∈ {1|17}

pending={e22}

deduce.grid9461: naked-singles

deduce.grid9461: hidden-singles

deduce.grid9461.rows. s8 is 3 by hidden-single.

pending={s8}

deduce.grid9461: naked-singles

deduce.grid9461: hidden-singles

deduce.grid9461.rows. s16 is 20 by hidden-single.

pending={s16}

deduce.grid9461: naked-singles

deduce.grid9461: hidden-singles

deduce.grid9461.rowt. t5 is 12 by hidden-single.

pending={t5}

deduce.grid9461: naked-singles

deduce.grid9461: hidden-singles

deduce.grid9461.col25. u25 is 17 by hidden-single.

pending={u25}

deduce.grid9461: naked-singles

deduce.grid9461: hidden-singles

deduce.grid9461.col21. o21 is 17 by hidden-single.

pending={o21}

deduce.grid9461: naked-singles

deduce.grid9461: hidden-singles

deduce.grid9461.col21. u21 is 25 by hidden-single.

pending={u21}

deduce.grid9461: naked-singles

deduce.grid9461: hidden-singles

deduce.grid9461.box25. v21 is 10 by hidden-single.

pending={v21}

deduce.grid9461: naked-singles

deduce.grid9461: hidden-singles

deduce.grid9461.col21. y21 is 15 by hidden-single.

pending={y21}

deduce.grid9461: naked-singles

deduce.grid9461: hidden-singles

deduce.grid9461: naked-pairs

two's heap=t11 {2|5}, l25 {2|7}, n14 {7|10}, r7 {5|11}, m19 {2|8}, i6 {6|15}, p16 {11|18}, r16 {5|11}, l4 {2|18}, l21 {8|9}, l14 {7|10}, n11 {8|21}, o4 {13|21}, j9 {12|19}, q8 {5|21}, q9 {13|18}, f3 {15|17}, s5 {5|19}, s18 {5|19}, j25 {7|12}, u9 {8|13}, v18 {1|15}, y10 {2|21}, g15 {18|25}, i8 {6|25}, i11 {17|25}, o17 {16|21}, h5 {18|25}, p17 {21|24}, p21 {8|24}, f23 {7|23}, h8 {8|25}, i2 {15|21}, k5 {19|21}, r21 {9|19}, s2 {11|25}, f24 {22|23}, k22 {8|21}, t9 {13|22}, g5 {18|25}, u7 {5|16}, f15 {8|18}, u14 {11|20}, i4 {17|21}, w14 {11|20}, n7 {18|22}, y25 {2|24}.

Naked-pair {7|10} in cells {l14, n14} contained within {col14, box13}, updating cells {k11, m11, m12, n11, u14, w14}:

Naked-pair {5|11} in cells {r7, r16} contained within {rowr}, updating cells {r3, r4, r5, r8, r11, r15, r20, r21, r23}:

Naked-pair {5|19} in cells {s5, s18} contained within {rows}, updating cells {s2, s11, s15}:

Naked-pair {11|20} in cells {u14, w14} contained within {col14, box23}, updating cells {l14, n14, u12, u15, v11, v12, w12, w15, x15, y15}:

Naked-pair {18|25} in cells {g5, g15, h5} contained within {rowg, col5, box6}, updating cells {f3, i2, i4, k5, o5, r5, s5, v5}:

backtrack.grid9461 → grid9462: f3 guess 15 ∈ {15|17}

pending={f3}

deduce.grid9462: naked-singles

grid9462 didn't work: naked-singles ran out of candidates.

…backtrack.grid9461 again

backtrack.grid9461 → grid9463: f3 guess 17 ∈ {15|17}

pending={f3}

deduce.grid9463: naked-singles

deduce.grid9463: hidden-singles

deduce.grid9463.rowh. h5 is 25 by hidden-single.

pending={h5}

deduce.grid9463: naked-singles

deduce.grid9463: hidden-singles

deduce.grid9463.rowv. v1 is 17 by hidden-single.

pending={v1}

deduce.grid9463: naked-singles

deduce.grid9463: hidden-singles

deduce.grid9463.rowm. m4 is 17 by hidden-single.

pending={m4}

deduce.grid9463: naked-singles

deduce.grid9463: hidden-singles

deduce.grid9463.col3. k3 is 15 by hidden-single.

pending={k3}

deduce.grid9463: naked-singles

deduce.grid9463: hidden-singles

deduce.grid9463.rowk. k2 is 2 by hidden-single.

pending={k2}

deduce.grid9463: naked-singles

deduce.grid9463: hidden-singles

deduce.grid9463.rowk. k1 is 24 by hidden-single.

pending={k1}

deduce.grid9463: naked-singles

deduce.grid9463: hidden-singles

deduce.grid9463.rowk. k9 is 22 by hidden-single.

pending={k9}

deduce.grid9463: naked-singles

deduce.grid9463: hidden-singles

deduce.grid9463.rowm. m1 is 20 by hidden-single.

pending={m1}

deduce.grid9463: naked-singles

deduce.grid9463: hidden-singles

deduce.grid9463.rowm. m22 is 10 by hidden-single.

pending={m22}

deduce.grid9463: naked-singles

deduce.grid9463: hidden-singles

deduce.grid9463.rowl. l14 is 10 by hidden-single.

pending={l14}

deduce.grid9463: naked-singles

deduce.grid9463: hidden-singles

deduce.grid9463.rowo. o20 is 25 by hidden-single.

deduce.grid9463.rowo. o23 is 19 by hidden-single.

pending={o20, o23}

deduce.grid9463: naked-singles

deduce.grid9463: hidden-singles

deduce.grid9463.rowo. o3 is 7 by hidden-single.

pending={o3}

deduce.grid9463: naked-singles

deduce.grid9463: hidden-singles

deduce.grid9463.rowp. p16 is 18 by hidden-single.

pending={p16}

deduce.grid9463: naked-singles

deduce.grid9463: hidden-singles

deduce.grid9463.rowu. u2 is 24 by hidden-single.

pending={u2}

deduce.grid9463: naked-singles

deduce.grid9463: hidden-singles

grid9463 didn't work: rowv is not bijective.

…backtrack.grid9461 again

grid9461 didn't work: exhaustive search revealed no solution.

…backtrack.grid9460 again

backtrack.grid9460 → grid9464: e22 guess 17 ∈ {1|17}

pending={e22}

deduce.grid9464: naked-singles

deduce.grid9464: hidden-singles

deduce.grid9464.rowf. f12 is 7 by hidden-single.

pending={f12}

deduce.grid9464: naked-singles

deduce.grid9464: hidden-singles

deduce.grid9464.rowf. f9 is 12 by hidden-single.

pending={f9}

deduce.grid9464: naked-singles

deduce.grid9464: hidden-singles

deduce.grid9464.rowf. f11 is 19 by hidden-single.

pending={f11}

deduce.grid9464: naked-singles

deduce.grid9464: hidden-singles

deduce.grid9464.rowh. h4 is 17 by hidden-single.

pending={h4}

deduce.grid9464: naked-singles

deduce.grid9464: hidden-singles

deduce.grid9464.rowh. h5 is 25 by hidden-single.

deduce.grid9464.rowh. h8 is 6 by hidden-single.

pending={h5, h8}

deduce.grid9464: naked-singles

deduce.grid9464: hidden-singles

deduce.grid9464.rowm. m1 is 17 by hidden-single.

deduce.grid9464.rowm. m10 is 15 by hidden-single.

deduce.grid9464.rowm. m12 is 19 by hidden-single.

pending={m1, m10, m12}

deduce.grid9464: naked-singles

deduce.grid9464: hidden-singles

deduce.grid9464.rowk. k2 is 15 by hidden-single.

pending={k2}

deduce.grid9464: naked-singles

deduce.grid9464: hidden-singles

deduce.grid9464.rowk. k1 is 24 by hidden-single.

deduce.grid9464.rowk. k3 is 2 by hidden-single.

pending={k1, k3}

deduce.grid9464: naked-singles

deduce.grid9464: hidden-singles

deduce.grid9464.rowk. k9 is 22 by hidden-single.

pending={k9}

deduce.grid9464: naked-singles

grid9464 didn't work: naked-singles ran out of candidates.

…backtrack.grid9460 again

grid9460 didn't work: exhaustive search revealed no solution.

…backtrack.grid9459 again

backtrack.grid9459 → grid9465: e21 guess 17 ∈ {3|17}

pending={e21}

deduce.grid9465: naked-singles

deduce.grid9465: hidden-singles

deduce.grid9465: naked-pairs

two's heap=t11 {2|5}, r20 {4|6}, l25 {2|7}, m19 {2|8}, n14 {7|10}, h22 {12|17}, r7 {5|11}, s24 {3|17}, l14 {7|10}, v18 {1|15}, f15 {8|18}, p16 {11|18}, j9 {12|19}, q9 {13|18}, q24 {8|13}, s18 {5|19}, s22 {12|17}, j25 {7|12}, u9 {8|13}, u14 {11|20}, y6 {1|15}, y25 {2|24}, o17 {16|21}, h5 {18|25}, p17 {21|24}, p21 {8|24}, q8 {5|21}, g5 {18|25}, k22 {8|21}, k5 {19|21}, i6 {6|15}, g15 {18|25}, s2 {11|25}, l4 {2|18}, f3 {15|17}, t9 {13|22}, i2 {15|21}, h4 {6|17}, u7 {5|16}, i8 {6|25}, n11 {8|21}, n7 {18|22}, w14 {11|20}, i11 {17|25}.

Naked-pair {7|10} in cells {l14, n14} contained within {col14, box13}, updating cells {k11, m11, m12, n11, u14, w14}:

Naked-pair {12|17} in cells {h22, s22} contained within {col22}, updating cells {k22, l22, m22, w22}:

Naked-pair {11|20} in cells {u14, w14} contained within {col14, box23}, updating cells {l14, n14, u12, u15, v11, v12, w12, w15, x15, y15}:

Naked-pair {18|25} in cells {g5, g15, h5} contained within {rowg, col5, box6}, updating cells {f3, h4, i2, i4, k5, o5, r5, s5, t5, v5}:

backtrack.grid9465 → grid9466: f3 guess 15 ∈ {15|17}

pending={f3}

deduce.grid9466: naked-singles

deduce.grid9466: hidden-singles

deduce.grid9466.rowi. i6 is 15 by hidden-single.

pending={i6}

deduce.grid9466: naked-singles

deduce.grid9466: hidden-singles

deduce.grid9466.rowm. m10 is 15 by hidden-single.

pending={m10}

deduce.grid9466: naked-singles

deduce.grid9466: hidden-singles

deduce.grid9466.rowk. k2 is 15 by hidden-single.

pending={k2}

deduce.grid9466: naked-singles

deduce.grid9466: hidden-singles

deduce.grid9466.rowk. k1 is 24 by hidden-single.

deduce.grid9466.rowk. k3 is 2 by hidden-single.

pending={k1, k3}

deduce.grid9466: naked-singles

deduce.grid9466: hidden-singles

deduce.grid9466.rowk. k9 is 22 by hidden-single.

pending={k9}

deduce.grid9466: naked-singles

grid9466 didn't work: naked-singles ran out of candidates.

…backtrack.grid9465 again

backtrack.grid9465 → grid9467: f3 guess 17 ∈ {15|17}

pending={f3}

deduce.grid9467: naked-singles

deduce.grid9467: hidden-singles

deduce.grid9467.rowh. h5 is 25 by hidden-single.

deduce.grid9467.rowh. h22 is 17 by hidden-single.

pending={h5, h22}

deduce.grid9467: naked-singles

deduce.grid9467: hidden-singles

deduce.grid9467.rows. s24 is 17 by hidden-single.

pending={s24}

deduce.grid9467: naked-singles

deduce.grid9467: hidden-singles

deduce.grid9467.rows. s8 is 3 by hidden-single.

pending={s8}

deduce.grid9467: naked-singles

deduce.grid9467: hidden-singles

deduce.grid9467.rowr. r21 is 3 by hidden-single.

pending={r21}

deduce.grid9467: naked-singles

deduce.grid9467: hidden-singles

deduce.grid9467.rowr. r23 is 9 by hidden-single.

pending={r23}

deduce.grid9467: naked-singles

deduce.grid9467: hidden-singles

deduce.grid9467.rows. s16 is 20 by hidden-single.

pending={s16}

deduce.grid9467: naked-singles

deduce.grid9467: hidden-singles

deduce.grid9467.rowt. t5 is 12 by hidden-single.

pending={t5}

deduce.grid9467: naked-singles

deduce.grid9467: hidden-singles

deduce.grid9467.rowv. v1 is 17 by hidden-single.

pending={v1}

deduce.grid9467: naked-singles

deduce.grid9467: hidden-singles

deduce.grid9467.rowm. m4 is 17 by hidden-single.

pending={m4}

deduce.grid9467: naked-singles

deduce.grid9467: hidden-singles

deduce.grid9467.rowo. o23 is 17 by hidden-single.

pending={o23}

deduce.grid9467: naked-singles

deduce.grid9467: hidden-singles

deduce.grid9467.rowo. o3 is 7 by hidden-single.

pending={o3}

deduce.grid9467: naked-singles

deduce.grid9467: hidden-singles

deduce.grid9467.rowu. u25 is 17 by hidden-single.

pending={u25}

deduce.grid9467: naked-singles

deduce.grid9467: hidden-singles

deduce.grid9467.rowy. y24 is 3 by hidden-single.

pending={y24}

deduce.grid9467: naked-singles

deduce.grid9467: hidden-singles

deduce.grid9467.col3. k3 is 15 by hidden-single.

pending={k3}

deduce.grid9467: naked-singles

deduce.grid9467: hidden-singles

deduce.grid9467.rowk. k2 is 2 by hidden-single.

pending={k2}

deduce.grid9467: naked-singles

grid9467 didn't work: naked-singles ran out of candidates.

…backtrack.grid9465 again

grid9465 didn't work: exhaustive search revealed no solution.

…backtrack.grid9459 again

grid9459 didn't work: exhaustive search revealed no solution.

…backtrack.grid9458 again

backtrack.grid9458 → grid9468: e16 guess 5 ∈ {2|5}

pending={e16}

deduce.grid9468: naked-singles

deduce.grid9468: hidden-singles

deduce.grid9468.col16. k16 is 2 by hidden-single.

pending={k16}

deduce.grid9468: naked-singles

deduce.grid9468: hidden-singles

deduce.grid9468.rowm. m4 is 2 by hidden-single.

pending={m4}

deduce.grid9468: naked-singles

deduce.grid9468: hidden-singles

deduce.grid9468.col3. u3 is 18 by hidden-single.

pending={u3}

deduce.grid9468: naked-singles

deduce.grid9468: hidden-singles

deduce.grid9468.col16. r16 is 6 by hidden-single.

pending={r16}

deduce.grid9468: naked-singles

deduce.grid9468: hidden-singles

deduce.grid9468.col16. s16 is 20 by hidden-single.

pending={s16}

deduce.grid9468: naked-singles

deduce.grid9468: hidden-singles

deduce.grid9468: naked-pairs

two's heap=r22 {1|3}, t11 {2|5}, y6 {1|15}, l25 {2|7}, s8 {3|5}, i6 {6|15}, o19 {1|16}, l10 {8|16}, q19 {1|11}, k14 {6|16}, u12 {8|13}, o17 {6|16}, m22 {10|17}, h4 {6|17}, f3 {15|17}, q9 {13|18}, h22 {12|17}, j25 {7|12}, r7 {5|11}, s24 {3|17}, e21 {3|17}, u7 {5|16}, v18 {1|15}, w14 {11|20}, y25 {2|24}, i11 {17|25}, n11 {8|21}, j9 {12|19}, p16 {11|18}, p17 {21|24}, p21 {8|24}, h5 {18|25}, q8 {5|21}, k5 {19|21}, q16 {11|18}, l6 {6|19}, e23 {1|17}, s2 {11|25}, f15 {8|18}, g5 {18|25}, s18 {5|19}, t9 {13|22}, m10 {15|20}, i2 {15|21}, m11 {4|19}, u14 {11|20}, m12 {4|19}, g15 {18|25}, n7 {18|22}, i8 {6|25}.

Naked-pair {11|18} in cells {p16, q16} contained within {col16, box19}, updating cells {p17, p20, q19, r20, s18, t17, t18, t20}:

Naked-pair {4|19} in cells {m11, m12} contained within {rowm, box13}, updating cells {k11, k14, l14, m1, m6, m10, m22, n11, n14, o14}:

Naked-pair {11|20} in cells {u14, w14} contained within {col14, box23}, updating cells {k14, l14, n14, o14, u12, u15, v11, v12, w12, w15, x15, y15}:

Naked-pair {18|25} in cells {g5, g15, h5} contained within {rowg, col5, box6}, updating cells {f3, h4, i2, i4, k5, o5, r5, s5, t5, v5}:

pending={q19}

deduce.grid9468: naked-singles

deduce.grid9468: hidden-singles

deduce.grid9468.rowk. k9 is 4 by hidden-single.

pending={k9}

deduce.grid9468: naked-singles

deduce.grid9468: hidden-singles

deduce.grid9468.rowk. k1 is 22 by hidden-single.

pending={k1}

deduce.grid9468: naked-singles

deduce.grid9468: hidden-singles

deduce.grid9468.rowk. k2 is 24 by hidden-single.

pending={k2}

deduce.grid9468: naked-singles

deduce.grid9468: hidden-singles

deduce.grid9468.rowy. y8 is 22 by hidden-single.

pending={y8}

deduce.grid9468: naked-singles

deduce.grid9468: hidden-singles

deduce.grid9468.rowv. v17 is 22 by hidden-single.

pending={v17}

deduce.grid9468: naked-singles

deduce.grid9468: hidden-singles

deduce.grid9468.rowu. u4 is 5 by hidden-single.

pending={u4}

deduce.grid9468: naked-singles

deduce.grid9468: hidden-singles

deduce.grid9468.rown. n3 is 5 by hidden-single.

pending={n3}

deduce.grid9468: naked-singles

deduce.grid9468: hidden-singles

deduce.grid9468.rown. n23 is 7 by hidden-single.

pending={n23}

deduce.grid9468: naked-singles

deduce.grid9468: hidden-singles

grid9468 didn't work: rowl is not bijective.

…backtrack.grid9458 again

grid9458 didn't work: exhaustive search revealed no solution.

…backtrack.grid9456 again

grid9456 didn't work: exhaustive search revealed no solution.

…backtrack.grid9455 again

backtrack.grid9455 → grid9469: d23 guess 23 ∈ {12|23}

pending={d23}

deduce.grid9469: naked-singles

deduce.grid9469: hidden-singles

deduce.grid9469.rowf. f12 is 7 by hidden-single.

pending={f12}

deduce.grid9469: naked-singles

deduce.grid9469: hidden-singles

deduce.grid9469.col3. u3 is 18 by hidden-single.

pending={u3}

deduce.grid9469: naked-singles

deduce.grid9469: hidden-singles

deduce.grid9469.col19. u19 is 20 by hidden-single.

pending={u19}

deduce.grid9469: naked-singles

deduce.grid9469: hidden-singles

deduce.grid9469: naked-pairs

two's heap=r22 {1|3}, e20 {2|5}, m19 {2|8}, t11 {2|5}, e18 {5|11}, i6 {6|15}, e21 {3|17}, r7 {5|11}, k16 {2|6}, u12 {8|13}, y21 {3|15}, l10 {8|16}, f15 {8|18}, p16 {11|18}, f23 {12|17}, q9 {13|18}, e23 {1|17}, j9 {12|19}, s24 {3|17}, u7 {5|16}, v18 {1|15}, k14 {6|16}, l6 {6|19}, h5 {18|25}, h22 {12|17}, n7 {18|22}, n11 {8|21}, i2 {15|21}, p17 {21|24}, p21 {8|24}, q8 {5|21}, i8 {6|25}, f25 {22|23}, i11 {17|25}, s2 {11|25}, g5 {18|25}, t9 {13|22}, j12 {12|19}, t25 {22|23}, g15 {18|25}, h4 {6|17}, k5 {19|21}, y6 {1|15}, f3 {15|17}.

Naked-pair {12|17} in cells {f23, h22} contained within {box10}, updating cells {f24, f25}:

Naked-pair {18|25} in cells {g5, g15, h5} contained within {rowg, col5, box6}, updating cells {f3, h4, i2, i4, k5, o5, r5, s5, t5, v5}:

backtrack.grid9469 → grid9470: e18 guess 5 ∈ {5|11}

pending={e18}

deduce.grid9470: naked-singles

deduce.grid9470: hidden-singles

deduce.grid9470.rowm. m4 is 2 by hidden-single.

pending={m4}

deduce.grid9470: naked-singles

deduce.grid9470: hidden-singles

deduce.grid9470.rowq. q9 is 18 by hidden-single.

pending={q9}

deduce.grid9470: naked-singles

deduce.grid9470: hidden-singles

deduce.grid9470.col7. n7 is 18 by hidden-single.

pending={n7}

deduce.grid9470: naked-singles

deduce.grid9470: hidden-singles

deduce.grid9470.rowk. k23 is 18 by hidden-single.

pending={k23}

deduce.grid9470: naked-singles

deduce.grid9470: hidden-singles

deduce.grid9470.col10. f10 is 18 by hidden-single.

pending={f10}

deduce.grid9470: naked-singles

deduce.grid9470: hidden-singles

deduce.grid9470.col11. s11 is 18 by hidden-single.

pending={s11}

deduce.grid9470: naked-singles

deduce.grid9470: hidden-singles

deduce.grid9470.col24. s24 is 17 by hidden-single.

pending={s24}

deduce.grid9470: naked-singles

deduce.grid9470: hidden-singles

deduce.grid9470.col24. y24 is 3 by hidden-single.

pending={y24}

deduce.grid9470: naked-singles

deduce.grid9470: hidden-singles

deduce.grid9470.box17. t9 is 13 by hidden-single.

pending={t9}

deduce.grid9470: naked-singles

deduce.grid9470: hidden-singles

deduce.grid9470: naked-pairs

two's heap=r22 {1|3}, r20 {1|4}, u9 {6|8}, r7 {5|11}, t11 {2|5}, v21 {8|10}, o17 {6|16}, p7 {11|22}, i6 {6|15}, q3 {8|10}, s8 {3|5}, u7 {5|16}, u6 {6|13}, n10 {8|20}, e23 {1|17}, p8 {22|23}, p21 {8|24}, j12 {12|19}, k14 {6|16}, l10 {8|16}, q19 {1|11}, s18 {11|19}, s22 {3|12}, f24 {22|23}, m22 {10|17}, o19 {1|16}, u12 {8|13}, y8 {14|22}, y10 {2|21}, i2 {15|21}, h22 {12|17}, g5 {18|25}, i8 {6|25}, i11 {17|25}, p17 {21|24}, g15 {18|25}, q4 {13|24}, f11 {17|19}, j9 {12|19}, k5 {19|21}, h4 {6|17}, s2 {11|25}, f23 {12|17}, h5 {18|25}, s15 {11|25}, l6 {6|19}, e21 {3|17}, t20 {8|24}, t25 {22|23}, m10 {15|20}, m11 {4|19}, m12 {4|19}, f3 {15|17}, h12 {12|18}, v18 {1|15}, f25 {22|23}, y1 {21|22}, n11 {8|21}.

Naked-pair {12|17} in cells {f23, h22} contained within {box10}, updating cells {f24, f25}:

Naked-pair {4|19} in cells {m11, m12} contained within {rowm, box13}, updating cells {k11, k14, l14, m1, m6, m10, m22, n11, n14, o14}:

Naked-pair {22|23} in cells {f24, f25, p8, t25} contained within {rowf, col25, box10}, updating cells {f3, f9, f11, f23, h22}:

Naked-pair {11|25} in cells {s2, s15} contained within {rows}, updating cells {s5, s8, s18, s22}:

Naked-pair {18|25} in cells {g5, g15, h5} contained within {rowg, col5, box6}, updating cells {f3, h4, i2, i4, k5, o5, r5, s5, t5, v5}:

pending={s18}

deduce.grid9470: naked-singles

deduce.grid9470: hidden-singles

deduce.grid9470.rowk. k9 is 4 by hidden-single.

pending={k9}

deduce.grid9470: naked-singles

deduce.grid9470: hidden-singles

deduce.grid9470.rowk. k1 is 22 by hidden-single.

pending={k1}

deduce.grid9470: naked-singles

deduce.grid9470: hidden-singles

deduce.grid9470.rowk. k2 is 24 by hidden-single.

pending={k2}

deduce.grid9470: naked-singles

deduce.grid9470: hidden-singles

deduce.grid9470.rown. n9 is 22 by hidden-single.

pending={n9}

deduce.grid9470: naked-singles

deduce.grid9470: hidden-singles

deduce.grid9470.rowu. u8 is 14 by hidden-single.

pending={u8}

deduce.grid9470: naked-singles

deduce.grid9470: hidden-singles

deduce.grid9470.rowv. v11 is 21 by hidden-single.

deduce.grid9470.rowv. v17 is 22 by hidden-single.

pending={v11, v17}

deduce.grid9470: naked-singles

grid9470 didn't work: naked-singles ran out of candidates.

…backtrack.grid9469 again

backtrack.grid9469 → grid9471: e18 guess 11 ∈ {5|11}

pending={e18}

deduce.grid9471: naked-singles

deduce.grid9471: hidden-singles

deduce.grid9471.rowx. x19 is 11 by hidden-single.

pending={x19}

deduce.grid9471: naked-singles

deduce.grid9471: hidden-singles

deduce.grid9471.col24. s24 is 17 by hidden-single.

pending={s24}

deduce.grid9471: naked-singles

deduce.grid9471: hidden-singles

deduce.grid9471.col24. y24 is 3 by hidden-single.

pending={y24}

deduce.grid9471: naked-singles

deduce.grid9471: hidden-singles

deduce.grid9471: naked-pairs

two's heap=r22 {1|3}, e16 {2|5}, m19 {2|8}, e20 {2|5}, t11 {2|5}, l10 {8|16}, f23 {12|17}, r7 {5|11}, q19 {1|8}, k16 {2|6}, v21 {8|10}, h4 {6|17}, e21 {3|17}, h22 {12|17}, i2 {15|21}, q9 {13|18}, i6 {6|15}, j9 {12|19}, s22 {3|12}, j12 {12|19}, u6 {6|13}, u7 {5|16}, u12 {8|13}, l6 {6|19}, f15 {8|18}, h5 {18|25}, n7 {18|22}, n11 {8|21}, p16 {11|18}, p17 {21|24}, p21 {8|24}, f24 {22|23}, q8 {5|21}, i8 {6|25}, e23 {1|17}, i11 {17|25}, s2 {11|25}, f25 {22|23}, s18 {5|19}, g5 {18|25}, t9 {13|22}, t25 {22|23}, k5 {19|21}, g15 {18|25}, k14 {6|16}, f3 {15|17}, v18 {1|15}, y1 {21|22}, y10 {2|21}.

Naked-pair {2|5} in cells {e16, e20, t11} contained within {rowe, box4}, updating cells {e21, e22, e23}:

Naked-pair {12|17} in cells {f23, h22} contained within {box10}, updating cells {f24, f25}:

Naked-pair {22|23} in cells {f24, f25, t25} contained within {rowf, col25, box10}, updating cells {f3, f9, f10, f11, f15, f23, h22}:

Naked-pair {18|25} in cells {g5, g15, h5} contained within {rowg, col5, box6}, updating cells {f3, h4, i2, i4, k5, o5, r5, s5, t5, v5}:

backtrack.grid9471 → grid9472: e16 guess 2 ∈ {2|5}

pending={e16}

deduce.grid9472: naked-singles

deduce.grid9472: hidden-singles

deduce.grid9472.rowl. l10 is 16 by hidden-single.

pending={l10}

deduce.grid9472: naked-singles

deduce.grid9472: hidden-singles

deduce.grid9472.rowo. o14 is 6 by hidden-single.

pending={o14}

deduce.grid9472: naked-singles

deduce.grid9472: hidden-singles

deduce.grid9472.rown. n9 is 6 by hidden-single.

pending={n9}

deduce.grid9472: naked-singles

deduce.grid9472: hidden-singles

deduce.grid9472: naked-pairs

two's heap=r22 {1|3}, t11 {2|5}, n14 {7|10}, m19 {2|8}, q19 {1|8}, e23 {1|17}, h22 {12|17}, l23 {7|9}, s22 {3|12}, l14 {7|10}, v21 {8|10}, y10 {2|21}, f3 {15|17}, p16 {11|18}, q8 {5|21}, q9 {13|18}, r7 {5|11}, j12 {12|19}, s18 {5|19}, h4 {6|17}, u6 {6|13}, u12 {8|13}, u9 {8|13}, n11 {8|21}, n7 {18|22}, i2 {15|21}, o17 {16|21}, f25 {22|23}, p17 {21|24}, i8 {6|25}, p21 {8|24}, g5 {18|25}, j9 {12|19}, i11 {17|25}, f15 {8|18}, g15 {18|25}, s2 {11|25}, k5 {19|21}, t9 {13|22}, k22 {8|21}, t25 {22|23}, f23 {12|17}, u7 {5|16}, h5 {18|25}, i6 {6|15}, e21 {3|17}, v18 {1|15}, f24 {22|23}, y1 {21|22}.

Naked-pair {7|10} in cells {l14, n14} contained within {col14, box13}, updating cells {k11, m11, m12, n11}:

Naked-pair {8|13} in cells {u9, u12} contained within {rowu}, updating cells {u1, u2, u4, u6, u7, u8, u15, u21, u23, u24}:

Naked-pair {12|17} in cells {f23, h22} contained within {box10}, updating cells {f24, f25}:

Naked-pair {22|23} in cells {f24, f25, t25} contained within {rowf, col25, box10}, updating cells {f3, f9, f10, f11, f15, f23, h22}:

Naked-pair {18|25} in cells {g5, g15, h5} contained within {rowg, col5, box6}, updating cells {f3, h4, i2, i4, k5, o5, r5, s5, t5, v5}:

pending={u6}

deduce.grid9472: naked-singles

deduce.grid9472: hidden-singles

deduce.grid9472.rowf. f3 is 15 by hidden-single.

pending={f3}

deduce.grid9472: naked-singles

deduce.grid9472: hidden-singles

deduce.grid9472.rowm. m10 is 15 by hidden-single.

pending={m10}

deduce.grid9472: naked-singles

deduce.grid9472: hidden-singles

deduce.grid9472.rowk. k2 is 15 by hidden-single.

pending={k2}

deduce.grid9472: naked-singles

deduce.grid9472: hidden-singles

deduce.grid9472.rowk. k1 is 24 by hidden-single.

deduce.grid9472.rowk. k3 is 2 by hidden-single.

pending={k1, k3}

deduce.grid9472: naked-singles

deduce.grid9472: hidden-singles

deduce.grid9472.rowk. k9 is 22 by hidden-single.

pending={k9}

deduce.grid9472: naked-singles

grid9472 didn't work: naked-singles ran out of candidates.

…backtrack.grid9471 again

backtrack.grid9471 → grid9473: e16 guess 5 ∈ {2|5}

pending={e16}

deduce.grid9473: naked-singles

deduce.grid9473: hidden-singles

deduce.grid9473.col16. k16 is 2 by hidden-single.

pending={k16}

deduce.grid9473: naked-singles

deduce.grid9473: hidden-singles

deduce.grid9473.rowl. l23 is 7 by hidden-single.

pending={l23}

deduce.grid9473: naked-singles

deduce.grid9473: hidden-singles

deduce.grid9473.rowm. m4 is 2 by hidden-single.

pending={m4}

deduce.grid9473: naked-singles

deduce.grid9473: hidden-singles

deduce.grid9473.rown. n3 is 7 by hidden-single.

pending={n3}

deduce.grid9473: naked-singles

deduce.grid9473: hidden-singles

deduce.grid9473.rown. n4 is 5 by hidden-single.

pending={n4}

deduce.grid9473: naked-singles

deduce.grid9473: hidden-singles

deduce.grid9473.col4. x4 is 22 by hidden-single.

pending={x4}

deduce.grid9473: naked-singles

deduce.grid9473: hidden-singles

grid9473 didn't work: rowu is not bijective.

…backtrack.grid9471 again

grid9471 didn't work: exhaustive search revealed no solution.

…backtrack.grid9469 again

grid9469 didn't work: exhaustive search revealed no solution.

…backtrack.grid9455 again

grid9455 didn't work: exhaustive search revealed no solution.

…backtrack.grid9454 again

backtrack.grid9454 → grid9474: d22 guess 12 ∈ {2|12}

pending={d22}

deduce.grid9474: naked-singles

grid9474 didn't work: naked-singles ran out of candidates.

…backtrack.grid9454 again

grid9454 didn't work: exhaustive search revealed no solution.

…backtrack.grid9453 again

backtrack.grid9453 → grid9475: d17 guess 21 ∈ {1|21}

pending={d17}

deduce.grid9475: naked-singles

deduce.grid9475: hidden-singles

deduce.grid9475: naked-pairs

two's heap=r22 {1|3}, t11 {2|5}, k16 {2|6}, l25 {2|7}, j25 {7|12}, p16 {11|18}, r7 {5|11}, u7 {5|16}, y6 {1|15}, h22 {12|17}, n11 {8|21}, p17 {1|24}, q8 {5|21}, h4 {6|17}, i6 {6|15}, f15 {8|18}, k14 {6|16}, d18 {1|20}, e21 {3|17}, g5 {18|25}, l6 {6|19}, n7 {18|22}, i2 {15|21}, g15 {18|25}, i8 {6|25}, i11 {17|25}, p21 {8|24}, j9 {12|19}, q9 {13|18}, f3 {15|17}, s2 {11|25}, h5 {18|25}, t9 {13|22}, k5 {19|21}, s24 {3|17}, u14 {11|20}, w14 {11|20}, l4 {2|18}, y25 {2|24}.

Naked-pair {11|20} in cells {u14, w14} contained within {col14, box23}, updating cells {k14, l14, n14, o14, u12, u15, v11, v12, w12, w15, x15, y15}:

Naked-pair {18|25} in cells {g5, g15, h5} contained within {rowg, col5, box6}, updating cells {f3, h4, i2, i4, k5, o5, r5, s5, t5, v5}:

backtrack.grid9475 → grid9476: d18 guess 1 ∈ {1|20}

pending={d18}

deduce.grid9476: naked-singles

deduce.grid9476: hidden-singles

deduce.grid9476.rowd. d19 is 20 by hidden-single.

pending={d19}

deduce.grid9476: naked-singles

deduce.grid9476: hidden-singles

deduce.grid9476.col19. e19 is 12 by hidden-single.

pending={e19}

deduce.grid9476: naked-singles

deduce.grid9476: hidden-singles

deduce.grid9476: naked-pairs

two's heap=r22 {1|3}, e20 {2|5}, l25 {2|7}, t11 {2|5}, e18 {5|11}, d22 {2|12}, i6 {6|15}, r7 {5|11}, k16 {2|6}, y6 {1|15}, k14 {6|16}, e23 {1|17}, h22 {12|17}, p16 {11|18}, f3 {15|17}, q9 {13|18}, j25 {7|12}, f15 {8|18}, u7 {5|16}, u14 {11|20}, e21 {3|17}, h4 {6|17}, l4 {2|18}, h5 {18|25}, l6 {6|19}, n7 {18|22}, n11 {8|21}, i2 {15|21}, p17 {1|24}, p21 {8|24}, q8 {5|21}, i8 {6|25}, d23 {12|23}, i11 {17|25}, s2 {11|25}, g5 {18|25}, t9 {13|22}, j9 {12|19}, s24 {3|17}, g15 {18|25}, v18 {15|20}, k5 {19|21}, w14 {11|20}, y25 {2|24}.

Naked-pair {11|20} in cells {u14, w14} contained within {col14, box23}, updating cells {k14, l14, n14, o14, u12, u15, v11, v12, w12, w15, x15, y15}:

Naked-pair {18|25} in cells {g5, g15, h5} contained within {rowg, col5, box6}, updating cells {f3, h4, i2, i4, k5, o5, r5, s5, t5, v5}:

backtrack.grid9476 → grid9477: d22 guess 2 ∈ {2|12}

pending={d22}

deduce.grid9477: naked-singles

deduce.grid9477: hidden-singles

deduce.grid9477: naked-pairs

two's heap=r22 {1|3}, e20 {2|5}, l25 {2|7}, t11 {2|5}, e18 {5|11}, i6 {6|15}, e23 {1|17}, r7 {5|11}, k16 {2|6}, y6 {1|15}, k14 {6|16}, h22 {12|17}, n11 {8|21}, p16 {11|18}, f3 {15|17}, q9 {13|18}, j25 {7|12}, f15 {8|18}, u7 {5|16}, u14 {11|20}, e21 {3|17}, h4 {6|17}, l4 {2|18}, h5 {18|25}, l6 {6|19}, d23 {12|23}, n7 {18|22}, i2 {15|21}, p17 {1|24}, p21 {8|24}, q8 {5|21}, i8 {6|25}, d25 {12|23}, i11 {17|25}, s2 {11|25}, g5 {18|25}, t9 {13|22}, j9 {12|19}, s24 {3|17}, g15 {18|25}, v18 {15|20}, k5 {19|21}, w14 {11|20}, y25 {2|24}.

Naked-pair {11|20} in cells {u14, w14} contained within {col14, box23}, updating cells {k14, l14, n14, o14, u12, u15, v11, v12, w12, w15, x15, y15}:

Naked-pair {12|23} in cells {d23, d25} contained within {rowd, box5}, updating cells {e21, e22, e23}:

Naked-pair {18|25} in cells {g5, g15, h5} contained within {rowg, col5, box6}, updating cells {f3, h4, i2, i4, k5, o5, r5, s5, t5, v5}:

backtrack.grid9477 → grid9478: d23 guess 12 ∈ {12|23}

pending={d23}

deduce.grid9478: naked-singles

deduce.grid9478: hidden-singles

deduce.grid9478: naked-pairs

two's heap=r22 {1|3}, e20 {2|5}, r7 {5|11}, t11 {2|5}, l25 {2|7}, e21 {3|17}, i6 {6|15}, j25 {7|12}, k16 {2|6}, y6 {1|15}, e18 {5|11}, n11 {8|21}, f15 {8|18}, p21 {8|24}, q9 {13|18}, e23 {1|17}, s24 {3|17}, u7 {5|16}, h4 {6|17}, h22 {12|17}, l4 {2|18}, l6 {6|19}, f3 {15|17}, n7 {18|22}, i2 {15|21}, p16 {11|18}, p17 {1|24}, g5 {18|25}, i8 {6|25}, i11 {17|25}, q8 {5|21}, g15 {18|25}, s2 {11|25}, j9 {12|19}, t9 {13|22}, k5 {19|21}, k14 {6|16}, u14 {11|20}, v18 {15|20}, h5 {18|25}, w14 {11|20}, y25 {2|24}.

Naked-pair {11|20} in cells {u14, w14} contained within {col14, box23}, updating cells {k14, l14, n14, o14, u12, u15, v11, v12, w12, w15, x15, y15}:

Naked-pair {18|25} in cells {g5, g15, h5} contained within {rowg, col5, box6}, updating cells {f3, h4, i2, i4, k5, o5, r5, s5, t5, v5}:

backtrack.grid9478 → grid9479: e18 guess 5 ∈ {5|11}

pending={e18}

deduce.grid9479: naked-singles

deduce.grid9479: hidden-singles

deduce.grid9479.rowm. m4 is 2 by hidden-single.

pending={m4}

deduce.grid9479: naked-singles

deduce.grid9479: hidden-singles

deduce.grid9479.rowq. q9 is 18 by hidden-single.

pending={q9}

deduce.grid9479: naked-singles

deduce.grid9479: hidden-singles

deduce.grid9479.col3. u3 is 18 by hidden-single.

pending={u3}

deduce.grid9479: naked-singles

deduce.grid9479: hidden-singles

deduce.grid9479.col7. n7 is 18 by hidden-single.

pending={n7}

deduce.grid9479: naked-singles

deduce.grid9479: hidden-singles

deduce.grid9479.rowk. k23 is 18 by hidden-single.

pending={k23}

deduce.grid9479: naked-singles

deduce.grid9479: hidden-singles

deduce.grid9479.col10. f10 is 18 by hidden-single.

pending={f10}

deduce.grid9479: naked-singles

deduce.grid9479: hidden-singles

deduce.grid9479.col11. s11 is 18 by hidden-single.

pending={s11}

deduce.grid9479: naked-singles

deduce.grid9479: hidden-singles

deduce.grid9479.box17. t9 is 13 by hidden-single.

pending={t9}

deduce.grid9479: naked-singles

deduce.grid9479: hidden-singles

deduce.grid9479: naked-pairs

two's heap=r22 {1|3}, r20 {1|4}, q3 {8|10}, s8 {3|5}, t11 {2|5}, y6 {1|15}, e23 {1|17}, r7 {5|11}, l25 {2|7}, u9 {6|8}, u12 {8|13}, h4 {6|17}, p7 {11|22}, p17 {1|24}, f3 {15|17}, k14 {6|16}, j25 {7|12}, e21 {3|17}, s24 {3|17}, l10 {8|16}, i6 {6|15}, u14 {11|20}, w14 {11|20}, n10 {8|20}, n11 {8|21}, i8 {6|25}, p8 {22|23}, i11 {17|25}, p21 {8|24}, j9 {12|19}, q4 {13|24}, h5 {18|25}, h12 {12|18}, k5 {19|21}, s2 {11|25}, f11 {17|19}, s15 {11|25}, s18 {11|19}, l6 {6|19}, g5 {18|25}, t17 {15|24}, h22 {12|17}, u7 {5|16}, i2 {15|21}, m19 {8|21}, m20 {8|21}, v18 {15|20}, g15 {18|25}, x18 {11|25}, y8 {14|22}, y25 {2|24}.

Naked-pair {11|20} in cells {u14, w14} contained within {col14, box23}, updating cells {k14, l14, n14, o14, u12, u15, v11, v12, w12, w15, x15, y15}:

Naked-pair {8|21} in cells {m19, m20, n11} contained within {rowm, box14}, updating cells {m1, m6, m10, m11, m12, m22, n20, o17, o19, o20}:

Naked-pair {11|25} in cells {s2, s15, x18} contained within {rows}, updating cells {s5, s8, s18, s22, s24}:

Naked-pair {18|25} in cells {g5, g15, h5} contained within {rowg, col5, box6}, updating cells {f3, h4, i2, i4, k5, o5, r5, s5, t5, v5}:

pending={s18}

deduce.grid9479: naked-singles

deduce.grid9479: hidden-singles

deduce.grid9479.col19. m19 is 21 by hidden-single.

pending={m19}

deduce.grid9479: naked-singles

deduce.grid9479: hidden-singles

deduce.grid9479.col19. q19 is 8 by hidden-single.

pending={q19}

deduce.grid9479: naked-singles

deduce.grid9479: hidden-singles

deduce.grid9479.rowq. q2 is 11 by hidden-single.

pending={q2}

deduce.grid9479: naked-singles

deduce.grid9479: hidden-singles

deduce.grid9479.rowp. p7 is 11 by hidden-single.

pending={p7}

deduce.grid9479: naked-singles

deduce.grid9479: hidden-singles

deduce.grid9479.rowl. l14 is 10 by hidden-single.

pending={l14}

deduce.grid9479: naked-singles

deduce.grid9479: hidden-singles

deduce.grid9479.rowl. l10 is 16 by hidden-single.

pending={l10}

deduce.grid9479: naked-singles

deduce.grid9479: hidden-singles

deduce.grid9479.rowk. k14 is 16 by hidden-single.

pending={k14}

deduce.grid9479: naked-singles

deduce.grid9479: hidden-singles

deduce.grid9479.rowm. m1 is 17 by hidden-single.

pending={m1}

deduce.grid9479: naked-singles

deduce.grid9479: hidden-singles

deduce.grid9479.rowr. r23 is 11 by hidden-single.

pending={r23}

deduce.grid9479: naked-singles

deduce.grid9479: hidden-singles

deduce.grid9479.rowr. r21 is 9 by hidden-single.

pending={r21}

deduce.grid9479: naked-singles

deduce.grid9479: hidden-singles

deduce.grid9479.rowr. r22 is 3 by hidden-single.

pending={r22}

deduce.grid9479: naked-singles

deduce.grid9479: hidden-singles

deduce.grid9479.rowo. o21 is 17 by hidden-single.

pending={o21}

deduce.grid9479: naked-singles

deduce.grid9479: hidden-singles

deduce.grid9479.rowt. t5 is 12 by hidden-single.

deduce.grid9479.rowt. t11 is 5 by hidden-single.

deduce.grid9479.rowt. t18 is 11 by hidden-single.

pending={t5, t11, t18}

deduce.grid9479: naked-singles

deduce.grid9479: hidden-singles

deduce.grid9479.rowt. t17 is 15 by hidden-single.

pending={t17}

deduce.grid9479: naked-singles

deduce.grid9479: hidden-singles

deduce.grid9479.rowu. u15 is 14 by hidden-single.

pending={u15}

deduce.grid9479: naked-singles

deduce.grid9479: hidden-singles

deduce.grid9479.rowv. v3 is 17 by hidden-single.

pending={v3}

deduce.grid9479: naked-singles

grid9479 didn't work: naked-singles ran out of candidates.

…backtrack.grid9478 again

backtrack.grid9478 → grid9480: e18 guess 11 ∈ {5|11}

pending={e18}

deduce.grid9480: naked-singles

deduce.grid9480: hidden-singles

deduce.grid9480: naked-pairs

two's heap=r22 {1|3}, e16 {2|5}, r7 {5|11}, e20 {2|5}, k16 {2|6}, e21 {3|17}, i6 {6|15}, j25 {7|12}, t11 {2|5}, y6 {1|15}, l25 {2|7}, n11 {8|21}, f15 {8|18}, p21 {8|24}, q9 {13|18}, e23 {1|17}, s24 {3|17}, u7 {5|16}, h4 {6|17}, w14 {11|20}, h22 {12|17}, l6 {6|19}, f3 {15|17}, n7 {18|22}, i2 {15|21}, p16 {11|18}, p17 {1|24}, g5 {18|25}, i8 {6|25}, i11 {17|25}, q8 {5|21}, g15 {18|25}, s2 {11|25}, j9 {12|19}, t9 {13|22}, k5 {19|21}, k14 {6|16}, u14 {11|20}, v18 {15|20}, h5 {18|25}, x18 {5|25}, l4 {2|18}, y25 {2|24}.

Naked-pair {2|5} in cells {e16, e20, t11} contained within {rowe, box4}, updating cells {e21, e22, e23}:

Naked-pair {11|20} in cells {u14, w14} contained within {col14, box23}, updating cells {k14, l14, n14, o14, u12, u15, v11, v12, w12, w15, x15, y15}:

Naked-pair {18|25} in cells {g5, g15, h5} contained within {rowg, col5, box6}, updating cells {f3, h4, i2, i4, k5, o5, r5, s5, t5, v5}:

backtrack.grid9480 → grid9481: e16 guess 2 ∈ {2|5}

pending={e16}

deduce.grid9481: naked-singles

deduce.grid9481: hidden-singles

deduce.grid9481.rowl. l10 is 16 by hidden-single.

pending={l10}

deduce.grid9481: naked-singles

deduce.grid9481: hidden-singles

deduce.grid9481.rowo. o14 is 6 by hidden-single.

pending={o14}

deduce.grid9481: naked-singles

deduce.grid9481: hidden-singles

deduce.grid9481.rown. n9 is 6 by hidden-single.

pending={n9}

deduce.grid9481: naked-singles

deduce.grid9481: hidden-singles

deduce.grid9481: naked-pairs

two's heap=r22 {1|3}, t11 {2|5}, l25 {2|7}, l14 {7|10}, n14 {7|10}, o17 {1|16}, r7 {5|11}, e23 {1|17}, u9 {8|13}, y6 {1|15}, j25 {7|12}, p16 {11|18}, p17 {1|24}, q9 {13|18}, i6 {6|15}, k22 {8|21}, s24 {3|17}, u7 {5|16}, l4 {2|18}, w14 {11|20}, e21 {3|17}, i2 {15|21}, n11 {8|21}, g15 {18|25}, i8 {6|25}, i11 {17|25}, p21 {8|24}, q8 {5|21}, j9 {12|19}, f3 {15|17}, h4 {6|17}, h5 {18|25}, s2 {11|25}, t9 {13|22}, k5 {19|21}, f15 {8|18}, h22 {12|17}, u14 {11|20}, v18 {15|20}, g5 {18|25}, x18 {5|25}, n7 {18|22}, y25 {2|24}.

Naked-pair {7|10} in cells {l14, n14} contained within {col14, box13}, updating cells {k11, m11, m12, n11, u14, w14}:

Naked-pair {11|20} in cells {u14, w14} contained within {col14, box23}, updating cells {l14, n14, u12, u15, v11, v12, w12, w15, x15, y15}:

Naked-pair {18|25} in cells {g5, g15, h5} contained within {rowg, col5, box6}, updating cells {f3, h4, i2, i4, k5, o5, r5, s5, t5, v5}:

backtrack.grid9481 → grid9482: e21 guess 3 ∈ {3|17}

pending={e21}

deduce.grid9482: naked-singles

deduce.grid9482: hidden-singles

deduce.grid9482.rowy. y24 is 3 by hidden-single.

pending={y24}

deduce.grid9482: naked-singles

deduce.grid9482: hidden-singles

deduce.grid9482: naked-pairs

two's heap=r22 {1|3}, t11 {2|5}, n14 {7|10}, l25 {2|7}, j25 {7|12}, o17 {1|16}, r7 {5|11}, s22 {3|12}, l14 {7|10}, i6 {6|15}, y6 {1|15}, e22 {1|17}, p16 {11|18}, q8 {5|21}, q9 {13|18}, h4 {6|17}, e23 {1|17}, l4 {2|18}, u9 {8|13}, u14 {11|20}, h22 {12|17}, n11 {8|21}, i2 {15|21}, g5 {18|25}, f3 {15|17}, i8 {6|25}, p17 {1|24}, g15 {18|25}, p21 {8|24}, i11 {17|25}, j9 {12|19}, r21 {9|19}, f15 {8|18}, s2 {11|25}, k5 {19|21}, h5 {18|25}, t9 {13|22}, k22 {8|21}, u7 {5|16}, f24 {22|23}, v18 {15|20}, w14 {11|20}, x18 {5|25}, n7 {18|22}, y21 {15|24}, y25 {2|24}.

Naked-pair {7|10} in cells {l14, n14} contained within {col14, box13}, updating cells {k11, m11, m12, n11, u14, w14}:

Naked-pair {11|20} in cells {u14, w14} contained within {col14, box23}, updating cells {l14, n14, u12, u15, v11, v12, w12, w15, x15, y15}:

Naked-pair {18|25} in cells {g5, g15, h5} contained within {rowg, col5, box6}, updating cells {f3, h4, i2, i4, k5, o5, r5, s5, t5, v5}:

backtrack.grid9482 → grid9483: e22 guess 1 ∈ {1|17}

pending={e22}

deduce.grid9483: naked-singles

deduce.grid9483: hidden-singles

deduce.grid9483.rows. s8 is 3 by hidden-single.

pending={s8}

deduce.grid9483: naked-singles

deduce.grid9483: hidden-singles

deduce.grid9483.rowt. t5 is 12 by hidden-single.

pending={t5}

deduce.grid9483: naked-singles

deduce.grid9483: hidden-singles

deduce.grid9483.col25. u25 is 17 by hidden-single.

pending={u25}

deduce.grid9483: naked-singles

deduce.grid9483: hidden-singles

deduce.grid9483.col21. o21 is 17 by hidden-single.

pending={o21}

deduce.grid9483: naked-singles

deduce.grid9483: hidden-singles

deduce.grid9483.col21. u21 is 25 by hidden-single.

pending={u21}

deduce.grid9483: naked-singles

deduce.grid9483: hidden-singles

deduce.grid9483.box25. v21 is 10 by hidden-single.

pending={v21}

deduce.grid9483: naked-singles

deduce.grid9483: hidden-singles

deduce.grid9483.col21. y21 is 15 by hidden-single.

pending={y21}

deduce.grid9483: naked-singles

deduce.grid9483: hidden-singles

deduce.grid9483: naked-pairs

two's heap=t11 {2|5}, l25 {2|7}, n14 {7|10}, l21 {8|9}, l14 {7|10}, i6 {6|15}, q9 {13|18}, f3 {15|17}, r7 {5|11}, j25 {7|12}, y10 {2|21}, o4 {13|21}, o17 {1|16}, p17 {1|24}, j9 {12|19}, r21 {9|19}, s5 {5|19}, l4 {2|18}, u9 {8|13}, u14 {11|20}, f15 {8|18}, n11 {8|21}, i4 {17|21}, g15 {18|25}, i8 {6|25}, i11 {17|25}, p16 {11|18}, h5 {18|25}, p21 {8|24}, f23 {7|23}, q8 {5|21}, h8 {8|25}, i2 {15|21}, s2 {11|25}, k5 {19|21}, f24 {22|23}, t9 {13|22}, k22 {8|21}, u7 {5|16}, g5 {18|25}, v18 {15|20}, w14 {11|20}, x18 {5|25}, n7 {18|22}, y25 {2|24}.

Naked-pair {7|10} in cells {l14, n14} contained within {col14, box13}, updating cells {k11, m11, m12, n11, u14, w14}:

Naked-pair {11|20} in cells {u14, w14} contained within {col14, box23}, updating cells {l14, n14, u12, u15, v11, v12, w12, w15, x15, y15}:

Naked-pair {18|25} in cells {g5, g15, h5} contained within {rowg, col5, box6}, updating cells {f3, i2, i4, k5, o5, r5, s5, v5}:

backtrack.grid9483 → grid9484: f3 guess 15 ∈ {15|17}

pending={f3}

deduce.grid9484: naked-singles

grid9484 didn't work: naked-singles ran out of candidates.

…backtrack.grid9483 again

backtrack.grid9483 → grid9485: f3 guess 17 ∈ {15|17}

pending={f3}

deduce.grid9485: naked-singles

deduce.grid9485: hidden-singles

deduce.grid9485.rowh. h5 is 25 by hidden-single.

pending={h5}

deduce.grid9485: naked-singles

deduce.grid9485: hidden-singles

deduce.grid9485.rowv. v1 is 17 by hidden-single.

pending={v1}

deduce.grid9485: naked-singles

deduce.grid9485: hidden-singles

deduce.grid9485.rowm. m4 is 17 by hidden-single.

pending={m4}

deduce.grid9485: naked-singles

deduce.grid9485: hidden-singles

deduce.grid9485.col3. k3 is 15 by hidden-single.

pending={k3}

deduce.grid9485: naked-singles

deduce.grid9485: hidden-singles

deduce.grid9485.rowk. k2 is 2 by hidden-single.

pending={k2}

deduce.grid9485: naked-singles

deduce.grid9485: hidden-singles

deduce.grid9485.rowk. k1 is 24 by hidden-single.

pending={k1}

deduce.grid9485: naked-singles

deduce.grid9485: hidden-singles

deduce.grid9485.rowk. k9 is 22 by hidden-single.

pending={k9}

deduce.grid9485: naked-singles

deduce.grid9485: hidden-singles

deduce.grid9485.rowm. m1 is 20 by hidden-single.

pending={m1}

deduce.grid9485: naked-singles

deduce.grid9485: hidden-singles

deduce.grid9485.rowm. m22 is 10 by hidden-single.

pending={m22}

deduce.grid9485: naked-singles

deduce.grid9485: hidden-singles

deduce.grid9485.rowl. l14 is 10 by hidden-single.

pending={l14}

deduce.grid9485: naked-singles

deduce.grid9485: hidden-singles

deduce.grid9485.rowo. o20 is 25 by hidden-single.

deduce.grid9485.rowo. o23 is 19 by hidden-single.

pending={o20, o23}

deduce.grid9485: naked-singles

deduce.grid9485: hidden-singles

deduce.grid9485.rowo. o3 is 7 by hidden-single.

pending={o3}

deduce.grid9485: naked-singles

deduce.grid9485: hidden-singles

deduce.grid9485.rows. s18 is 19 by hidden-single.

pending={s18}

deduce.grid9485: naked-singles

deduce.grid9485: hidden-singles

deduce.grid9485.rows. s16 is 20 by hidden-single.

pending={s16}

deduce.grid9485: naked-singles

deduce.grid9485: hidden-singles

deduce.grid9485.rowu. u2 is 24 by hidden-single.

pending={u2}

deduce.grid9485: naked-singles

deduce.grid9485: hidden-singles

deduce.grid9485.rowv. v18 is 20 by hidden-single.

pending={v18}

deduce.grid9485: naked-singles

deduce.grid9485: hidden-singles

deduce.grid9485.rowv. v17 is 15 by hidden-single.

pending={v17}

deduce.grid9485: naked-singles

deduce.grid9485: hidden-singles

deduce.grid9485.rowt. t18 is 15 by hidden-single.

pending={t18}

deduce.grid9485: naked-singles

deduce.grid9485: hidden-singles

deduce.grid9485.rowv. v8 is 22 by hidden-single.

pending={v8}

deduce.grid9485: naked-singles

deduce.grid9485: hidden-singles

deduce.grid9485.roww. w15 is 18 by hidden-single.

pending={w15}

deduce.grid9485: naked-singles

deduce.grid9485: hidden-singles

deduce.grid9485.rowp. p16 is 18 by hidden-single.

pending={p16}

deduce.grid9485: naked-singles

deduce.grid9485: hidden-singles

deduce.grid9485.rowr. r11 is 25 by hidden-single.

pending={r11}

deduce.grid9485: naked-singles

deduce.grid9485: hidden-singles

deduce.grid9485.rowu. u3 is 18 by hidden-single.

pending={u3}

deduce.grid9485: naked-singles

deduce.grid9485: hidden-singles

deduce.grid9485.rowu. u1 is 10 by hidden-single.

pending={u1}

deduce.grid9485: naked-singles

deduce.grid9485: hidden-singles

deduce.grid9485.rowy. y1 is 22 by hidden-single.

deduce.grid9485.rowy. y25 is 24 by hidden-single.

pending={y1, y25}

deduce.grid9485: naked-singles

deduce.grid9485: hidden-singles

deduce.grid9485.rown. n4 is 22 by hidden-single.

pending={n4}

deduce.grid9485: naked-singles

deduce.grid9485: hidden-singles

deduce.grid9485.rown. n3 is 5 by hidden-single.

pending={n3}

deduce.grid9485: naked-singles

deduce.grid9485: hidden-singles

deduce.grid9485.rown. n2 is 10 by hidden-single.

pending={n2}

deduce.grid9485: naked-singles

deduce.grid9485: hidden-singles

deduce.grid9485.rowq. q3 is 10 by hidden-single.

pending={q3}

deduce.grid9485: naked-singles

deduce.grid9485: hidden-singles

deduce.grid9485.rowx. x17 is 22 by hidden-single.

pending={x17}

deduce.grid9485: naked-singles

deduce.grid9485: hidden-singles

deduce.grid9485.col1. t1 is 6 by hidden-single.

pending={t1}

deduce.grid9485: naked-singles

deduce.grid9485: hidden-singles

deduce.grid9485.rowp. p21 is 24 by hidden-single.

pending={p21}

deduce.grid9485: naked-singles

deduce.grid9485: hidden-singles

deduce.grid9485.rowr. r20 is 6 by hidden-single.

pending={r20}

deduce.grid9485: naked-singles

deduce.grid9485: hidden-singles

deduce.grid9485.rowr. r15 is 4 by hidden-single.

pending={r15}

deduce.grid9485: naked-singles

deduce.grid9485: hidden-singles

deduce.grid9485.rowp. p20 is 4 by hidden-single.

pending={p20}

deduce.grid9485: naked-singles

deduce.grid9485: hidden-singles

deduce.grid9485.rowr. r4 is 16 by hidden-single.

pending={r4}

deduce.grid9485: naked-singles

deduce.grid9485: hidden-singles

deduce.grid9485.rowr. r8 is 20 by hidden-single.

pending={r8}

deduce.grid9485: naked-singles

deduce.grid9485: hidden-singles

deduce.grid9485.rowt. t4 is 20 by hidden-single.

pending={t4}

deduce.grid9485: naked-singles

deduce.grid9485: hidden-singles

deduce.grid9485.rowt. t3 is 2 by hidden-single.

pending={t3}

deduce.grid9485: naked-singles

deduce.grid9485: hidden-singles

deduce.grid9485.rowt. t21 is 19 by hidden-single.

pending={t21}

deduce.grid9485: naked-singles

deduce.grid9485: hidden-singles

deduce.grid9485.rowr. r3 is 19 by hidden-single.

pending={r3}

deduce.grid9485: naked-singles

deduce.grid9485: hidden-singles

deduce.grid9485.roww. w20 is 24 by hidden-single.

pending={w20}

deduce.grid9485: naked-singles

deduce.grid9485: hidden-singles

deduce.grid9485.rowx. x3 is 6 by hidden-single.

pending={x3}

deduce.grid9485: naked-singles

deduce.grid9485: hidden-singles

deduce.grid9485.rowv. v24 is 6 by hidden-single.

pending={v24}

deduce.grid9485: naked-singles

deduce.grid9485: hidden-singles

deduce.grid9485.rowx. x2 is 8 by hidden-single.

deduce.grid9485.rowx. x19 is 11 by hidden-single.

pending={x2, x19}

deduce.grid9485: naked-singles

deduce.grid9485: hidden-singles

deduce.grid9485.rowx. x7 is 16 by hidden-single.

pending={x7}

deduce.grid9485: naked-singles

deduce.grid9485: hidden-singles

deduce.grid9485: naked-pairs

two's heap=f12 {7|12}, f25 {7|12}, j12 {7|12}, j25 {7|12}, o2 {1|21}, o5 {1|21}, v2 {1|21}, v5 {1|21}, w4 {5|25}, w18 {5|25}, x4 {5|25}, x18 {5|25}.

Naked-pair {1|21} in cells {o2, o5, v2, v5} contained within {rowo, rowv, col2, col5, box11, box21}, updating cells {w4, x4}:

Naked-pair {5|25} in cells {w4, w18, x4, x18} contained within {roww, rowx, col4, col18, box21, box24}, updating cells {v2, v5}:

backtrack.grid9485 → grid9486: f12 guess 7 ∈ {7|12}

pending={f12}

deduce.grid9486: naked-singles

deduce.grid9486: hidden-singles

deduce.grid9486: naked-pairs

two's heap=o2 {1|21}, o5 {1|21}, v2 {1|21}, v5 {1|21}, w4 {5|25}, w18 {5|25}, x4 {5|25}, x18 {5|25}.

Naked-pair {1|21} in cells {o2, o5, v2, v5} contained within {rowo, rowv, col2, col5, box11, box21}, updating cells {w4, x4}:

Naked-pair {5|25} in cells {w4, w18, x4, x18} contained within {roww, rowx, col4, col18, box21, box24}, updating cells {v2, v5}:

backtrack.grid9486 → grid9487: o2 guess 1 ∈ {1|21}

pending={o2}

deduce.grid9487: naked-singles

deduce.grid9487: hidden-singles

deduce.grid9487: naked-pairs

two's heap=w4 {5|25}, w18 {5|25}, x4 {5|25}, x18 {5|25}.

backtrack.grid9487 → grid9488: w4 guess 5 ∈ {5|25}

pending={w4}

deduce.grid9488: naked-singles

deduce.grid9488. Solved.

grid9488. Copying solution to raw grid.

>500 suppressed.