16x16 tough.txt

Order 4: digits 16; houses 48, cells 256.

Grid.grid1: initial copying

pending={a1, a2, a3, a6, a10, a12, a13, a16, b3, b4, b5, b6, b7, b8, b9, b10, b12, c2, c4, c7, c8, c11, c13, d6, d9, d10, d12, d16, e3, e4, e9, e13, e15, f6, f8, f13, f15, f16, g1, g5, g8, g9, g12, g14, h2, h4, h7, h8, h9, h10, h13, h14, i2, i3, i5, i8, i16, j2, j7, j9, j11, j12, k1, k4, k5, k7, k9, k10, k14, l1, l2, l3, l5, l14, l15, m4, m5, m6, m7, m11, m14, m15, n1, n3, n10, n14, o2, o3, o7, o10, o12, o14, p2, p5, p6, p16}

deduce.grid1: naked-singles

a7 is 1 by naked-single. pending={a7}

deduce.grid1: hidden-singles

deduce.grid1.rowb. b11 is 6 by hidden-single.

pending={b11}

deduce.grid1: naked-singles

deduce.grid1: hidden-singles

deduce.grid1.rowb. b2 is 12 by hidden-single.

pending={b2}

deduce.grid1: naked-singles

deduce.grid1: hidden-singles

deduce.grid1.rowc. c1 is 13 by hidden-single.

pending={c1}

deduce.grid1: naked-singles

deduce.grid1: hidden-singles

deduce.grid1.rowh. h1 is 10 by hidden-single.

pending={h1}

deduce.grid1: naked-singles

deduce.grid1: hidden-singles

deduce.grid1.rowj. j10 is 12 by hidden-single.

pending={j10}

deduce.grid1: naked-singles

c10 is 14 by naked-single. pending={c10}

deduce.grid1: hidden-singles

deduce.grid1.rowc. c9 is 12 by hidden-single.

pending={c9}

deduce.grid1: naked-singles

deduce.grid1: hidden-singles

deduce.grid1.rowe. e11 is 12 by hidden-single.

pending={e11}

deduce.grid1: naked-singles

deduce.grid1: hidden-singles

deduce.grid1.rowf. f3 is 12 by hidden-single.

pending={f3}

deduce.grid1: naked-singles

deduce.grid1: hidden-singles

deduce.grid1.rowi. i7 is 12 by hidden-single.

pending={i7}

deduce.grid1: naked-singles

deduce.grid1: hidden-singles

deduce.grid1.rowl. l16 is 11 by hidden-single.

pending={l16}

deduce.grid1: naked-singles

deduce.grid1: hidden-singles

deduce.grid1.rowm. m10 is 10 by hidden-single.

pending={m10}

deduce.grid1: naked-singles

deduce.grid1: hidden-singles

deduce.grid1.col2. d2 is 10 by hidden-single.

pending={d2}

deduce.grid1: naked-singles

deduce.grid1: hidden-singles

deduce.grid1.col3. h3 is 9 by hidden-single.

pending={h3}

deduce.grid1: naked-singles

deduce.grid1: hidden-singles

deduce.grid1.rowh. h12 is 15 by hidden-single.

deduce.grid1.rowh. h15 is 14 by hidden-single.

pending={h12, h15}

deduce.grid1: naked-singles

deduce.grid1: hidden-singles

deduce.grid1.rowe. e1 is 14 by hidden-single.

pending={e1}

deduce.grid1: naked-singles

deduce.grid1: hidden-singles

deduce.grid1.col3. j3 is 15 by hidden-single.

pending={j3}

deduce.grid1: naked-singles

deduce.grid1: hidden-singles

deduce.grid1.box6. g6 is 11 by hidden-single.

pending={g6}

deduce.grid1: naked-singles

c6 is 4 by naked-single. pending={c6}

deduce.grid1: hidden-singles

deduce.grid1.box9. i1 is 5 by hidden-single.

pending={i1}

deduce.grid1: naked-singles

deduce.grid1: hidden-singles

deduce.grid1: naked-pairs

two's heap=c12 {1|2}, d7 {3|6}, h6 {2|7}, a8 {5|11}, a9 {7|9}, h5 {5|7}, c5 {5|10}, b1 {1|15}, d5 {3|16}, b15 {15|16}, g2 {2|16}, c3 {1|11}, a5 {5|10}, h16 {5|13}.

Naked-pair {5|10} in cells {a5, c5} contained within {col5, box2}, updating cells {a8, d5, d7, d8, e5, f5, h5, j5, n5, o5}:

a8: {5|11} → {11}. Solved.
e5: {1|3|4|5|9} → {1|3|4|9}.
f5: {1|3|4|5|7|9} → {1|3|4|7|9}.
h5: {5|7} → {7}. Solved.

pending={a8, h5}

deduce.grid1: naked-singles

h6 is 2 by naked-single. pending={h6}
h11 is 13 by naked-single. pending={h11}
h16 is 5 by naked-single. pending={h16}

deduce.grid1: hidden-singles

deduce.grid1.rowf. f2 is 5 by hidden-single.

pending={f2}

deduce.grid1: naked-singles

deduce.grid1: hidden-singles

deduce.grid1.rowe. e8 is 5 by hidden-single.

pending={e8}

deduce.grid1: naked-singles

deduce.grid1: hidden-singles

deduce.grid1.col2. n2 is 15 by hidden-single.

pending={n2}

deduce.grid1: naked-singles

deduce.grid1: hidden-singles

deduce.grid1.rown. n12 is 11 by hidden-single.

pending={n12}

deduce.grid1: naked-singles

deduce.grid1: hidden-singles

deduce.grid1.rowf. f10 is 11 by hidden-single.

pending={f10}

deduce.grid1: naked-singles

deduce.grid1: hidden-singles

deduce.grid1.col2. k2 is 11 by hidden-single.

pending={k2}

deduce.grid1: naked-singles

deduce.grid1: hidden-singles

deduce.grid1.col2. m2 is 13 by hidden-single.

pending={m2}

deduce.grid1: naked-singles

deduce.grid1: hidden-singles

deduce.grid1.box10. k8 is 2 by hidden-single.

pending={k8}

deduce.grid1: naked-singles

deduce.grid1: hidden-singles

deduce.grid1.rowk. k6 is 9 by hidden-single.

pending={k6}

deduce.grid1: naked-singles

deduce.grid1: hidden-singles

deduce.grid1.rowe. e5 is 9 by hidden-single.

pending={e5}

deduce.grid1: naked-singles

deduce.grid1: hidden-singles

deduce.grid1: naked-pairs

two's heap=c12 {1|2}, d7 {3|6}, o1 {4|8}, a5 {5|10}, c3 {1|11}, a9 {7|9}, c5 {5|10}, b15 {15|16}, d5 {3|16}, e2 {2|16}, g2 {2|16}, b1 {1|15}, o6 {1|15}.

Naked-pair {5|10} in cells {a5, c5} contained within {col5, box2}, updating cells {d5, d7, d8, f5, j5, n5, o5}:

Naked-pair {2|16} in cells {e2, g2} contained within {col2, box5}, updating cells {f1, f4, g3, g4}:

f1: {1|4|15|16} → {1|4|15}.
g3: {1|4|16} → {1|4}.
g4: {1|2|3|4} → {1|3|4}.

grid1

	2
		7

		15


5
	10


		7
9

	2
		7
9

	2
		7

		15


5
9	10
		15

1


		15

1	3
	7

		16

1
		7

		15




		15	16

1	3
	7

		16

1

		11


5
	10

1	2

1	2
		8


5			8
	10	11

1	2

	10

1	2

		11

1
		7
		11
	14

1	2
		7

	14

		3


			16

		3
	6

	3
6

		16

1	2
		7
9

1	2	3	4
		7
9
			16

1	2		4
		7

		4

9	11
		16

	2


			16

1		3
	6

	3	4
6		8

	3
6

		16

2	3
6		8

1		4
	6

1		4
	6

		16

1		4


	15

1	3	4


	15

1	3	4

	3	4
6


	6	7
9
			16


	7
9
		16

		3
	6	7

1		4
	6

	2


			16

1			4

1	3	4

	3	4
6		8

	3
6

		16

	2
			8

			16

1			4

			12
			16

		4
	6
		12
13		16

1		4
	6

13		16

1

	10
13

1
	6	7

		15	16

1
	6	7

13	14		16


	6	7

13			16

1
		7
	10
	14		16

1
	6	7

2
	7

14		16

	2
	6	7

13	14	15


	6
	10
13		15	16

1			4


			16

1		4

	10
13

1	3


13		16

1		3
	6	7

			16

1		3
	6

			16

		3	4
		7	8

			16

			4
	6	7	8

13

		4
	6	8
	10
13		16

		3	4
	6	7
	10
13			16

1			4


			16

1		4
	7	8

		16

1		4
	7	8

			4
		7	8

			16

			4
			8

13			16

		4
	7

13		16

		4

	10
13

	3
6

	15	16

		3
	6

13

	3
6

	15	16


	6

13	14	16


	6

13		16

		4
5
	10
	14	16

		4
5	6

	3	4


14		16

	2		4
			8

			16

			4


	14		16

1
			8

			16

1
	6	8

	14	16

1		4
	6	8

1	2	4
		8

	14

1	2	4
	6

2		4
6	7

14

1	3	4


13		16

1	3


		16

	2	3	4
			8

13	14

1	3
		8

		16

1
	6	7	8

13	14		16

1			4
		7	8

	14		16

1	2		4
		7	8

	14

		4
	6	8

13

1	2		4
	6	7

13

			4
			8

		4
6	7

14

1			4


13

1


		15

1
		8
9
	15

1
	6	7	8

13	14

1			4
5		7	8

	14

1			4
5		7	8
9
	14

		4
5	6	8
9
13

1			4
	6	7

13

2		4
		8
	11
		16

		4
	7
	11
14		16

2		4
	7

14

	2	3	4
			8

13	14

	3
		8
9
		16


		7	8

13	14		16

	3
	7

13		16

			4
5		7	8

	14		16

	3	4
5	7	8

	2		4
5		7	8
9			12
	14

	2		4
		7	8

13	14

			4
5			8
9			12
13

backtrack.grid1 → grid2: a5 guess 5 ∈ {5|10}

pending={a5}

deduce.grid2: naked-singles

c5 is 10 by naked-single. pending={c5}

deduce.grid2: hidden-singles

deduce.grid2.rowa. a15 is 10 by hidden-single.

pending={a15}

deduce.grid2: naked-singles

deduce.grid2: hidden-singles

deduce.grid2.rowc. c15 is 5 by hidden-single.

pending={c15}

deduce.grid2: naked-singles

deduce.grid2: hidden-singles

deduce.grid2.rowc. c3 is 11 by hidden-single.

deduce.grid2.rowc. c14 is 8 by hidden-single.

pending={c3, c14}

deduce.grid2: naked-singles

deduce.grid2: hidden-singles

deduce.grid2.rowd. d15 is 11 by hidden-single.

pending={d15}

deduce.grid2: naked-singles

deduce.grid2: hidden-singles

deduce.grid2.rowp. p1 is 11 by hidden-single.

pending={p1}

deduce.grid2: naked-singles

deduce.grid2: hidden-singles

deduce.grid2.col16. j16 is 10 by hidden-single.

pending={j16}

deduce.grid2: naked-singles

deduce.grid2: hidden-singles

deduce.grid2.col16. b16 is 3 by hidden-single.

pending={b16}

deduce.grid2: naked-singles

deduce.grid2: hidden-singles

deduce.grid2.box4. d13 is 9 by hidden-single.

pending={d13}

deduce.grid2: naked-singles

deduce.grid2: hidden-singles

deduce.grid2.rowd. d14 is 4 by hidden-single.

pending={d14}

deduce.grid2: naked-singles

deduce.grid2: hidden-singles

deduce.grid2: naked-pairs

two's heap=c12 {1|2}, c16 {1|2}, d1 {1|2}, d7 {3|6}, e14 {1|6}, g3 {1|4}, o1 {4|8}, b1 {1|15}, e2 {2|16}, a9 {7|9}, f14 {1|6}, b15 {15|16}, g2 {2|16}, d5 {3|16}, o6 {1|15}.

Naked-pair {1|6} in cells {e14, f14} contained within {col14, box8}, updating cells {a14, b14, e16, g13, g15, g16, i14, j14, p14}:

b14: {1|7|15} → {7|15}.
e16: {1|4|6|16} → {4|16}.
g13: {1|4|12|16} → {4|12|16}.
g15: {4|6|12|13|16} → {4|12|13|16}.
g16: {1|4|6|13|16} → {4|13|16}.
i14: {2|6|7|13|14|15} → {2|7|13|14|15}.
j14: {6|7|13} → {7|13}.

Naked-pair {2|16} in cells {e2, g2} contained within {col2, box5}, updating cells {f1, f4, g3, g4}:

grid2

	2
		7

		15


		7
9

	2
		7
9

	2
		7

		15

1


		15

1
	7

		16


		7

		15




		15	16

1	2

1	2

1	2

1
		7

	14

1	2
		7

	14

		3


			16

		3
	6

	3
6

		16

1	2
		7

	2


			16

1		3
	6

	3	4
6		8

	3
6

		16

2	3
6		8

1
	6

			4


			16

1		4


	15

1	3	4


	15

1	3	4

	3	4
6


	6	7
9
			16


	7
9
		16

		3
	6	7

1
	6

	2


			16

1			4

1	3	4

	3	4
6		8

	3
6

		16

	2
			8

			16

			4

			12
			16

			4

			12
13			16

			4


13			16

1

	10
13

1
	6	7

		15	16

1
	6	7

13	14		16


	6	7

13			16

1
		7
	10
	14		16

1
	6	7

2
	7

14		16

	2
		7

13	14	15


	6

13		15	16

1			4


			16

1			4


13

1	3


13		16

1		3
	6	7

			16

1		3
	6

			16

		3	4
		7	8

			16


		7

13

		4
	6	8

13		16

1			4


			16

1		4
	7	8

		16

1		4
	7	8

			4
		7	8

			16

			4
			8

13			16

		4
	7

13		16

		4

	10
13

	3
6

	15	16

		3
	6

13

	3
6

	15	16


	6

13	14	16


	6

13		16

		4
5
	10
	14	16

		4
5	6

	3	4


14		16

	2		4
			8

			16

			4


	14		16

1
			8

			16

1
	6	8

	14	16

1		4
	6	8

1	2	4
		8

	14

1	2	4
	6

2		4
6	7

14

1	3	4


13		16

1	3


		16

	2	3	4
			8

13	14

1	3
		8

		16

1
	6	7	8

13	14		16

1			4
		7	8

	14		16

1	2		4
		7	8

	14

		4
	6	8

13

1	2		4
	6	7

13

			4
			8

		4
6	7

14

1			4


13

1


		15

1
		8
9
	15

1
	6	7	8

13	14

1			4
5		7	8

	14

1			4
5		7	8

	14

		4
	6	8
9
13

1			4
	6	7

13

		4
	7

14		16

2		4
	7

14

	2	3	4
			8

13	14

	3
		8
9
		16


		7	8

13	14		16

	3
	7

13		16

			4
5		7	8

	14		16

	3	4
5	7	8

	2		4
5		7	8
			12
	14

	2
		7

13	14

			4
			8
9			12
13

backtrack.grid2 → grid3: a9 guess 7 ∈ {7|9}

pending={a9}

deduce.grid3: naked-singles

deduce.grid3: hidden-singles

deduce.grid3.rowa. a11 is 9 by hidden-single.

pending={a11}

deduce.grid3: naked-singles

deduce.grid3: hidden-singles

deduce.grid3.rowf. f9 is 9 by hidden-single.

pending={f9}

deduce.grid3: naked-singles

deduce.grid3: hidden-singles

deduce.grid3.rowf. f11 is 16 by hidden-single.

pending={f11}

deduce.grid3: naked-singles

deduce.grid3: hidden-singles

deduce.grid3.rowf. f12 is 7 by hidden-single.

pending={f12}

deduce.grid3: naked-singles

deduce.grid3: hidden-singles

deduce.grid3: naked-pairs

two's heap=c12 {1|2}, d1 {1|2}, c16 {1|2}, g3 {1|4}, d11 {1|2}, e10 {3|6}, e14 {1|6}, a14 {2|15}, f14 {1|6}, i12 {1|6}, d7 {3|6}, o6 {1|15}, a4 {2|15}, b1 {1|15}, e16 {4|16}, b14 {7|15}, g2 {2|16}, d5 {3|16}, g10 {3|6}, b15 {15|16}, g11 {2|8}, j14 {7|13}, o1 {4|8}, e2 {2|16}.

Naked-pair {1|2} in cells {c12, c16, d1, d11} contained within {rowc, rowd, box3}, updating cells {d3, d4, d5, d7, d8}:

d3: {1|7|14} → {7|14}.
d4: {1|2|7|14} → {7|14}.

Naked-pair {1|6} in cells {e14, f14, i12} contained within {col14, box8}, updating cells {a14, b14, e16, g13, g15, g16, i14, j14, p14}:

Naked-pair {3|6} in cells {d7, e10, g10} contained within {col10, box7}, updating cells {e12, g11, i10, l10, p10}:

e12: {2|3|6|8} → {2|8}.
i10: {6|7|13|16} → {7|13|16}.
l10: {6|13|16} → {13|16}.
p10: {3|7|13|16} → {7|13|16}.

Naked-pair {2|16} in cells {e2, g2} contained within {col2, box5}, updating cells {f1, f4, g3, g4}:

grid3

	2


		15

	2


		15

1


		15

1
	7

		16


		7

		15




		15	16

1	2

1	2

1	2


		7

	14


		7

	14

		3


			16

		3
	6

	3
6

		16

1	2

	2


			16

1		3
	6

	3	4
6		8

		3
	6

	2
			8

1
	6

			4


			16

1		4


	15

1	3	4


	15

1	3	4

	3	4
6

1
	6

	2


			16

1			4

1	3	4

	3	4
6		8

		3
	6

	2
			8

			4

			12
			16

			4

			12
13			16

			4


13			16

1

	10
13

1
	6	7

		15	16

1
	6

13	14	16


	7

13		16

1
		7
	10
	14

1
	6

2
	7

14		16

	2
		7

13	14	15


	6

13		15	16

1			4


			16

1			4


13

1	3


13		16

1		3
	6	7

			16

1		3
	6

			16

		3	4
		7	8

			16


		7

13

		4
	6	8

13		16

1			4


			16

1		4
	7	8

1			4
			8

			4
		7	8

			16

			4
			8

13			16

		4
	7

13		16

		4

	10
13

	3
6

	15	16

		3
	6

13

	3
6

	15	16


	6

13	14	16




13			16

		4
5
	10
	14

		4
5	6

	3	4


14		16

	2		4
			8

			16

			4


	14		16

1
			8

			16

1
	6	8

	14	16

1		4
	6	8

1	2	4
		8

	14

1	2	4
	6

2		4
6	7

14

1	3	4


13		16

1	3


		16

	2	3	4
			8

13	14

1	3
		8

		16

1
	6	8

13	14	16

1			4
		7	8

	14

1	2		4
		7	8

	14

		4
	6	8

13

1	2		4
	6	7

13

			4
			8

		4
6	7

14

1			4


13

1


		15

1
		8
9
	15

1
	6	8

13	14

1			4
5		7	8

	14

1			4
5		7	8

	14

		4
	6	8
9
13

1			4
	6	7

13

		4
	7

14		16

2		4
	7

14

	2	3	4
			8

13	14

	3
		8
9
		16


		8

13	14	16


	7

13		16

			4
5		7	8

	14

	3	4
5		8

	2		4
5		7	8
			12
	14

	2
		7

13	14

			4
			8
9			12
13

backtrack.grid3 → grid4: a4 guess 2 ∈ {2|15}

pending={a4}

deduce.grid4: naked-singles

a14 is 15 by naked-single. pending={a14}
b14 is 7 by naked-single. pending={b14}
b15 is 16 by naked-single. pending={b15}
b13 is 1 by naked-single. pending={b13}
b1 is 15 by naked-single. pending={b1}
c16 is 2 by naked-single. pending={c16}
c12 is 1 by naked-single. pending={c12}
d1 is 1 by naked-single. pending={d1}
d11 is 2 by naked-single. pending={d11}
f1 is 4 by naked-single. pending={f1}
g3 is 1 by naked-single. pending={g3}
g4 is 3 by naked-single. pending={g4}
f4 is 15 by naked-single. pending={f4}
g10 is 6 by naked-single. pending={g10}
e10 is 3 by naked-single. pending={e10}
g11 is 8 by naked-single. pending={g11}
e12 is 2 by naked-single. pending={e12}
e2 is 16 by naked-single. pending={e2}
e16 is 4 by naked-single. pending={e16}
g2 is 2 by naked-single. pending={g2}
g7 is 4 by naked-single. pending={g7}
i12 is 6 by naked-single. pending={i12}
j1 is 16 by naked-single. pending={j1}
j14 is 13 by naked-single. pending={j14}
i15 is 15 by naked-single. pending={i15}
k3 is 4 by naked-single. pending={k3}
j4 is 1 by naked-single. pending={j4}
j5 is 3 by naked-single. pending={j5}
d5 is 16 by naked-single. pending={d5}
f5 is 1 by naked-single. pending={f5}
e6 is 6 by naked-single. pending={e6}
e7 is 8 by naked-single. pending={e7}
e14 is 1 by naked-single. pending={e14}
f7 is 3 by naked-single. pending={f7}
d7 is 6 by naked-single. pending={d7}
d8 is 3 by naked-single. pending={d8}
f14 is 6 by naked-single. pending={f14}
j6 is 7 by naked-single. pending={j6}
j8 is 6 by naked-single. pending={j8}
k12 is 8 by naked-single. pending={k12}

grid4 didn't work: naked-singles ran out of candidates.

…backtrack.grid3 again

backtrack.grid3 → grid5: a4 guess 15 ∈ {2|15}

pending={a4}

deduce.grid5: naked-singles

a14 is 2 by naked-single. pending={a14}
b1 is 1 by naked-single. pending={b1}
c16 is 1 by naked-single. pending={c16}
c12 is 2 by naked-single. pending={c12}
d1 is 2 by naked-single. pending={d1}
d11 is 1 by naked-single. pending={d11}
e12 is 8 by naked-single. pending={e12}
g11 is 2 by naked-single. pending={g11}
g2 is 16 by naked-single. pending={g2}
e2 is 2 by naked-single. pending={e2}

deduce.grid5: hidden-singles

deduce.grid5.rowe. e16 is 16 by hidden-single.

pending={e16}

deduce.grid5: naked-singles

deduce.grid5: hidden-singles

deduce.grid5.rowe. e7 is 4 by hidden-single.

pending={e7}

deduce.grid5: naked-singles

deduce.grid5: hidden-singles

deduce.grid5.rowf. f1 is 15 by hidden-single.

pending={f1}

deduce.grid5: naked-singles

deduce.grid5: hidden-singles

deduce.grid5.rowf. f4 is 4 by hidden-single.

pending={f4}

deduce.grid5: naked-singles

g3 is 1 by naked-single. pending={g3}
g4 is 3 by naked-single. pending={g4}
g10 is 6 by naked-single. pending={g10}
e10 is 3 by naked-single. pending={e10}
g7 is 8 by naked-single. pending={g7}

deduce.grid5: hidden-singles

deduce.grid5.rowi. i13 is 2 by hidden-single.

pending={i13}

deduce.grid5: naked-singles

deduce.grid5: hidden-singles

deduce.grid5.rowk. k12 is 1 by hidden-single.

pending={k12}

deduce.grid5: naked-singles

i12 is 6 by naked-single. pending={i12}
m12 is 4 by naked-single. pending={m12}
l12 is 5 by naked-single. pending={l12}
p12 is 3 by naked-single. pending={p12}

deduce.grid5: hidden-singles

deduce.grid5.rowm. m16 is 2 by hidden-single.

pending={m16}

deduce.grid5: naked-singles

deduce.grid5: hidden-singles

deduce.grid5.rowm. m9 is 6 by hidden-single.

pending={m9}

deduce.grid5: naked-singles

deduce.grid5: hidden-singles

deduce.grid5.box11. k11 is 8 by hidden-single.

pending={k11}

deduce.grid5: naked-singles

deduce.grid5: hidden-singles

deduce.grid5.col11. l11 is 4 by hidden-single.

pending={l11}

deduce.grid5: naked-singles

deduce.grid5: hidden-singles

deduce.grid5.rowl. l4 is 10 by hidden-single.

pending={l4}

deduce.grid5: naked-singles

deduce.grid5: hidden-singles

deduce.grid5.rowi. i11 is 10 by hidden-single.

pending={i11}

deduce.grid5: naked-singles

deduce.grid5: hidden-singles

deduce.grid5.box11. i10 is 7 by hidden-single.

pending={i10}

deduce.grid5: naked-singles

deduce.grid5: hidden-singles

deduce.grid5.col6. j6 is 7 by hidden-single.

pending={j6}

deduce.grid5: naked-singles

j14 is 13 by naked-single. pending={j14}
j4 is 1 by naked-single. pending={j4}
i4 is 13 by naked-single. pending={i4}

deduce.grid5: hidden-singles

deduce.grid5.rowi. i6 is 1 by hidden-single.

pending={i6}

deduce.grid5: naked-singles

e6 is 6 by naked-single. pending={e6}
e14 is 1 by naked-single. pending={e14}
f7 is 3 by naked-single. pending={f7}
d7 is 6 by naked-single. pending={d7}
f5 is 1 by naked-single. pending={f5}
f14 is 6 by naked-single. pending={f14}
l7 is 13 by naked-single. pending={l7}
l10 is 16 by naked-single. pending={l10}
i9 is 14 by naked-single. pending={i9}
i14 is 15 by naked-single. pending={i14}
b14 is 7 by naked-single. pending={b14}
b13 is 16 by naked-single. pending={b13}
b15 is 15 by naked-single. pending={b15}
i15 is 16 by naked-single. pending={i15}
k15 is 4 by naked-single. pending={k15}
k3 is 16 by naked-single. pending={k3}
j1 is 4 by naked-single. pending={j1}
k13 is 7 by naked-single. pending={k13}

grid5 didn't work: naked-singles ran out of candidates.

…backtrack.grid3 again

grid3 didn't work: exhaustive search revealed no solution.

…backtrack.grid2 again

backtrack.grid2 → grid6: a9 guess 9 ∈ {7|9}

pending={a9}

deduce.grid6: naked-singles

deduce.grid6: hidden-singles

deduce.grid6.rowf. f11 is 9 by hidden-single.

pending={f11}

deduce.grid6: naked-singles

deduce.grid6: hidden-singles

deduce.grid6.rowf. f9 is 16 by hidden-single.

pending={f9}

deduce.grid6: naked-singles

deduce.grid6: hidden-singles

deduce.grid6.rowf. f12 is 7 by hidden-single.

pending={f12}

deduce.grid6: naked-singles

deduce.grid6: hidden-singles

deduce.grid6: naked-pairs

two's heap=c12 {1|2}, g3 {1|4}, c16 {1|2}, i12 {1|6}, e10 {3|6}, e14 {1|6}, d1 {1|2}, g10 {3|6}, d7 {3|6}, o1 {4|8}, b1 {1|15}, b14 {7|15}, e16 {4|16}, f14 {1|6}, g2 {2|16}, b15 {15|16}, a11 {2|7}, d5 {3|16}, g11 {2|8}, e2 {2|16}, j14 {7|13}, o6 {1|15}.

Naked-pair {1|6} in cells {e14, f14, i12} contained within {col14, box8}, updating cells {a14, b14, e16, g13, g15, g16, i14, j14, p14}:

Naked-pair {3|6} in cells {d7, e10, g10} contained within {col10, box7}, updating cells {e12, g11, i10, l10, p10}:

e12: {2|3|6|8} → {2|8}.
i10: {6|7|13|16} → {7|13|16}.
l10: {6|13|16} → {13|16}.
p10: {3|7|13|16} → {7|13|16}.

Naked-pair {2|16} in cells {e2, g2} contained within {col2, box5}, updating cells {f1, f4, g3, g4}:

grid6

	2
		7

		15

	2
		7

	2
		7

		15

1


		15

1
	7

		16


		7

		15




		15	16

1	2

1	2

1	2

1
		7

	14

1	2
		7

	14

		3


			16

		3
	6

	3
6

		16

1	2
		7

	2


			16

1		3
	6

	3	4
6		8

		3
	6

	2
			8

1
	6

			4


			16

1		4


	15

1	3	4


	15

1	3	4

	3	4
6

1
	6

	2


			16

1			4

1	3	4

	3	4
6		8

		3
	6

	2
			8

			4

			12
			16

			4

			12
13			16

			4


13			16

1

	10
13

1
	6	7

		15	16

1
	6	7

13	14


	7

13		16

1
		7
	10
	14		16

1
	6

2
	7

14		16

	2
		7

13	14	15


	6

13		15	16

1			4


			16

1			4


13

1	3


13		16

1		3
	6	7

			16

1		3
	6

			16

		3	4
		7	8

			16


		7

13

		4
	6	8

13		16

1			4


			16

1		4
	7	8

		16

1			4
			8

			4
		7	8

			16

			4
			8

13			16

		4
	7

13		16

		4

	10
13

	3
6

	15	16

		3
	6

13

	3
6

	15	16


	6

13	14




13			16

		4
5
	10
	14	16

		4
5	6

	3	4


14		16

	2		4
			8

			16

			4


	14		16

1
			8

			16

1
	6	8

	14

1		4
	6	8

1	2	4
		8

	14

1	2	4
	6

2		4
6	7

14

1	3	4


13		16

1	3


		16

	2	3	4
			8

13	14

1	3
		8

		16

1
	6	7	8

13	14

1			4
		7	8

	14		16

1	2		4
		7	8

	14

		4
	6	8

13

1	2		4
	6	7

13

			4
			8

		4
6	7

14

1			4


13

1


		15

1
		8
9
	15

1
	6	7	8

13	14

1			4
5		7	8

	14

1			4
5		7	8

	14

		4
	6	8
9
13

1			4
	6	7

13

		4
	7

14		16

2		4
	7

14

	2	3	4
			8

13	14

	3
		8
9
		16


		7	8

13	14


	7

13		16

			4
5		7	8

	14		16

	3	4
5		8

	2		4
5		7	8
			12
	14

	2
		7

13	14

			4
			8
9			12
13

backtrack.grid6 → grid7: a11 guess 2 ∈ {2|7}

pending={a11}

deduce.grid7: naked-singles

c12 is 1 by naked-single. pending={c12}
c16 is 2 by naked-single. pending={c16}
d11 is 7 by naked-single. pending={d11}
g11 is 8 by naked-single. pending={g11}
e12 is 2 by naked-single. pending={e12}
e2 is 16 by naked-single. pending={e2}
e16 is 4 by naked-single. pending={e16}
g2 is 2 by naked-single. pending={g2}
i12 is 6 by naked-single. pending={i12}

deduce.grid7: hidden-singles

deduce.grid7.rowe. e7 is 8 by hidden-single.

pending={e7}

deduce.grid7: naked-singles

deduce.grid7: hidden-singles

deduce.grid7.col3. p3 is 7 by hidden-single.

pending={p3}

deduce.grid7: naked-singles

deduce.grid7: hidden-singles

deduce.grid7.col4. a4 is 7 by hidden-single.

pending={a4}

deduce.grid7: naked-singles

a14 is 15 by naked-single. pending={a14}
b14 is 7 by naked-single. pending={b14}
b15 is 16 by naked-single. pending={b15}
b13 is 1 by naked-single. pending={b13}
b1 is 15 by naked-single. pending={b1}
j14 is 13 by naked-single. pending={j14}
i15 is 15 by naked-single. pending={i15}

deduce.grid7: hidden-singles

deduce.grid7.rowf. f4 is 15 by hidden-single.

pending={f4}

deduce.grid7: naked-singles

deduce.grid7: hidden-singles

grid7 didn't work: rowk is not bijective.

…backtrack.grid6 again

backtrack.grid6 → grid8: a11 guess 7 ∈ {2|7}

pending={a11}

deduce.grid8: naked-singles

deduce.grid8: hidden-singles

deduce.grid8.col12. p12 is 3 by hidden-single.

pending={p12}

deduce.grid8: naked-singles

deduce.grid8: hidden-singles

deduce.grid8.col12. l12 is 5 by hidden-single.

pending={l12}

deduce.grid8: naked-singles

deduce.grid8: hidden-singles

deduce.grid8: naked-pairs

two's heap=c12 {1|2}, d1 {1|2}, c16 {1|2}, g3 {1|4}, d11 {1|2}, e10 {3|6}, e14 {1|6}, a14 {2|15}, f14 {1|6}, g10 {3|6}, i12 {1|6}, o1 {4|8}, o6 {1|15}, b1 {1|15}, e12 {2|8}, e16 {4|16}, b14 {7|15}, d5 {3|16}, g2 {2|16}, b15 {15|16}, g11 {2|8}, d7 {3|6}, j14 {7|13}, l10 {13|16}, e2 {2|16}, a4 {2|15}.

Naked-pair {1|2} in cells {c12, c16, d1, d11} contained within {rowc, rowd, box3}, updating cells {d3, d4, d5, d7, d8}:

d3: {1|7|14} → {7|14}.
d4: {1|2|7|14} → {7|14}.

Naked-pair {1|6} in cells {e14, f14, i12} contained within {col14, box8}, updating cells {a14, b14, e16, g13, g15, g16, i14, j14, p14}:

Naked-pair {3|6} in cells {d7, e10, g10} contained within {col10, box7}, updating cells {e12, g11, i10, l10, p10}:

Naked-pair {2|8} in cells {e12, g11} contained within {box7}, updating cells {e10, g10}:

Naked-pair {2|16} in cells {e2, g2} contained within {col2, box5}, updating cells {f1, f4, g3, g4}:

grid8

	2


		15

	2


		15

1


		15

1
	7

		16


		7

		15




		15	16

1	2

1	2

1	2


		7

	14


		7

	14

		3


			16

		3
	6

	3
6

		16

1	2

	2


			16

1		3
	6

	3	4
6		8

		3
	6

	2
			8

1
	6

			4


			16

1		4


	15

1	3	4


	15

1	3	4

	3	4
6

1
	6

	2


			16

1			4

1	3	4

	3	4
6		8

		3
	6

	2
			8

			4

			12
			16

			4

			12
13			16

			4


13			16

1

	10
13

1
	6	7

		15	16

1
	6	7

13	14


	7

13		16

1

	10
	14	16

1
	6

2
	7

14		16

	2
		7

13	14	15


	6

13		15	16

1			4


			16

1			4


13

1	3


13		16

1		3
	6	7

			16

1		3
	6

			16

		3	4
		7	8

			16


		7

13

		4
	6	8

13		16

1			4


			16

1			4
			8

			16

1			4
			8

			4
		7	8

			16

			4
			8

13			16

		4
	7

13		16

		4

	10
13

	3
6

	15	16

		3
	6

13

	3
6

	15	16


	6

13	14




13			16

			4

	10
	14		16

	3	4


14		16

	2		4
			8

			16

			4


	14		16

1
			8

			16

1
	6	8

	14

1		4
	6	8

1	2	4
		8

	14

1	2	4
	6

2		4
6	7

14

1	3	4


13		16

1	3


		16

	2	3	4
			8

13	14

1	3
		8

		16

1
	6	7	8

13	14

1		4
		8

	14	16

1	2		4
		7	8

	14

		4
	6	8

13

1	2		4
	6	7

13

			4
			8

		4
6	7

14

1			4


13

1


		15

1
		8
9
	15

1
	6	7	8

13	14

1		4
5		8

	14

1			4
5		7	8

	14

		4
	6	8
9
13

1			4
	6	7

13

		4
	7

14		16

2		4
	7

14

	2	4
		8

13	14


			8
9
			16


		7	8

13	14


	7

13		16

		4
5		8

	14	16

	2		4
5		7	8
			12
	14

	2
		7

13	14

			4
			8
9			12
13

backtrack.grid8 → grid9: a4 guess 2 ∈ {2|15}

pending={a4}

deduce.grid9: naked-singles

a14 is 15 by naked-single. pending={a14}
b14 is 7 by naked-single. pending={b14}
b15 is 16 by naked-single. pending={b15}
b13 is 1 by naked-single. pending={b13}
b1 is 15 by naked-single. pending={b1}
c16 is 2 by naked-single. pending={c16}
c12 is 1 by naked-single. pending={c12}
d1 is 1 by naked-single. pending={d1}
d11 is 2 by naked-single. pending={d11}
f1 is 4 by naked-single. pending={f1}
g3 is 1 by naked-single. pending={g3}
g4 is 3 by naked-single. pending={g4}
f4 is 15 by naked-single. pending={f4}
g10 is 6 by naked-single. pending={g10}
e10 is 3 by naked-single. pending={e10}
g11 is 8 by naked-single. pending={g11}
e12 is 2 by naked-single. pending={e12}
e2 is 16 by naked-single. pending={e2}
e16 is 4 by naked-single. pending={e16}
g2 is 2 by naked-single. pending={g2}
g7 is 4 by naked-single. pending={g7}
i12 is 6 by naked-single. pending={i12}
j1 is 16 by naked-single. pending={j1}
j14 is 13 by naked-single. pending={j14}
i15 is 15 by naked-single. pending={i15}
k3 is 4 by naked-single. pending={k3}
j4 is 1 by naked-single. pending={j4}
j5 is 3 by naked-single. pending={j5}
d5 is 16 by naked-single. pending={d5}
f5 is 1 by naked-single. pending={f5}
e6 is 6 by naked-single. pending={e6}
e7 is 8 by naked-single. pending={e7}
e14 is 1 by naked-single. pending={e14}
f7 is 3 by naked-single. pending={f7}
d7 is 6 by naked-single. pending={d7}
d8 is 3 by naked-single. pending={d8}
f14 is 6 by naked-single. pending={f14}
j6 is 7 by naked-single. pending={j6}
j8 is 6 by naked-single. pending={j8}
k12 is 8 by naked-single. pending={k12}

grid9 didn't work: naked-singles ran out of candidates.

…backtrack.grid8 again

backtrack.grid8 → grid10: a4 guess 15 ∈ {2|15}

pending={a4}

deduce.grid10: naked-singles

a14 is 2 by naked-single. pending={a14}
b1 is 1 by naked-single. pending={b1}
c16 is 1 by naked-single. pending={c16}
c12 is 2 by naked-single. pending={c12}
d1 is 2 by naked-single. pending={d1}
d11 is 1 by naked-single. pending={d11}
e12 is 8 by naked-single. pending={e12}
g11 is 2 by naked-single. pending={g11}
g2 is 16 by naked-single. pending={g2}
e2 is 2 by naked-single. pending={e2}

deduce.grid10: hidden-singles

deduce.grid10.rowe. e16 is 16 by hidden-single.

pending={e16}

deduce.grid10: naked-singles

deduce.grid10: hidden-singles

deduce.grid10.rowe. e7 is 4 by hidden-single.

pending={e7}

deduce.grid10: naked-singles

deduce.grid10: hidden-singles

deduce.grid10.rowf. f1 is 15 by hidden-single.

pending={f1}

deduce.grid10: naked-singles

deduce.grid10: hidden-singles

deduce.grid10.rowf. f4 is 4 by hidden-single.

pending={f4}

deduce.grid10: naked-singles

g3 is 1 by naked-single. pending={g3}
g4 is 3 by naked-single. pending={g4}
g10 is 6 by naked-single. pending={g10}
e10 is 3 by naked-single. pending={e10}
g7 is 8 by naked-single. pending={g7}

deduce.grid10: hidden-singles

deduce.grid10.rowi. i13 is 2 by hidden-single.

pending={i13}

deduce.grid10: naked-singles

deduce.grid10: hidden-singles

deduce.grid10.rowk. k12 is 1 by hidden-single.

pending={k12}

deduce.grid10: naked-singles

i12 is 6 by naked-single. pending={i12}
m12 is 4 by naked-single. pending={m12}

deduce.grid10: hidden-singles

deduce.grid10.rowm. m16 is 2 by hidden-single.

pending={m16}

deduce.grid10: naked-singles

deduce.grid10: hidden-singles

deduce.grid10.rowm. m9 is 6 by hidden-single.

pending={m9}

deduce.grid10: naked-singles

deduce.grid10: hidden-singles

deduce.grid10.box11. k11 is 8 by hidden-single.

pending={k11}

deduce.grid10: naked-singles

deduce.grid10: hidden-singles

deduce.grid10.col11. l11 is 4 by hidden-single.

pending={l11}

deduce.grid10: naked-singles

deduce.grid10: hidden-singles

deduce.grid10.rowl. l4 is 10 by hidden-single.

pending={l4}

deduce.grid10: naked-singles

deduce.grid10: hidden-singles

deduce.grid10.rowi. i11 is 10 by hidden-single.

pending={i11}

deduce.grid10: naked-singles

deduce.grid10: hidden-singles

deduce.grid10.box12. j15 is 6 by hidden-single.

pending={j15}

deduce.grid10: naked-singles

deduce.grid10: hidden-singles

deduce.grid10.rowj. j13 is 8 by hidden-single.

pending={j13}

deduce.grid10: naked-singles

deduce.grid10: hidden-singles

deduce.grid10.rowj. j1 is 4 by hidden-single.

pending={j1}

deduce.grid10: naked-singles

k3 is 16 by naked-single. pending={k3}
m3 is 14 by naked-single. pending={m3}
d3 is 7 by naked-single. pending={d3}
d4 is 14 by naked-single. pending={d4}
m13 is 1 by naked-single. pending={m13}
o1 is 8 by naked-single. pending={o1}
m1 is 16 by naked-single. pending={m1}
m8 is 8 by naked-single. pending={m8}
p3 is 4 by naked-single. pending={p3}

deduce.grid10: hidden-singles

deduce.grid10.col13. l13 is 3 by hidden-single.

pending={l13}

deduce.grid10: naked-singles

deduce.grid10: hidden-singles

deduce.grid10.rowl. l9 is 14 by hidden-single.

pending={l9}

deduce.grid10: naked-singles

deduce.grid10: hidden-singles

deduce.grid10.rowi. i14 is 14 by hidden-single.

pending={i14}

deduce.grid10: naked-singles

deduce.grid10: hidden-singles

deduce.grid10.col13. b13 is 16 by hidden-single.

pending={b13}

deduce.grid10: naked-singles

b15 is 15 by naked-single. pending={b15}
b14 is 7 by naked-single. pending={b14}
j14 is 13 by naked-single. pending={j14}
i15 is 16 by naked-single. pending={i15}
j4 is 1 by naked-single. pending={j4}
i4 is 13 by naked-single. pending={i4}
i9 is 7 by naked-single. pending={i9}

grid10 didn't work: naked-singles ran out of candidates.

…backtrack.grid8 again

grid8 didn't work: exhaustive search revealed no solution.

…backtrack.grid6 again

grid6 didn't work: exhaustive search revealed no solution.

…backtrack.grid2 again

grid2 didn't work: exhaustive search revealed no solution.

…backtrack.grid1 again

backtrack.grid1 → grid11: a5 guess 10 ∈ {5|10}

pending={a5}

deduce.grid11: naked-singles

c5 is 5 by naked-single. pending={c5}

deduce.grid11: hidden-singles

deduce.grid11.rowa. a15 is 5 by hidden-single.

pending={a15}

deduce.grid11: naked-singles

deduce.grid11: hidden-singles

deduce.grid11: naked-pairs

two's heap=c12 {1|2}, g3 {1|4}, d7 {3|6}, b1 {1|15}, o1 {4|8}, o6 {1|15}, d5 {3|16}, e2 {2|16}, g2 {2|16}, c3 {1|11}, a9 {7|9}, b15 {15|16}.

Naked-pair {2|16} in cells {e2, g2} contained within {col2, box5}, updating cells {f1, f4, g3, g4}:

grid11

	2
		7

		15


		7
9

	2
		7
9

	2
		7

		15

1


		15

1	3
	7

		16

1
		7

		15




		15	16

1	3
	7

		16

1

		11

1	2

1	2
		8


		8
10	11

1	2

	10

1	2

		11

1
		7
		11
	14

1	2
		7

	14

		3


			16

		3
	6

	3
6

		16

1	2
		7
9

1	2	3	4
		7
9
			16

1	2		4
		7

		4

9	11
		16

	2


			16

1		3
	6

	3	4
6		8

	3
6

		16

2	3
6		8

1		4
	6

1		4
	6

		16

1		4


	15

1	3	4


	15

1	3	4

	3	4
6


	6	7
9
			16


	7
9
		16

		3
	6	7

1		4
	6

	2


			16

1			4

1	3	4

	3	4
6		8

	3
6

		16

	2
			8

			16

1			4

			12
			16

		4
	6
		12
13		16

1		4
	6

13		16

1

	10
13

1
	6	7

		15	16

1
	6	7

13	14		16


	6	7

13			16

1
		7
	10
	14		16

1
	6	7

2
	7

14		16

	2
	6	7

13	14	15


	6
	10
13		15	16

1			4


			16

1		4

	10
13

1	3


13		16

1		3
	6	7

			16

1		3
	6

			16

		3	4
		7	8

			16

			4
	6	7	8

13

		4
	6	8
	10
13		16

		3	4
	6	7
	10
13			16

1			4


			16

1		4
	7	8

		16

1		4
	7	8

			4
		7	8

			16

			4
			8

13			16

		4
	7

13		16

		4

	10
13

	3
6

	15	16

		3
	6

13

	3
6

	15	16


	6

13	14	16


	6

13		16

		4
5
	10
	14	16

		4
5	6

	3	4


14		16

	2		4
			8

			16

			4


	14		16

1
			8

			16

1
	6	8

	14	16

1		4
	6	8

1	2	4
		8

	14

1	2	4
	6

2		4
6	7

14

1	3	4


13		16

1	3


		16

	2	3	4
			8

13	14

1	3
		8

		16

1
	6	7	8

13	14		16

1			4
		7	8

	14		16

1	2		4
		7	8

	14

		4
	6	8

13

1	2		4
	6	7

13

			4
			8

		4
6	7

14

1			4


13

1


		15

1
		8
9
	15

1
	6	7	8

13	14

1			4
5		7	8

	14

1			4
5		7	8
9
	14

		4
	6	8
9
13

1			4
	6	7

13

2		4
		8
	11
		16

		4
	7
	11
14		16

2		4
	7

14

	2	3	4
			8

13	14

	3
		8
9
		16


		7	8

13	14		16

	3
	7

13		16

			4
5		7	8

	14		16

	3	4
5	7	8

	2		4
5		7	8
9			12
	14

	2		4
		7	8

13	14

			4
			8
9			12
13

backtrack.grid11 → grid12: a9 guess 7 ∈ {7|9}

pending={a9}

deduce.grid12: naked-singles

deduce.grid12: hidden-singles

deduce.grid12.rowa. a11 is 9 by hidden-single.

pending={a11}

deduce.grid12: naked-singles

deduce.grid12: hidden-singles

deduce.grid12.rowf. f9 is 9 by hidden-single.

pending={f9}

deduce.grid12: naked-singles

deduce.grid12: hidden-singles

deduce.grid12.rowf. f11 is 16 by hidden-single.

pending={f11}

deduce.grid12: naked-singles

deduce.grid12: hidden-singles

deduce.grid12.rowf. f12 is 7 by hidden-single.

pending={f12}

deduce.grid12: naked-singles

deduce.grid12: hidden-singles

deduce.grid12: naked-pairs

two's heap=c12 {1|2}, d11 {1|2}, g3 {1|4}, i12 {1|6}, e10 {3|6}, c3 {1|11}, g10 {3|6}, d7 {3|6}, b1 {1|15}, e2 {2|16}, a14 {2|15}, g2 {2|16}, a4 {2|15}, d5 {3|16}, g11 {2|8}, b15 {15|16}, o1 {4|8}, o6 {1|15}.

Naked-pair {3|6} in cells {d7, e10, g10} contained within {col10, box7}, updating cells {e12, g11, i10, l10, p10}:

e12: {2|3|6|8} → {2|8}.
i10: {6|7|13|16} → {7|13|16}.
l10: {6|13|16} → {13|16}.
p10: {3|7|13|16} → {7|13|16}.

Naked-pair {2|16} in cells {e2, g2} contained within {col2, box5}, updating cells {f1, f4, g3, g4}:

grid12

	2


		15

	2


		15

1


		15

1	3
	7

		16

1
		7

		15




		15	16

1	3
	7

		16

1

		11

1	2

1	2
		8


		8
10	11

1	2

	10

1	2

		11

1
		7
		11
	14

1	2
		7

	14

		3


			16

		3
	6

	3
6

		16

1	2

1	2	3	4
		7
9
			16

1	2		4
		7

		4

9	11
		16

	2


			16

1		3
	6

	3	4
6		8

		3
	6

	2
			8

1		4
	6

1		4
	6

		16

1		4


	15

1	3	4


	15

1	3	4

	3	4
6

1		4
	6

	2


			16

1			4

1	3	4

	3	4
6		8

		3
	6

	2
			8

1			4

			12
			16

		4
	6
		12
13		16

1		4
	6

13		16

1

	10
13

1
	6	7

		15	16

1
	6

13	14	16


	7

13		16

1
		7
	10
	14

1
	6

2
	7

14		16

	2
	6	7

13	14	15


	6
	10
13		15	16

1			4


			16

1		4

	10
13

1	3


13		16

1		3
	6	7

			16

1		3
	6

			16

		3	4
		7	8

			16

			4
	6	7	8

13

		4
	6	8
	10
13		16

		3	4
	6	7
	10
13			16

1			4


			16

1		4
	7	8

1			4
			8

			4
		7	8

			16

			4
			8

13			16

		4
	7

13		16

		4

	10
13

	3
6

	15	16

		3
	6

13

	3
6

	15	16


	6

13	14	16




13			16

		4
5
	10
	14

		4
5	6

	3	4


14		16

	2		4
			8

			16

			4


	14		16

1
			8

			16

1
	6	8

	14	16

1		4
	6	8

1	2	4
		8

	14

1	2	4
	6

2		4
6	7

14

1	3	4


13		16

1	3


		16

	2	3	4
			8

13	14

1	3
		8

		16

1
	6	8

13	14	16

1			4
		7	8

	14

1	2		4
		7	8

	14

		4
	6	8

13

1	2		4
	6	7

13

			4
			8

		4
6	7

14

1			4


13

1


		15

1
		8
9
	15

1
	6	8

13	14

1			4
5		7	8

	14

1			4
5		7	8
9
	14

		4
	6	8
9
13

1			4
	6	7

13

2		4
		8
	11
		16

		4
	7
	11
14		16

2		4
	7

14

	2	3	4
			8

13	14

	3
		8
9
		16


		8

13	14	16


	7

13		16

			4
5		7	8

	14

	3	4
5		8

	2		4
5		7	8
9			12
	14

	2		4
		7	8

13	14

			4
			8
9			12
13

backtrack.grid12 → grid13: a4 guess 2 ∈ {2|15}

pending={a4}

deduce.grid13: naked-singles

a14 is 15 by naked-single. pending={a14}
b15 is 16 by naked-single. pending={b15}

deduce.grid13: hidden-singles

deduce.grid13.rowb. b1 is 15 by hidden-single.

pending={b1}

deduce.grid13: naked-singles

deduce.grid13: hidden-singles

deduce.grid13.rowf. f4 is 15 by hidden-single.

pending={f4}

deduce.grid13: naked-singles

deduce.grid13: hidden-singles

deduce.grid13.col4. g4 is 3 by hidden-single.

pending={g4}

deduce.grid13: naked-singles

g10 is 6 by naked-single. pending={g10}
e10 is 3 by naked-single. pending={e10}

deduce.grid13: hidden-singles

deduce.grid13.col12. p12 is 3 by hidden-single.

pending={p12}

deduce.grid13: naked-singles

deduce.grid13: hidden-singles

deduce.grid13.col12. l12 is 5 by hidden-single.

pending={l12}

deduce.grid13: naked-singles

deduce.grid13: hidden-singles

deduce.grid13.col15. i15 is 15 by hidden-single.

pending={i15}

deduce.grid13: naked-singles

deduce.grid13: hidden-singles

deduce.grid13: naked-pairs

two's heap=c12 {1|2}, f1 {1|4}, d11 {1|2}, i12 {1|6}, e6 {1|6}, g3 {1|4}, d7 {3|6}, c3 {1|11}, o1 {4|8}, d5 {3|16}, e12 {2|8}, g2 {2|16}, b14 {1|7}, g7 {4|8}, g11 {2|8}, e2 {2|16}, l10 {13|16}, d1 {1|11}, o6 {1|15}.

Naked-pair {1|4} in cells {f1, g3} contained within {box5}, updating cells {e2, g2}:

Naked-pair {1|11} in cells {c3, d1} contained within {box1}, updating cells {d3, d4}:

d3: {1|7|11|14} → {7|14}.
d4: {1|7|14} → {7|14}.

Naked-pair {2|16} in cells {e2, g2} contained within {col2, box5}, updating cells {f1, g3}:

grid13

1		3
		7

1
		7

1		3
		7

1

		11

1	2

1	2
		8


		8
10	11

1	2

	10

1

		11


		7

	14


		7

	14

		3


			16

		3
	6

	3
6

		16

1	2

1	2	3	4
		7
9

1	2		4
		7

		4

9	11

	2


			16

1
	6

			4
	6		8

	2
			8

1		4
	6

1		4
	6

		16

1			4

1	3	4

	3	4
6

1		4
	6

	2


			16

1			4

			4
			8

	2
			8

1			4

			12
			16

			4

			12
13

1			4


13			16

1

	10
13

1
	6	7

			16

1
	6

13	14	16


	7

13		16

1
		7
	10
	14

1
	6

2
	7

14		16

	2
	6	7

13	14

1			4


			16

1		4

	10
13

1	3


13		16

1		3
	6	7

			16

1		3
	6

			16

		3	4
		7	8

			16

			4
	6	7	8

13

		4
	6	8
	10
13

		3	4
	6	7
	10
13			16

1			4


			16

1		4
	7	8

1			4
			8

			4
		7	8

			16

			4
			8

13

		4
	7

13		16

		4

	10
13

	3
6

	15	16

		3
	6

13

	3
6

	15	16


	6

13	14	16




13			16

			4

	10
	14

	3	4


14		16

	2		4
			8

			16

			4


	14		16

1
			8

			16

1
	6	8

	14	16

1		4
	6	8

1	2	4
		8

	14

1	2	4
	6

		4
6	7

14

1	3	4


13		16

1	3


		16

	2	3	4
			8

13	14

1	3
		8

		16

1
	6	8

13	14	16

1			4
		7	8

	14

1	2		4
		7	8

	14

		4
	6	8

13

1	2		4
	6	7

13

			4
			8

		4
6	7

14

1			4


13

1


		15

1
		8
9
	15

1
	6	8

13	14

1			4
5		7	8

	14

1			4
5		7	8
9
	14

		4
	6	8
9
13

1			4
	6	7

13

2		4
		8
	11
		16

		4
	7
	11
14		16

		4
	7

14

	2	4
		8

13	14


			8
9
			16


		8

13	14	16


	7

13		16

			4
5		7	8

	14

	2		4
5		7	8
9			12
	14

	2		4
		7	8

13	14

			4
			8
9			12
13

backtrack.grid13 → grid14: b14 guess 1 ∈ {1|7}

pending={b14}

deduce.grid14: naked-singles

deduce.grid14: hidden-singles

deduce.grid14: naked-pairs

two's heap=c12 {1|2}, f1 {1|4}, d11 {1|2}, d7 {3|6}, g3 {1|4}, o1 {4|8}, e6 {1|6}, e14 {4|6}, f14 {4|6}, b13 {3|7}, i12 {1|6}, c16 {2|10}, o6 {1|15}, d1 {1|11}, e12 {2|8}, d3 {7|14}, b16 {3|7}, d4 {7|14}, g2 {2|16}, d5 {3|16}, g7 {4|8}, g11 {2|8}, c14 {2|8}, l10 {13|16}, c3 {1|11}, e2 {2|16}.

Naked-pair {1|4} in cells {f1, g3} contained within {box5}, updating cells {e2, g2}:

Naked-pair {4|6} in cells {e14, f14} contained within {col14, box8}, updating cells {c14, d14, e16, g13, g15, g16, i14, j14, p14}:

d14: {2|4|7} → {2|7}.
e16: {1|4|6|16} → {1|16}.
g13: {1|4|12|16} → {1|12|16}.
g15: {4|12|13} → {12|13}.
g16: {1|4|13|16} → {1|13|16}.
i14: {2|6|7|13|14} → {2|7|13|14}.
j14: {4|6|7|8|13} → {7|8|13}.
p14: {2|4|7|8|13|14} → {2|7|8|13|14}.

Naked-pair {3|7} in cells {b13, b16} contained within {rowb, box4}, updating cells {c14, c15, c16, d13, d14, d15}:

d13: {2|3|4|7|9} → {2|4|9}.
d14: {2|7} → {2}. Solved.

Naked-pair {1|11} in cells {c3, d1} contained within {box1}, updating cells {d3, d4}:

Naked-pair {7|14} in cells {d3, d4} contained within {rowd, box1}, updating cells {c3, d1, d5, d7, d8, d11, d13, d14, d15}:

Naked-pair {2|16} in cells {e2, g2} contained within {col2, box5}, updating cells {f1, g3}:

pending={d14}

deduce.grid14: naked-singles

c14 is 8 by naked-single. pending={c14}
c16 is 10 by naked-single. pending={c16}
c15 is 11 by naked-single. pending={c15}
c3 is 1 by naked-single. pending={c3}
c12 is 2 by naked-single. pending={c12}
d1 is 11 by naked-single. pending={d1}
d11 is 1 by naked-single. pending={d11}
e12 is 8 by naked-single. pending={e12}
g3 is 4 by naked-single. pending={g3}
f1 is 1 by naked-single. pending={f1}
g7 is 8 by naked-single. pending={g7}
g11 is 2 by naked-single. pending={g11}
g2 is 16 by naked-single. pending={g2}
e2 is 2 by naked-single. pending={e2}
k3 is 16 by naked-single. pending={k3}
j1 is 4 by naked-single. pending={j1}
m3 is 14 by naked-single. pending={m3}
d3 is 7 by naked-single. pending={d3}
d4 is 14 by naked-single. pending={d4}
o1 is 8 by naked-single. pending={o1}
p3 is 11 by naked-single. pending={p3}

deduce.grid14: hidden-singles

deduce.grid14.rowe. e16 is 16 by hidden-single.

pending={e16}

deduce.grid14: naked-singles

deduce.grid14: hidden-singles

deduce.grid14.rowe. e6 is 1 by hidden-single.

pending={e6}

deduce.grid14: naked-singles

o6 is 15 by naked-single. pending={o6}

deduce.grid14: hidden-singles

deduce.grid14.rowi. i13 is 2 by hidden-single.

pending={i13}

deduce.grid14: naked-singles

deduce.grid14: hidden-singles

deduce.grid14.rowk. k12 is 1 by hidden-single.

pending={k12}

deduce.grid14: naked-singles

i12 is 6 by naked-single. pending={i12}
m12 is 4 by naked-single. pending={m12}

deduce.grid14: hidden-singles

deduce.grid14.rowi. i4 is 1 by hidden-single.

pending={i4}

deduce.grid14: naked-singles

deduce.grid14: hidden-singles

deduce.grid14.rowi. i11 is 10 by hidden-single.

pending={i11}

deduce.grid14: naked-singles

deduce.grid14: hidden-singles

deduce.grid14.rowl. l4 is 10 by hidden-single.

deduce.grid14.rowl. l8 is 15 by hidden-single.

pending={l4, l8}

deduce.grid14: naked-singles

j4 is 13 by naked-single. pending={j4}
j14 is 7 by naked-single. pending={j14}

deduce.grid14: hidden-singles

deduce.grid14.rowj. j15 is 10 by hidden-single.

pending={j15}

deduce.grid14: naked-singles

deduce.grid14: hidden-singles

deduce.grid14.rowj. j13 is 8 by hidden-single.

pending={j13}

deduce.grid14: naked-singles

k13 is 4 by naked-single. pending={k13}
d13 is 9 by naked-single. pending={d13}
d15 is 4 by naked-single. pending={d15}
k15 is 13 by naked-single. pending={k15}
g15 is 12 by naked-single. pending={g15}
g13 is 1 by naked-single. pending={g13}
g16 is 13 by naked-single. pending={g16}
i14 is 14 by naked-single. pending={i14}

grid14 didn't work: naked-singles ran out of candidates.

…backtrack.grid13 again

backtrack.grid13 → grid15: b14 guess 7 ∈ {1|7}

pending={b14}

deduce.grid15: naked-singles

deduce.grid15: hidden-singles

deduce.grid15: naked-pairs

two's heap=c12 {1|2}, d11 {1|2}, f1 {1|4}, b16 {1|3}, b13 {1|3}, e12 {2|8}, e6 {1|6}, g3 {1|4}, i12 {1|6}, o1 {4|8}, o6 {1|15}, d3 {7|14}, c3 {1|11}, d4 {7|14}, g2 {2|16}, d5 {3|16}, g7 {4|8}, g11 {2|8}, d7 {3|6}, l10 {13|16}, d1 {1|11}, e2 {2|16}.

Naked-pair {1|3} in cells {b13, b16} contained within {rowb, box4}, updating cells {c14, c15, c16, d13, d14, d15}:

c14: {1|2|8} → {2|8}.
c16: {1|2|10} → {2|10}.
d13: {1|2|3|4|9} → {2|4|9}.
d14: {1|2|4} → {2|4}.

Naked-pair {1|4} in cells {f1, g3} contained within {box5}, updating cells {e2, g2}:

Naked-pair {1|11} in cells {c3, d1} contained within {box1}, updating cells {d3, d4}:

Naked-pair {7|14} in cells {d3, d4} contained within {rowd, box1}, updating cells {c3, d1, d5, d7, d8, d11, d13, d14, d15}:

Naked-pair {2|16} in cells {e2, g2} contained within {col2, box5}, updating cells {f1, g3}:

grid15

1		3

1		3

1

		11

1	2

	2
			8


		8
10	11

	2

	10

1

		11


		7

	14


		7

	14

		3


			16

		3
	6

	3
6

		16

1	2

	2	4

9

	2		4

		4

9	11

	2


			16

1
	6

			4
	6		8

	2
			8

1		4
	6

1		4
	6

		16

1			4

1	3	4

	3	4
6

1		4
	6

	2


			16

1			4

			4
			8

	2
			8

1			4

			12
			16

			4

			12
13

1			4


13			16

1

	10
13

1
	6	7

			16

1
	6

13	14	16


	7

13		16

1
		7
	10
	14

1
	6

2
	7

14		16

	2
	6

13	14

1			4


			16

1		4

	10
13

1	3


13		16

1		3
	6	7

			16

1		3
	6

			16

		3	4
		7	8

			16

		4
	6	8

13

		4
	6	8
	10
13

		3	4
	6	7
	10
13			16

1			4


			16

1		4
	7	8

1			4
			8

			4
		7	8

			16

			4
			8

13

		4
	7

13		16

		4

	10
13

	3
6

	15	16

		3
	6

13

	3
6

	15	16


	6

13	14	16




13			16

			4

	10
	14

	3	4


14		16

	2		4
			8

			16

			4


	14		16

1
			8

			16

1
	6	8

	14	16

1		4
	6	8

1	2	4
		8

	14

1	2	4
	6

		4
6	7

14

1	3	4


13		16

1	3


		16

	2	3	4
			8

13	14

1	3
		8

		16

1
	6	8

13	14	16

1			4
		7	8

	14

1	2		4
		7	8

	14

		4
	6	8

13

1	2		4
	6	7

13

			4
			8

		4
6	7

14

1			4


13

1


		15

1
		8
9
	15

1
	6	8

13	14

1			4
5		7	8

	14

1			4
5		7	8
9
	14

		4
	6	8
9
13

1			4
	6	7

13

2		4
		8
	11
		16

		4
	7
	11
14		16

		4
	7

14

	2	4
		8

13	14


			8
9
			16


		8

13	14	16


	7

13		16

			4
5		7	8

	14

	2		4
5		7	8
9			12
	14

	2	4
		8

13	14

			4
			8
9			12
13

backtrack.grid15 → grid16: b13 guess 1 ∈ {1|3}

pending={b13}

deduce.grid16: naked-singles

b16 is 3 by naked-single. pending={b16}

deduce.grid16: hidden-singles

deduce.grid16: naked-pairs

two's heap=c12 {1|2}, d11 {1|2}, f1 {1|4}, g3 {1|4}, d14 {2|4}, c14 {2|8}, e6 {1|6}, c16 {2|10}, g11 {2|8}, i12 {1|6}, d7 {3|6}, e2 {2|16}, d3 {7|14}, d4 {7|14}, e12 {2|8}, d5 {3|16}, g2 {2|16}, c3 {1|11}, g7 {4|8}, d1 {1|11}, l10 {13|16}, o1 {4|8}, o6 {1|15}.

Naked-pair {1|4} in cells {f1, g3} contained within {box5}, updating cells {e2, g2}:

Naked-pair {1|11} in cells {c3, d1} contained within {box1}, updating cells {d3, d4}:

Naked-pair {7|14} in cells {d3, d4} contained within {rowd, box1}, updating cells {c3, d1, d5, d7, d8, d11, d13, d14, d15}:

Naked-pair {2|16} in cells {e2, g2} contained within {col2, box5}, updating cells {f1, g3}:

grid16

1

		11

1	2

	2
			8


		8
10	11

	2

	10

1

		11


		7

	14


		7

	14

		3


			16

		3
	6

	3
6

		16

1	2

	2	4

9

	2		4

		4

9	11

	2


			16

1
	6

			4
	6		8

	2
			8

1		4
	6

1		4
	6

		16

1			4

1	3	4

	3	4
6

1		4
	6

	2


			16

1			4

			4
			8

	2
			8

			4

			12
			16

			4

			12
13

1			4


13			16

1

	10
13

1
	6	7

			16

1
	6

13	14	16


	7

13		16

1
		7
	10
	14

1
	6

2
	7

14		16

	2
	6

13	14

1			4


			16

1		4

	10
13

1	3


13		16

1		3
	6	7

			16

1		3
	6

			16

		3	4
		7	8

			16

		4
	6	8

13

		4
	6	8
	10
13

			4
	6	7
	10
13			16

1			4


			16

1		4
	7	8

1			4
			8

			4
		7	8

			16

			4
			8

13

		4
	7

13		16

		4

	10
13

	3
6

	15	16

		3
	6

13

	3
6

	15	16


	6

13	14	16




13			16

			4

	10
	14

	3	4


14		16

	2		4
			8

			16

			4


	14		16

1
			8

			16

1
	6	8

	14	16

1		4
	6	8

	2		4
			8

	14

1	2	4
	6

		4
6	7

14

1	3	4


13		16

1	3


		16

	2	3	4
			8

13	14

1	3
		8

		16

1
	6	8

13	14	16

1			4
		7	8

	14

2		4
	7	8

14

		4
	6	8

13

1	2		4
	6	7

13

			4
			8

		4
6	7

14

1			4


13

1


		15

1
		8
9
	15

1
	6	8

13	14

1			4
5		7	8

	14

			4
5		7	8
9
	14

		4
	6	8
9
13

1			4
	6	7

13

2		4
		8
	11
		16

		4
	7
	11
14		16

		4
	7

14

	2	4
		8

13	14


			8
9
			16


		8

13	14	16


	7

13		16

			4
5		7	8

	14

	2		4
5		7	8
9			12
	14

	2	4
		8

13	14

			4
			8
9			12
13

backtrack.grid16 → grid17: c3 guess 1 ∈ {1|11}

pending={c3}

deduce.grid17: naked-singles

c12 is 2 by naked-single. pending={c12}
c14 is 8 by naked-single. pending={c14}
c16 is 10 by naked-single. pending={c16}
c15 is 11 by naked-single. pending={c15}
d1 is 11 by naked-single. pending={d1}
d11 is 1 by naked-single. pending={d11}
e12 is 8 by naked-single. pending={e12}
g3 is 4 by naked-single. pending={g3}
f1 is 1 by naked-single. pending={f1}
g7 is 8 by naked-single. pending={g7}
g11 is 2 by naked-single. pending={g11}
g2 is 16 by naked-single. pending={g2}
e2 is 2 by naked-single. pending={e2}
g13 is 12 by naked-single. pending={g13}
g15 is 13 by naked-single. pending={g15}
g16 is 1 by naked-single. pending={g16}
k3 is 16 by naked-single. pending={k3}
j1 is 4 by naked-single. pending={j1}
m3 is 14 by naked-single. pending={m3}
d3 is 7 by naked-single. pending={d3}
d4 is 14 by naked-single. pending={d4}
o1 is 8 by naked-single. pending={o1}
p3 is 11 by naked-single. pending={p3}

deduce.grid17: hidden-singles

deduce.grid17.rowe. e6 is 1 by hidden-single.

deduce.grid17.rowe. e16 is 16 by hidden-single.

pending={e6, e16}

deduce.grid17: naked-singles

o6 is 15 by naked-single. pending={o6}

deduce.grid17: hidden-singles

deduce.grid17.rowk. k12 is 1 by hidden-single.

deduce.grid17.rowk. k16 is 13 by hidden-single.

pending={k12, k16}

deduce.grid17: naked-singles

i12 is 6 by naked-single. pending={i12}
j14 is 6 by naked-single. pending={j14}
e14 is 4 by naked-single. pending={e14}
d14 is 2 by naked-single. pending={d14}
e7 is 6 by naked-single. pending={e7}
d7 is 3 by naked-single. pending={d7}
d5 is 16 by naked-single. pending={d5}
d8 is 6 by naked-single. pending={d8}
f7 is 4 by naked-single. pending={f7}
f5 is 3 by naked-single. pending={f5}

grid17 didn't work: naked-singles ran out of candidates.

…backtrack.grid16 again

backtrack.grid16 → grid18: c3 guess 11 ∈ {1|11}

pending={c3}

deduce.grid18: naked-singles

d1 is 1 by naked-single. pending={d1}
d11 is 2 by naked-single. pending={d11}
c12 is 1 by naked-single. pending={c12}
d14 is 4 by naked-single. pending={d14}
d13 is 9 by naked-single. pending={d13}
d15 is 11 by naked-single. pending={d15}
f1 is 4 by naked-single. pending={f1}
g3 is 1 by naked-single. pending={g3}
g11 is 8 by naked-single. pending={g11}
e12 is 2 by naked-single. pending={e12}
e2 is 16 by naked-single. pending={e2}
g2 is 2 by naked-single. pending={g2}
g7 is 4 by naked-single. pending={g7}
i12 is 6 by naked-single. pending={i12}
j1 is 16 by naked-single. pending={j1}
k3 is 4 by naked-single. pending={k3}
k12 is 8 by naked-single. pending={k12}
k15 is 13 by naked-single. pending={k15}
g15 is 12 by naked-single. pending={g15}
g13 is 16 by naked-single. pending={g13}
g16 is 13 by naked-single. pending={g16}
k13 is 7 by naked-single. pending={k13}
k11 is 1 by naked-single. pending={k11}
k16 is 16 by naked-single. pending={k16}
m12 is 4 by naked-single. pending={m12}
o1 is 8 by naked-single. pending={o1}
m1 is 2 by naked-single. pending={m1}
p1 is 11 by naked-single. pending={p1}

deduce.grid18: hidden-singles

deduce.grid18.rowe. e7 is 8 by hidden-single.

deduce.grid18.rowe. e16 is 4 by hidden-single.

pending={e7, e16}

deduce.grid18: naked-singles

deduce.grid18: hidden-singles

deduce.grid18.rowj. j6 is 7 by hidden-single.

pending={j6}

deduce.grid18: naked-singles

deduce.grid18: hidden-singles

deduce.grid18.rowp. p13 is 12 by hidden-single.

pending={p13}

deduce.grid18: naked-singles

deduce.grid18: hidden-singles

deduce.grid18.rowp. p11 is 5 by hidden-single.

pending={p11}

deduce.grid18: naked-singles

deduce.grid18: hidden-singles

deduce.grid18.rowo. o13 is 5 by hidden-single.

pending={o13}

deduce.grid18: naked-singles

deduce.grid18: hidden-singles

deduce.grid18.col11. l11 is 4 by hidden-single.

pending={l11}

deduce.grid18: naked-singles

deduce.grid18: hidden-singles

deduce.grid18.rowl. l4 is 10 by hidden-single.

pending={l4}

deduce.grid18: naked-singles

deduce.grid18: hidden-singles

deduce.grid18.rowi. i11 is 10 by hidden-single.

pending={i11}

deduce.grid18: naked-singles

deduce.grid18: hidden-singles

deduce.grid18.rowi. i10 is 7 by hidden-single.

pending={i10}

deduce.grid18: naked-singles

deduce.grid18: hidden-singles

deduce.grid18.col14. p14 is 13 by hidden-single.

pending={p14}

deduce.grid18: naked-singles

p10 is 16 by naked-single. pending={p10}
l10 is 13 by naked-single. pending={l10}

deduce.grid18: hidden-singles

deduce.grid18.rowi. i4 is 13 by hidden-single.

pending={i4}

deduce.grid18: naked-singles

j4 is 1 by naked-single. pending={j4}

deduce.grid18: hidden-singles

deduce.grid18.rowi. i6 is 1 by hidden-single.

pending={i6}

deduce.grid18: naked-singles

e6 is 6 by naked-single. pending={e6}
e14 is 1 by naked-single. pending={e14}
f7 is 3 by naked-single. pending={f7}
d7 is 6 by naked-single. pending={d7}
f5 is 1 by naked-single. pending={f5}
f14 is 6 by naked-single. pending={f14}
j14 is 8 by naked-single. pending={j14}
c14 is 2 by naked-single. pending={c14}
c16 is 10 by naked-single. pending={c16}
c15 is 8 by naked-single. pending={c15}
i14 is 14 by naked-single. pending={i14}
i9 is 16 by naked-single. pending={i9}
i13 is 2 by naked-single. pending={i13}
j16 is 6 by naked-single. pending={j16}
j8 is 3 by naked-single. pending={j8}
d8 is 16 by naked-single. pending={d8}
d5 is 3 by naked-single. pending={d5}
j5 is 13 by naked-single. pending={j5}
j13 is 4 by naked-single. pending={j13}
j15 is 10 by naked-single. pending={j15}

grid18 didn't work: naked-singles ran out of candidates.

…backtrack.grid16 again

grid16 didn't work: exhaustive search revealed no solution.

…backtrack.grid15 again

backtrack.grid15 → grid19: b13 guess 3 ∈ {1|3}

pending={b13}

deduce.grid19: naked-singles

b16 is 1 by naked-single. pending={b16}

deduce.grid19: hidden-singles

deduce.grid19.col16. j16 is 3 by hidden-single.

pending={j16}

deduce.grid19: naked-singles

deduce.grid19: hidden-singles

deduce.grid19.col16. c16 is 10 by hidden-single.

pending={c16}

deduce.grid19: naked-singles

deduce.grid19: hidden-singles

deduce.grid19.col15. j15 is 10 by hidden-single.

pending={j15}

deduce.grid19: naked-singles

deduce.grid19: hidden-singles

deduce.grid19: naked-pairs

two's heap=c12 {1|2}, d11 {1|2}, f1 {1|4}, g3 {1|4}, d14 {2|4}, c14 {2|8}, e6 {1|6}, c3 {1|11}, g11 {2|8}, i12 {1|6}, d7 {3|6}, e2 {2|16}, d3 {7|14}, d4 {7|14}, e12 {2|8}, d5 {3|16}, g2 {2|16}, c15 {8|11}, g7 {4|8}, d1 {1|11}, l10 {13|16}, o1 {4|8}, o6 {1|15}.

Naked-pair {1|4} in cells {f1, g3} contained within {box5}, updating cells {e2, g2}:

Naked-pair {1|11} in cells {c3, d1} contained within {box1}, updating cells {d3, d4}:

Naked-pair {7|14} in cells {d3, d4} contained within {rowd, box1}, updating cells {c3, d1, d5, d7, d8, d11, d13, d14, d15}:

Naked-pair {2|16} in cells {e2, g2} contained within {col2, box5}, updating cells {f1, g3}:

grid19

1

		11

1	2

	2
			8


			8
		11

1

		11


		7

	14


		7

	14

		3


			16

		3
	6

	3
6

		16

1	2

	2	4

9

	2		4

		4

9	11

	2


			16

1
	6

			4
	6		8

	2
			8

1		4
	6

			4
	6

			16

1			4

1	3	4

	3	4
6

1		4
	6

	2


			16

1			4

			4
			8

	2
			8

1			4

			12
			16

			4

			12
13

			4


13			16

1

	10
13

1
	6	7

			16

1
	6

13	14	16


	7

13		16

1
		7
	10
	14

1
	6

2
	7

14		16

	2
	6

13	14

1			4


			16

1			4


13

1


13			16

1
	6	7

			16

1
	6

		16

			4
		7	8

			16

		4
	6	8

13

1			4


			16

1		4
	7	8

1			4
			8

			4
		7	8

			16

			4
			8

13

		4
	7

13		16

		4

	10
13

	3
6

	15	16

		3
	6

13

	3
6

	15	16


	6

13	14	16




13			16

			4

	10
	14

			4


	14		16

	2		4
			8

			16

			4


	14		16

1
			8

			16

1
	6	8

	14	16

1		4
	6	8

1	2	4
		8

	14

	2		4
	6

		4
6	7

14

1	3	4


13		16

1	3


		16

	2	3	4
			8

13	14

1	3
		8

		16

1
	6	8

13	14	16

1			4
		7	8

	14

1	2		4
		7	8

	14

		4
	6	8

13

	2		4
	6	7

13

			4
			8

		4
6	7

14

1			4


13

1


		15

1
		8
9
	15

1
	6	8

13	14

1			4
5		7	8

	14

1			4
5		7	8
9
	14

		4
	6	8
9
13

			4
	6	7

13

2		4
		8
	11
		16

		4
	7
	11
14		16

		4
	7

14

	2	4
		8

13	14


			8
9
			16


		8

13	14	16


	7

13		16

			4
5		7	8

	14

	2		4
5		7	8
9			12
	14

	2	4
		8

13	14

			4
			8
9			12
13

backtrack.grid19 → grid20: c3 guess 1 ∈ {1|11}

pending={c3}

deduce.grid20: naked-singles

c12 is 2 by naked-single. pending={c12}
c14 is 8 by naked-single. pending={c14}
c15 is 11 by naked-single. pending={c15}
d1 is 11 by naked-single. pending={d1}
d11 is 1 by naked-single. pending={d11}
e12 is 8 by naked-single. pending={e12}
g3 is 4 by naked-single. pending={g3}
f1 is 1 by naked-single. pending={f1}
g7 is 8 by naked-single. pending={g7}
g11 is 2 by naked-single. pending={g11}
g2 is 16 by naked-single. pending={g2}
e2 is 2 by naked-single. pending={e2}
g16 is 13 by naked-single. pending={g16}
g15 is 12 by naked-single. pending={g15}
g13 is 1 by naked-single. pending={g13}
k3 is 16 by naked-single. pending={k3}
j1 is 4 by naked-single. pending={j1}
m3 is 14 by naked-single. pending={m3}
d3 is 7 by naked-single. pending={d3}
d4 is 14 by naked-single. pending={d4}
o1 is 8 by naked-single. pending={o1}
p3 is 11 by naked-single. pending={p3}

deduce.grid20: hidden-singles

deduce.grid20.rowe. e6 is 1 by hidden-single.

deduce.grid20.rowe. e16 is 16 by hidden-single.

pending={e6, e16}

deduce.grid20: naked-singles

o6 is 15 by naked-single. pending={o6}

deduce.grid20: hidden-singles

deduce.grid20.rowj. j13 is 8 by hidden-single.

pending={j13}

deduce.grid20: naked-singles

deduce.grid20: hidden-singles

deduce.grid20.rowj. j6 is 7 by hidden-single.

pending={j6}

deduce.grid20: naked-singles

deduce.grid20: hidden-singles

deduce.grid20.rowk. k11 is 8 by hidden-single.

deduce.grid20.rowk. k12 is 1 by hidden-single.

deduce.grid20.rowk. k15 is 13 by hidden-single.

pending={k11, k12, k15}

deduce.grid20: naked-singles

i12 is 6 by naked-single. pending={i12}
i6 is 16 by naked-single. pending={i6}
j14 is 6 by naked-single. pending={j14}
e14 is 4 by naked-single. pending={e14}
d14 is 2 by naked-single. pending={d14}
e7 is 6 by naked-single. pending={e7}
d7 is 3 by naked-single. pending={d7}
d5 is 16 by naked-single. pending={d5}
d8 is 6 by naked-single. pending={d8}
f7 is 4 by naked-single. pending={f7}
f5 is 3 by naked-single. pending={f5}

grid20 didn't work: naked-singles ran out of candidates.

…backtrack.grid19 again

backtrack.grid19 → grid21: c3 guess 11 ∈ {1|11}

pending={c3}

deduce.grid21: naked-singles

c15 is 8 by naked-single. pending={c15}
c14 is 2 by naked-single. pending={c14}
c12 is 1 by naked-single. pending={c12}
d1 is 1 by naked-single. pending={d1}
d11 is 2 by naked-single. pending={d11}
d14 is 4 by naked-single. pending={d14}
d13 is 9 by naked-single. pending={d13}
d15 is 11 by naked-single. pending={d15}
f1 is 4 by naked-single. pending={f1}
g3 is 1 by naked-single. pending={g3}
g11 is 8 by naked-single. pending={g11}
e12 is 2 by naked-single. pending={e12}
e2 is 16 by naked-single. pending={e2}
g2 is 2 by naked-single. pending={g2}
g7 is 4 by naked-single. pending={g7}
i12 is 6 by naked-single. pending={i12}
j1 is 16 by naked-single. pending={j1}
k3 is 4 by naked-single. pending={k3}
k12 is 8 by naked-single. pending={k12}
k15 is 13 by naked-single. pending={k15}
g15 is 12 by naked-single. pending={g15}
g13 is 16 by naked-single. pending={g13}
g16 is 13 by naked-single. pending={g16}
i14 is 14 by naked-single. pending={i14}
k13 is 7 by naked-single. pending={k13}
i13 is 2 by naked-single. pending={i13}
k11 is 1 by naked-single. pending={k11}
k16 is 16 by naked-single. pending={k16}
l13 is 4 by naked-single. pending={l13}
j13 is 8 by naked-single. pending={j13}
j14 is 6 by naked-single. pending={j14}
e14 is 1 by naked-single. pending={e14}
e6 is 6 by naked-single. pending={e6}
e7 is 8 by naked-single. pending={e7}
e16 is 4 by naked-single. pending={e16}
f7 is 3 by naked-single. pending={f7}
d7 is 6 by naked-single. pending={d7}
f5 is 1 by naked-single. pending={f5}

grid21 didn't work: naked-singles ran out of candidates.

…backtrack.grid19 again

grid19 didn't work: exhaustive search revealed no solution.

…backtrack.grid15 again

grid15 didn't work: exhaustive search revealed no solution.

…backtrack.grid13 again

grid13 didn't work: exhaustive search revealed no solution.

…backtrack.grid12 again

backtrack.grid12 → grid22: a4 guess 15 ∈ {2|15}

pending={a4}

deduce.grid22: naked-singles

a14 is 2 by naked-single. pending={a14}
b1 is 1 by naked-single. pending={b1}
c3 is 11 by naked-single. pending={c3}
d1 is 2 by naked-single. pending={d1}
d11 is 1 by naked-single. pending={d11}
c12 is 2 by naked-single. pending={c12}
e12 is 8 by naked-single. pending={e12}
g11 is 2 by naked-single. pending={g11}
g2 is 16 by naked-single. pending={g2}
e2 is 2 by naked-single. pending={e2}

deduce.grid22: hidden-singles

deduce.grid22.rowd. d15 is 11 by hidden-single.

pending={d15}

deduce.grid22: naked-singles

deduce.grid22: hidden-singles

deduce.grid22.rowd. d13 is 9 by hidden-single.

pending={d13}

deduce.grid22: naked-singles

deduce.grid22: hidden-singles

deduce.grid22.rowd. d14 is 4 by hidden-single.

pending={d14}

deduce.grid22: naked-singles

deduce.grid22: hidden-singles

deduce.grid22.rowe. e16 is 16 by hidden-single.

pending={e16}

deduce.grid22: naked-singles

deduce.grid22: hidden-singles

deduce.grid22.rowe. e7 is 4 by hidden-single.

pending={e7}

deduce.grid22: naked-singles

deduce.grid22: hidden-singles

deduce.grid22.rowf. f1 is 15 by hidden-single.

pending={f1}

deduce.grid22: naked-singles

deduce.grid22: hidden-singles

deduce.grid22.rowf. f4 is 4 by hidden-single.

pending={f4}

deduce.grid22: naked-singles

g3 is 1 by naked-single. pending={g3}
g4 is 3 by naked-single. pending={g4}
g10 is 6 by naked-single. pending={g10}
e10 is 3 by naked-single. pending={e10}
g7 is 8 by naked-single. pending={g7}

deduce.grid22: hidden-singles

deduce.grid22.rowi. i13 is 2 by hidden-single.

pending={i13}

deduce.grid22: naked-singles

deduce.grid22: hidden-singles

deduce.grid22.rowk. k12 is 1 by hidden-single.

pending={k12}

deduce.grid22: naked-singles

i12 is 6 by naked-single. pending={i12}
m12 is 4 by naked-single. pending={m12}
l12 is 5 by naked-single. pending={l12}
p12 is 3 by naked-single. pending={p12}

deduce.grid22: hidden-singles

deduce.grid22.rowm. m16 is 2 by hidden-single.

pending={m16}

deduce.grid22: naked-singles

deduce.grid22: hidden-singles

deduce.grid22.rowm. m9 is 6 by hidden-single.

pending={m9}

deduce.grid22: naked-singles

deduce.grid22: hidden-singles

deduce.grid22.rowp. p1 is 11 by hidden-single.

pending={p1}

deduce.grid22: naked-singles

deduce.grid22: hidden-singles

deduce.grid22.box11. k11 is 8 by hidden-single.

pending={k11}

deduce.grid22: naked-singles

deduce.grid22: hidden-singles

deduce.grid22.col11. l11 is 4 by hidden-single.

pending={l11}

deduce.grid22: naked-singles

deduce.grid22: hidden-singles

deduce.grid22.rowl. l4 is 10 by hidden-single.

pending={l4}

deduce.grid22: naked-singles

deduce.grid22: hidden-singles

deduce.grid22.col11. i11 is 10 by hidden-single.

pending={i11}

deduce.grid22: naked-singles

deduce.grid22: hidden-singles

deduce.grid22.box11. i10 is 7 by hidden-single.

pending={i10}

deduce.grid22: naked-singles

deduce.grid22: hidden-singles

deduce.grid22.col6. j6 is 7 by hidden-single.

pending={j6}

deduce.grid22: naked-singles

deduce.grid22: hidden-singles

deduce.grid22: naked-pairs

two's heap=f5 {1|3}, d7 {3|6}, e6 {1|6}, g13 {4|12}, b16 {3|7}, e14 {1|6}, f14 {1|6}, g16 {4|13}, i4 {1|13}, c15 {8|10}, c14 {1|8}, n11 {7|14}, o1 {4|8}, d3 {7|14}, f7 {3|6}, b15 {15|16}, d4 {7|14}, d5 {3|16}, j1 {4|16}, j4 {1|13}, k3 {4|16}, l10 {13|16}, m1 {8|16}, m3 {14|16}, b14 {7|15}, c16 {1|10}, o6 {1|15}, p10 {13|16}.

Naked-pair {1|6} in cells {e6, e14, f14} contained within {rowe, col14, box8}, updating cells {b14, c14, g13, g15, g16, i14, j14, p14}:

c14: {1|8} → {8}. Solved.
j14: {6|8|13} → {8|13}.

Naked-pair {3|6} in cells {d7, f7} contained within {col7}, updating cells {l7, n7, p7}:

l7: {3|6|13} → {13}. Solved.
n7: {2|3|13|14} → {2|13|14}.

Naked-pair {1|13} in cells {i4, j4} contained within {col4, box9}, updating cells {d4, j1, k3, n4, o4, p4}:

Naked-pair {7|14} in cells {d3, d4, n11} contained within {rowd, box1}, updating cells {d5, d7, d8}:

Naked-pair {4|16} in cells {j1, k3} contained within {box9}, updating cells {i4, j4}:

pending={c14, l7}

deduce.grid22: naked-singles

c15 is 10 by naked-single. pending={c15}
c16 is 1 by naked-single. pending={c16}
j14 is 13 by naked-single. pending={j14}
j4 is 1 by naked-single. pending={j4}
i4 is 13 by naked-single. pending={i4}
l10 is 16 by naked-single. pending={l10}
i9 is 14 by naked-single. pending={i9}
i14 is 15 by naked-single. pending={i14}
b14 is 7 by naked-single. pending={b14}
b16 is 3 by naked-single. pending={b16}
b13 is 16 by naked-single. pending={b13}
b15 is 15 by naked-single. pending={b15}
i15 is 16 by naked-single. pending={i15}
i6 is 1 by naked-single. pending={i6}
e6 is 6 by naked-single. pending={e6}
e14 is 1 by naked-single. pending={e14}
f7 is 3 by naked-single. pending={f7}
d7 is 6 by naked-single. pending={d7}
f5 is 1 by naked-single. pending={f5}
f14 is 6 by naked-single. pending={f14}
k15 is 4 by naked-single. pending={k15}
k3 is 16 by naked-single. pending={k3}
j1 is 4 by naked-single. pending={j1}
k13 is 7 by naked-single. pending={k13}

grid22 didn't work: naked-singles ran out of candidates.

…backtrack.grid12 again

grid12 didn't work: exhaustive search revealed no solution.

…backtrack.grid11 again

backtrack.grid11 → grid23: a9 guess 9 ∈ {7|9}

pending={a9}

deduce.grid23: naked-singles

deduce.grid23: hidden-singles

deduce.grid23.rowf. f11 is 9 by hidden-single.

pending={f11}

deduce.grid23: naked-singles

deduce.grid23: hidden-singles

deduce.grid23.rowf. f9 is 16 by hidden-single.

pending={f9}

deduce.grid23: naked-singles

deduce.grid23: hidden-singles

deduce.grid23.rowf. f12 is 7 by hidden-single.

pending={f12}

deduce.grid23: naked-singles

deduce.grid23: hidden-singles

deduce.grid23: naked-pairs

two's heap=c12 {1|2}, g3 {1|4}, i12 {1|6}, a11 {2|7}, e10 {3|6}, g10 {3|6}, d7 {3|6}, o6 {1|15}, b1 {1|15}, g2 {2|16}, c3 {1|11}, b15 {15|16}, g11 {2|8}, d5 {3|16}, o1 {4|8}, e2 {2|16}.

Naked-pair {3|6} in cells {d7, e10, g10} contained within {col10, box7}, updating cells {e12, g11, i10, l10, p10}:

e12: {2|3|6|8} → {2|8}.
i10: {6|7|13|16} → {7|13|16}.
l10: {6|13|16} → {13|16}.
p10: {3|7|13|16} → {7|13|16}.

Naked-pair {2|16} in cells {e2, g2} contained within {col2, box5}, updating cells {f1, f4, g3, g4}:

grid23

	2
		7

		15

	2
		7

	2
		7

		15

1


		15

1	3
	7

		16

1
		7

		15




		15	16

1	3
	7

		16

1

		11

1	2

1	2
		8


		8
10	11

1	2

	10

1	2

		11

1
		7
		11
	14

1	2
		7

	14

		3


			16

		3
	6

	3
6

		16

1	2
		7

1	2	3	4
		7
9
			16

1	2		4
		7

		4

9	11
		16

	2


			16

1		3
	6

	3	4
6		8

		3
	6

	2
			8

1		4
	6

1		4
	6

		16

1		4


	15

1	3	4


	15

1	3	4

	3	4
6

1		4
	6

	2


			16

1			4

1	3	4

	3	4
6		8

		3
	6

	2
			8

1			4

			12
			16

		4
	6
		12
13		16

1		4
	6

13		16

1

	10
13

1
	6	7

		15	16

1
	6	7

13	14


	7

13		16

1
		7
	10
	14		16

1
	6

2
	7

14		16

	2
	6	7

13	14	15


	6
	10
13		15	16

1			4


			16

1		4

	10
13

1	3


13		16

1		3
	6	7

			16

1		3
	6

			16

		3	4
		7	8

			16

			4
	6	7	8

13

		4
	6	8
	10
13		16

		3	4
	6	7
	10
13			16

1			4


			16

1		4
	7	8

		16

1			4
			8

			4
		7	8

			16

			4
			8

13			16

		4
	7

13		16

		4

	10
13

	3
6

	15	16

		3
	6

13

	3
6

	15	16


	6

13	14




13			16

		4
5
	10
	14	16

		4
5	6

	3	4


14		16

	2		4
			8

			16

			4


	14		16

1
			8

			16

1
	6	8

	14

1		4
	6	8

1	2	4
		8

	14

1	2	4
	6

2		4
6	7

14

1	3	4


13		16

1	3


		16

	2	3	4
			8

13	14

1	3
		8

		16

1
	6	7	8

13	14

1			4
		7	8

	14		16

1	2		4
		7	8

	14

		4
	6	8

13

1	2		4
	6	7

13

			4
			8

		4
6	7

14

1			4


13

1


		15

1
		8
9
	15

1
	6	7	8

13	14

1			4
5		7	8

	14

1			4
5		7	8
9
	14

		4
	6	8
9
13

1			4
	6	7

13

2		4
		8
	11
		16

		4
	7
	11
14		16

2		4
	7

14

	2	3	4
			8

13	14

	3
		8
9
		16


		7	8

13	14


	7

13		16

			4
5		7	8

	14		16

	3	4
5		8

	2		4
5		7	8
9			12
	14

	2		4
		7	8

13	14

			4
			8
9			12
13

backtrack.grid23 → grid24: a11 guess 2 ∈ {2|7}

pending={a11}

deduce.grid24: naked-singles

c12 is 1 by naked-single. pending={c12}
c3 is 11 by naked-single. pending={c3}
d11 is 7 by naked-single. pending={d11}
g11 is 8 by naked-single. pending={g11}
e12 is 2 by naked-single. pending={e12}
e2 is 16 by naked-single. pending={e2}
g2 is 2 by naked-single. pending={g2}
i12 is 6 by naked-single. pending={i12}

deduce.grid24: hidden-singles

deduce.grid24.rowd. d15 is 11 by hidden-single.

pending={d15}

deduce.grid24: naked-singles

deduce.grid24: hidden-singles

deduce.grid24.rowd. d13 is 9 by hidden-single.

pending={d13}

deduce.grid24: naked-singles

deduce.grid24: hidden-singles

deduce.grid24.rowd. d14 is 4 by hidden-single.

pending={d14}

deduce.grid24: naked-singles

deduce.grid24: hidden-singles

deduce.grid24.rowe. e7 is 8 by hidden-single.

pending={e7}

deduce.grid24: naked-singles

deduce.grid24: hidden-singles

deduce.grid24.rowe. e16 is 4 by hidden-single.

pending={e16}

deduce.grid24: naked-singles

deduce.grid24: hidden-singles

deduce.grid24.rowp. p1 is 11 by hidden-single.

pending={p1}

deduce.grid24: naked-singles

deduce.grid24: hidden-singles

deduce.grid24.col3. p3 is 7 by hidden-single.

pending={p3}

deduce.grid24: naked-singles

deduce.grid24: hidden-singles

deduce.grid24.col4. a4 is 7 by hidden-single.

pending={a4}

deduce.grid24: naked-singles

a14 is 15 by naked-single. pending={a14}
b15 is 16 by naked-single. pending={b15}

deduce.grid24: hidden-singles

deduce.grid24.rowb. b1 is 15 by hidden-single.

pending={b1}

deduce.grid24: naked-singles

deduce.grid24: hidden-singles

deduce.grid24.rowf. f4 is 15 by hidden-single.

pending={f4}

deduce.grid24: naked-singles

deduce.grid24: hidden-singles

deduce.grid24.col4. g4 is 3 by hidden-single.

pending={g4}

deduce.grid24: naked-singles

g10 is 6 by naked-single. pending={g10}
e10 is 3 by naked-single. pending={e10}
g7 is 4 by naked-single. pending={g7}
g3 is 1 by naked-single. pending={g3}
d3 is 14 by naked-single. pending={d3}
f1 is 4 by naked-single. pending={f1}
o1 is 8 by naked-single. pending={o1}

deduce.grid24: hidden-singles

deduce.grid24.rowk. k11 is 1 by hidden-single.

pending={k11}

deduce.grid24: naked-singles

deduce.grid24: hidden-singles

deduce.grid24.col10. i10 is 7 by hidden-single.

pending={i10}

deduce.grid24: naked-singles

deduce.grid24: hidden-singles

deduce.grid24.col6. j6 is 7 by hidden-single.

pending={j6}

deduce.grid24: naked-singles

deduce.grid24: hidden-singles

deduce.grid24.col12. p12 is 3 by hidden-single.

pending={p12}

deduce.grid24: naked-singles

deduce.grid24: hidden-singles

deduce.grid24.col12. l12 is 5 by hidden-single.

pending={l12}

deduce.grid24: naked-singles

deduce.grid24: hidden-singles

deduce.grid24.col14. b14 is 7 by hidden-single.

pending={b14}

deduce.grid24: naked-singles

deduce.grid24: hidden-singles

deduce.grid24.col15. i15 is 15 by hidden-single.

pending={i15}

deduce.grid24: naked-singles

deduce.grid24: hidden-singles

deduce.grid24.box11. k12 is 8 by hidden-single.

pending={k12}

deduce.grid24: naked-singles

m12 is 4 by naked-single. pending={m12}
m3 is 16 by naked-single. pending={m3}
k3 is 4 by naked-single. pending={k3}
k15 is 13 by naked-single. pending={k15}
g15 is 12 by naked-single. pending={g15}
g13 is 16 by naked-single. pending={g13}
g16 is 13 by naked-single. pending={g16}
k13 is 7 by naked-single. pending={k13}
k16 is 16 by naked-single. pending={k16}
m1 is 2 by naked-single. pending={m1}
d1 is 1 by naked-single. pending={d1}
d4 is 2 by naked-single. pending={d4}
j1 is 16 by naked-single. pending={j1}

deduce.grid24: hidden-singles

deduce.grid24.rowp. p13 is 12 by hidden-single.

pending={p13}

deduce.grid24: naked-singles

deduce.grid24: hidden-singles

deduce.grid24.rowp. p11 is 5 by hidden-single.

pending={p11}

deduce.grid24: naked-singles

o11 is 14 by naked-single. pending={o11}
n11 is 16 by naked-single. pending={n11}
i11 is 10 by naked-single. pending={i11}
l11 is 4 by naked-single. pending={l11}
p10 is 13 by naked-single. pending={p10}
l10 is 16 by naked-single. pending={l10}
p9 is 8 by naked-single. pending={p9}

deduce.grid24: hidden-singles

deduce.grid24.rowi. i6 is 16 by hidden-single.

pending={i6}

deduce.grid24: naked-singles

deduce.grid24: hidden-singles

deduce.grid24.rowi. i4 is 1 by hidden-single.

pending={i4}

deduce.grid24: naked-singles

deduce.grid24: hidden-singles

deduce.grid24.rowi. i9 is 13 by hidden-single.

pending={i9}

deduce.grid24: naked-singles

l9 is 14 by naked-single. pending={l9}
l13 is 3 by naked-single. pending={l13}
b13 is 1 by naked-single. pending={b13}
b16 is 3 by naked-single. pending={b16}

deduce.grid24: hidden-singles

deduce.grid24.rowl. l4 is 10 by hidden-single.

pending={l4}

deduce.grid24: naked-singles

j4 is 13 by naked-single. pending={j4}

deduce.grid24: hidden-singles

deduce.grid24.rowl. l7 is 13 by hidden-single.

pending={l7}

deduce.grid24: naked-singles

deduce.grid24: hidden-singles

deduce.grid24.rowm. m13 is 14 by hidden-single.

pending={m13}

deduce.grid24: naked-singles

i13 is 2 by naked-single. pending={i13}
i14 is 14 by naked-single. pending={i14}
p14 is 2 by naked-single. pending={p14}
c14 is 8 by naked-single. pending={c14}
c15 is 10 by naked-single. pending={c15}
c16 is 2 by naked-single. pending={c16}
j14 is 6 by naked-single. pending={j14}
e14 is 1 by naked-single. pending={e14}
e6 is 6 by naked-single. pending={e6}
f7 is 3 by naked-single. pending={f7}
d7 is 6 by naked-single. pending={d7}
f5 is 1 by naked-single. pending={f5}

grid24 didn't work: naked-singles ran out of candidates.

…backtrack.grid23 again

backtrack.grid23 → grid25: a11 guess 7 ∈ {2|7}

pending={a11}

deduce.grid25: naked-singles

deduce.grid25: hidden-singles

deduce.grid25.col12. p12 is 3 by hidden-single.

pending={p12}

deduce.grid25: naked-singles

deduce.grid25: hidden-singles

deduce.grid25.col12. l12 is 5 by hidden-single.

pending={l12}

deduce.grid25: naked-singles

deduce.grid25: hidden-singles

deduce.grid25: naked-pairs

two's heap=c12 {1|2}, d11 {1|2}, g3 {1|4}, i12 {1|6}, e10 {3|6}, c3 {1|11}, g10 {3|6}, d7 {3|6}, o1 {4|8}, o6 {1|15}, a14 {2|15}, a4 {2|15}, g2 {2|16}, d5 {3|16}, e12 {2|8}, b15 {15|16}, g11 {2|8}, l10 {13|16}, b1 {1|15}, e2 {2|16}.

Naked-pair {3|6} in cells {d7, e10, g10} contained within {col10, box7}, updating cells {e12, g11, i10, l10, p10}:

Naked-pair {2|8} in cells {e12, g11} contained within {box7}, updating cells {e10, g10}:

Naked-pair {2|16} in cells {e2, g2} contained within {col2, box5}, updating cells {f1, f4, g3, g4}:

grid25

	2


		15

	2


		15

1


		15

1	3
	7

		16

1
		7

		15




		15	16

1	3
	7

		16

1

		11

1	2

1	2
		8


		8
10	11

1	2

	10

1	2

		11

1
		7
		11
	14

1	2
		7

	14

		3


			16

		3
	6

	3
6

		16

1	2

1	2	3	4
		7
9
			16

1	2		4
		7

		4

9	11
		16

	2


			16

1		3
	6

	3	4
6		8

		3
	6

	2
			8

1		4
	6

1		4
	6

		16

1		4


	15

1	3	4


	15

1	3	4

	3	4
6

1		4
	6

	2


			16

1			4

1	3	4

	3	4
6		8

		3
	6

	2
			8

1			4

			12
			16

		4
	6
		12
13		16

1		4
	6

13		16

1

	10
13

1
	6	7

		15	16

1
	6	7

13	14


	7

13		16

1

	10
	14	16

1
	6

2
	7

14		16

	2
	6	7

13	14	15


	6
	10
13		15	16

1			4


			16

1		4

	10
13

1	3


13		16

1		3
	6	7

			16

1		3
	6

			16

		3	4
		7	8

			16

			4
	6	7	8

13

		4
	6	8
	10
13		16

		3	4
	6	7
	10
13			16

1			4


			16

1			4
			8

			16

1			4
			8

			4
		7	8

			16

			4
			8

13			16

		4
	7

13		16

		4

	10
13

	3
6

	15	16

		3
	6

13

	3
6

	15	16


	6

13	14




13			16

			4

	10
	14		16

	3	4


14		16

	2		4
			8

			16

			4


	14		16

1
			8

			16

1
	6	8

	14

1		4
	6	8

1	2	4
		8

	14

1	2	4
	6

2		4
6	7

14

1	3	4


13		16

1	3


		16

	2	3	4
			8

13	14

1	3
		8

		16

1
	6	7	8

13	14

1		4
		8

	14	16

1	2		4
		7	8

	14

		4
	6	8

13

1	2		4
	6	7

13

			4
			8

		4
6	7

14

1			4


13

1


		15

1
		8
9
	15

1
	6	7	8

13	14

1		4
5		8

	14

1			4
5		7	8
9
	14

		4
	6	8
9
13

1			4
	6	7

13

2		4
		8
	11
		16

		4
	7
	11
14		16

2		4
	7

14

	2	4
		8

13	14


			8
9
			16


		7	8

13	14


	7

13		16

		4
5		8

	14	16

	2		4
5		7	8
9			12
	14

	2		4
		7	8

13	14

			4
			8
9			12
13

backtrack.grid25 → grid26: a4 guess 2 ∈ {2|15}

pending={a4}

deduce.grid26: naked-singles

a14 is 15 by naked-single. pending={a14}
b15 is 16 by naked-single. pending={b15}

deduce.grid26: hidden-singles

deduce.grid26.rowb. b1 is 15 by hidden-single.

pending={b1}

deduce.grid26: naked-singles

deduce.grid26: hidden-singles

deduce.grid26.rowf. f4 is 15 by hidden-single.

pending={f4}

deduce.grid26: naked-singles

deduce.grid26: hidden-singles

deduce.grid26.col4. g4 is 3 by hidden-single.

pending={g4}

deduce.grid26: naked-singles

g10 is 6 by naked-single. pending={g10}
e10 is 3 by naked-single. pending={e10}

deduce.grid26: hidden-singles

deduce.grid26.col15. i15 is 15 by hidden-single.

pending={i15}

deduce.grid26: naked-singles

deduce.grid26: hidden-singles

deduce.grid26: naked-pairs

Naked-pair {1|4} in cells {f1, g3} contained within {box5}, updating cells {e2, g2}:

Naked-pair {1|11} in cells {c3, d1} contained within {box1}, updating cells {d3, d4}:

d3: {1|7|11|14} → {7|14}.
d4: {1|7|14} → {7|14}.

Naked-pair {2|16} in cells {e2, g2} contained within {col2, box5}, updating cells {f1, g3}:

grid26

1		3
		7

1
		7

1		3
		7

1

		11

1	2

1	2
		8


		8
10	11

1	2

	10

1

		11


		7

	14


		7

	14

		3


			16

		3
	6

	3
6

		16

1	2

1	2	3	4
		7
9

1	2		4
		7

		4

9	11

	2


			16

1
	6

			4
	6		8

	2
			8

1		4
	6

1		4
	6

		16

1			4

1	3	4

	3	4
6

1		4
	6

	2


			16

1			4

			4
			8

	2
			8

1			4

			12
			16

			4

			12
13

1			4


13			16

1

	10
13

1
	6	7

			16

1
	6	7

13	14


	7

13		16

1

	10
	14	16

1
	6

2
	7

14		16

	2
	6	7

13	14

1			4


			16

1		4

	10
13

1	3


13		16

1		3
	6	7

			16

1		3
	6

			16

		3	4
		7	8

			16

			4
	6	7	8

13

		4
	6	8
	10
13

		3	4
	6	7
	10
13			16

1			4


			16

1			4
			8

			16

1			4
			8

			4
		7	8

			16

			4
			8

13

		4
	7

13		16

		4

	10
13

	3
6

	15	16

		3
	6

13

	3
6

	15	16


	6

13	14




13			16

			4

	10
	14		16

	3	4


14		16

	2		4
			8

			16

			4


	14		16

1
			8

			16

1
	6	8

	14

1		4
	6	8

1	2	4
		8

	14

1	2	4
	6

		4
6	7

14

1	3	4


13		16

1	3


		16

	2	3	4
			8

13	14

1	3
		8

		16

1
	6	7	8

13	14

1		4
		8

	14	16

1	2		4
		7	8

	14

		4
	6	8

13

1	2		4
	6	7

13

			4
			8

		4
6	7

14

1			4


13

1


		15

1
		8
9
	15

1
	6	7	8

13	14

1		4
5		8

	14

1			4
5		7	8
9
	14

		4
	6	8
9
13

1			4
	6	7

13

2		4
		8
	11
		16

		4
	7
	11
14		16

		4
	7

14

	2	4
		8

13	14


			8
9
			16


		7	8

13	14


	7

13		16

		4
5		8

	14	16

	2		4
5		7	8
9			12
	14

	2		4
		7	8

13	14

			4
			8
9			12
13

backtrack.grid26 → grid27: b14 guess 1 ∈ {1|7}

pending={b14}

deduce.grid27: naked-singles

deduce.grid27: hidden-singles

deduce.grid27: naked-pairs

Naked-pair {1|4} in cells {f1, g3} contained within {box5}, updating cells {e2, g2}:

Naked-pair {4|6} in cells {e14, f14} contained within {col14, box8}, updating cells {c14, d14, e16, g13, g15, g16, i14, j14, p14}:

d14: {2|4|7} → {2|7}.
e16: {1|4|6|16} → {1|16}.
g13: {1|4|12|16} → {1|12|16}.
g15: {4|12|13} → {12|13}.
g16: {1|4|13|16} → {1|13|16}.
i14: {2|6|7|13|14} → {2|7|13|14}.
j14: {4|6|7|8|13} → {7|8|13}.
p14: {2|4|7|8|13|14} → {2|7|8|13|14}.

Naked-pair {3|7} in cells {b13, b16} contained within {rowb, box4}, updating cells {c14, c15, c16, d13, d14, d15}:

d13: {2|3|4|7|9} → {2|4|9}.
d14: {2|7} → {2}. Solved.

Naked-pair {1|11} in cells {c3, d1} contained within {box1}, updating cells {d3, d4}:

Naked-pair {7|14} in cells {d3, d4} contained within {rowd, box1}, updating cells {c3, d1, d5, d7, d8, d11, d13, d14, d15}:

Naked-pair {2|16} in cells {e2, g2} contained within {col2, box5}, updating cells {f1, g3}:

pending={d14}

deduce.grid27: naked-singles

c14 is 8 by naked-single. pending={c14}
c16 is 10 by naked-single. pending={c16}
c15 is 11 by naked-single. pending={c15}
c3 is 1 by naked-single. pending={c3}
c12 is 2 by naked-single. pending={c12}
d1 is 11 by naked-single. pending={d1}
d11 is 1 by naked-single. pending={d11}
e12 is 8 by naked-single. pending={e12}
g3 is 4 by naked-single. pending={g3}
f1 is 1 by naked-single. pending={f1}
g7 is 8 by naked-single. pending={g7}
g11 is 2 by naked-single. pending={g11}
g2 is 16 by naked-single. pending={g2}
e2 is 2 by naked-single. pending={e2}
k3 is 16 by naked-single. pending={k3}
j1 is 4 by naked-single. pending={j1}
m3 is 14 by naked-single. pending={m3}
d3 is 7 by naked-single. pending={d3}
d4 is 14 by naked-single. pending={d4}
o1 is 8 by naked-single. pending={o1}
p3 is 11 by naked-single. pending={p3}

deduce.grid27: hidden-singles

deduce.grid27.rowe. e16 is 16 by hidden-single.

pending={e16}

deduce.grid27: naked-singles

deduce.grid27: hidden-singles

deduce.grid27.rowe. e6 is 1 by hidden-single.

pending={e6}

deduce.grid27: naked-singles

o6 is 15 by naked-single. pending={o6}

deduce.grid27: hidden-singles

deduce.grid27.rowi. i13 is 2 by hidden-single.

pending={i13}

deduce.grid27: naked-singles

deduce.grid27: hidden-singles

deduce.grid27.rowk. k12 is 1 by hidden-single.

pending={k12}

deduce.grid27: naked-singles

i12 is 6 by naked-single. pending={i12}
m12 is 4 by naked-single. pending={m12}

deduce.grid27: hidden-singles

deduce.grid27.rowi. i4 is 1 by hidden-single.

pending={i4}

deduce.grid27: naked-singles

deduce.grid27: hidden-singles

deduce.grid27.rowi. i11 is 10 by hidden-single.

pending={i11}

deduce.grid27: naked-singles

deduce.grid27: hidden-singles

deduce.grid27.rowl. l4 is 10 by hidden-single.

deduce.grid27.rowl. l8 is 15 by hidden-single.

pending={l4, l8}

deduce.grid27: naked-singles

j4 is 13 by naked-single. pending={j4}
j14 is 7 by naked-single. pending={j14}

deduce.grid27: hidden-singles

deduce.grid27.rowj. j15 is 10 by hidden-single.

pending={j15}

deduce.grid27: naked-singles

deduce.grid27: hidden-singles

deduce.grid27.rowj. j13 is 8 by hidden-single.

pending={j13}

deduce.grid27: naked-singles

k13 is 4 by naked-single. pending={k13}
d13 is 9 by naked-single. pending={d13}
d15 is 4 by naked-single. pending={d15}
k11 is 8 by naked-single. pending={k11}
k15 is 13 by naked-single. pending={k15}
g15 is 12 by naked-single. pending={g15}
g13 is 1 by naked-single. pending={g13}
g16 is 13 by naked-single. pending={g16}
i14 is 14 by naked-single. pending={i14}

grid27 didn't work: naked-singles ran out of candidates.

…backtrack.grid26 again

backtrack.grid26 → grid28: b14 guess 7 ∈ {1|7}

pending={b14}

deduce.grid28: naked-singles

deduce.grid28: hidden-singles

deduce.grid28: naked-pairs

Naked-pair {1|3} in cells {b13, b16} contained within {rowb, box4}, updating cells {c14, c15, c16, d13, d14, d15}:

c14: {1|2|8} → {2|8}.
c16: {1|2|10} → {2|10}.
d13: {1|2|3|4|9} → {2|4|9}.
d14: {1|2|4} → {2|4}.

Naked-pair {1|4} in cells {f1, g3} contained within {box5}, updating cells {e2, g2}:

Naked-pair {1|11} in cells {c3, d1} contained within {box1}, updating cells {d3, d4}:

Naked-pair {7|14} in cells {d3, d4} contained within {rowd, box1}, updating cells {c3, d1, d5, d7, d8, d11, d13, d14, d15}:

Naked-pair {2|16} in cells {e2, g2} contained within {col2, box5}, updating cells {f1, g3}:

grid28

1		3

1		3

1

		11

1	2

	2
			8


		8
10	11

	2

	10

1

		11


		7

	14


		7

	14

		3


			16

		3
	6

	3
6

		16

1	2

	2	4

9

	2		4

		4

9	11

	2


			16

1
	6

			4
	6		8

	2
			8

1		4
	6

1		4
	6

		16

1			4

1	3	4

	3	4
6

1		4
	6

	2


			16

1			4

			4
			8

	2
			8

1			4

			12
			16

			4

			12
13

1			4


13			16

1

	10
13

1
	6	7

			16

1
	6	7

13	14


	7

13		16

1

	10
	14	16

1
	6

2
	7

14		16

	2
	6

13	14

1			4


			16

1		4

	10
13

1	3


13		16

1		3
	6	7

			16

1		3
	6

			16

		3	4
		7	8

			16

		4
	6	8

13

		4
	6	8
	10
13

		3	4
	6	7
	10
13			16

1			4


			16

1			4
			8

			16

1			4
			8

			4
		7	8

			16

			4
			8

13

		4
	7

13		16

		4

	10
13

	3
6

	15	16

		3
	6

13

	3
6

	15	16


	6

13	14




13			16

			4

	10
	14		16

	3	4


14		16

	2		4
			8

			16

			4


	14		16

1
			8

			16

1
	6	8

	14

1		4
	6	8

1	2	4
		8

	14

1	2	4
	6

		4
6	7

14

1	3	4


13		16

1	3


		16

	2	3	4
			8

13	14

1	3
		8

		16

1
	6	7	8

13	14

1		4
		8

	14	16

1	2		4
		7	8

	14

		4
	6	8

13

1	2		4
	6	7

13

			4
			8

		4
6	7

14

1			4


13

1


		15

1
		8
9
	15

1
	6	7	8

13	14

1		4
5		8

	14

1			4
5		7	8
9
	14

		4
	6	8
9
13

1			4
	6	7

13

2		4
		8
	11
		16

		4
	7
	11
14		16

		4
	7

14

	2	4
		8

13	14


			8
9
			16


		7	8

13	14


	7

13		16

		4
5		8

	14	16

	2		4
5		7	8
9			12
	14

	2	4
		8

13	14

			4
			8
9			12
13

backtrack.grid28 → grid29: b13 guess 1 ∈ {1|3}

pending={b13}

deduce.grid29: naked-singles

b16 is 3 by naked-single. pending={b16}

deduce.grid29: hidden-singles

deduce.grid29: naked-pairs

Naked-pair {1|4} in cells {f1, g3} contained within {box5}, updating cells {e2, g2}:

Naked-pair {1|11} in cells {c3, d1} contained within {box1}, updating cells {d3, d4}:

Naked-pair {7|14} in cells {d3, d4} contained within {rowd, box1}, updating cells {c3, d1, d5, d7, d8, d11, d13, d14, d15}:

Naked-pair {2|16} in cells {e2, g2} contained within {col2, box5}, updating cells {f1, g3}:

grid29

1

		11

1	2

	2
			8


		8
10	11

	2

	10

1

		11


		7

	14


		7

	14

		3


			16

		3
	6

	3
6

		16

1	2

	2	4

9

	2		4

		4

9	11

	2


			16

1
	6

			4
	6		8

	2
			8

1		4
	6

1		4
	6

		16

1			4

1	3	4

	3	4
6

1		4
	6

	2


			16

1			4

			4
			8

	2
			8

			4

			12
			16

			4

			12
13

1			4


13			16

1

	10
13

1
	6	7

			16

1
	6	7

13	14


	7

13		16

1

	10
	14	16

1
	6

2
	7

14		16

	2
	6

13	14

1			4


			16

1		4

	10
13

1	3


13		16

1		3
	6	7

			16

1		3
	6

			16

		3	4
		7	8

			16

		4
	6	8

13

		4
	6	8
	10
13

			4
	6	7
	10
13			16

1			4


			16

1			4
			8

			16

1			4
			8

			4
		7	8

			16

			4
			8

13

		4
	7

13		16

		4

	10
13

	3
6

	15	16

		3
	6

13

	3
6

	15	16


	6

13	14




13			16

			4

	10
	14		16

	3	4


14		16

	2		4
			8

			16

			4


	14		16

1
			8

			16

1
	6	8

	14

1		4
	6	8

	2		4
			8

	14

1	2	4
	6

		4
6	7

14

1	3	4


13		16

1	3


		16

	2	3	4
			8

13	14

1	3
		8

		16

1
	6	7	8

13	14

1		4
		8

	14	16

2		4
	7	8

14

		4
	6	8

13

1	2		4
	6	7

13

			4
			8

		4
6	7

14

1			4


13

1


		15

1
		8
9
	15

1
	6	7	8

13	14

1		4
5		8

	14

			4
5		7	8
9
	14

		4
	6	8
9
13

1			4
	6	7

13

2		4
		8
	11
		16

		4
	7
	11
14		16

		4
	7

14

	2	4
		8

13	14


			8
9
			16


		7	8

13	14


	7

13		16

		4
5		8

	14	16

	2		4
5		7	8
9			12
	14

	2	4
		8

13	14

			4
			8
9			12
13

backtrack.grid29 → grid30: c3 guess 1 ∈ {1|11}

pending={c3}

deduce.grid30: naked-singles

c12 is 2 by naked-single. pending={c12}
c14 is 8 by naked-single. pending={c14}
c16 is 10 by naked-single. pending={c16}
c15 is 11 by naked-single. pending={c15}
d1 is 11 by naked-single. pending={d1}
d11 is 1 by naked-single. pending={d11}
e12 is 8 by naked-single. pending={e12}
g3 is 4 by naked-single. pending={g3}
f1 is 1 by naked-single. pending={f1}
g7 is 8 by naked-single. pending={g7}
g11 is 2 by naked-single. pending={g11}
g2 is 16 by naked-single. pending={g2}
e2 is 2 by naked-single. pending={e2}
g13 is 12 by naked-single. pending={g13}
g15 is 13 by naked-single. pending={g15}
g16 is 1 by naked-single. pending={g16}
k3 is 16 by naked-single. pending={k3}
j1 is 4 by naked-single. pending={j1}
m3 is 14 by naked-single. pending={m3}
d3 is 7 by naked-single. pending={d3}
d4 is 14 by naked-single. pending={d4}
o1 is 8 by naked-single. pending={o1}
p3 is 11 by naked-single. pending={p3}

deduce.grid30: hidden-singles

deduce.grid30.rowe. e6 is 1 by hidden-single.

deduce.grid30.rowe. e16 is 16 by hidden-single.

pending={e6, e16}

deduce.grid30: naked-singles

o6 is 15 by naked-single. pending={o6}

deduce.grid30: hidden-singles

deduce.grid30.rowk. k12 is 1 by hidden-single.

deduce.grid30.rowk. k16 is 13 by hidden-single.

pending={k12, k16}

deduce.grid30: naked-singles

i12 is 6 by naked-single. pending={i12}
j14 is 6 by naked-single. pending={j14}
e14 is 4 by naked-single. pending={e14}
d14 is 2 by naked-single. pending={d14}
e7 is 6 by naked-single. pending={e7}
d7 is 3 by naked-single. pending={d7}
d5 is 16 by naked-single. pending={d5}
d8 is 6 by naked-single. pending={d8}
f7 is 4 by naked-single. pending={f7}
f5 is 3 by naked-single. pending={f5}

grid30 didn't work: naked-singles ran out of candidates.

…backtrack.grid29 again

backtrack.grid29 → grid31: c3 guess 11 ∈ {1|11}

pending={c3}

deduce.grid31: naked-singles

d1 is 1 by naked-single. pending={d1}
d11 is 2 by naked-single. pending={d11}
c12 is 1 by naked-single. pending={c12}
d14 is 4 by naked-single. pending={d14}
d13 is 9 by naked-single. pending={d13}
d15 is 11 by naked-single. pending={d15}
f1 is 4 by naked-single. pending={f1}
g3 is 1 by naked-single. pending={g3}
g11 is 8 by naked-single. pending={g11}
e12 is 2 by naked-single. pending={e12}
e2 is 16 by naked-single. pending={e2}
g2 is 2 by naked-single. pending={g2}
g7 is 4 by naked-single. pending={g7}
i12 is 6 by naked-single. pending={i12}
j1 is 16 by naked-single. pending={j1}
k3 is 4 by naked-single. pending={k3}
k12 is 8 by naked-single. pending={k12}
k15 is 13 by naked-single. pending={k15}
g15 is 12 by naked-single. pending={g15}
g13 is 16 by naked-single. pending={g13}
g16 is 13 by naked-single. pending={g16}
k13 is 7 by naked-single. pending={k13}
k16 is 16 by naked-single. pending={k16}
k11 is 1 by naked-single. pending={k11}
m12 is 4 by naked-single. pending={m12}
o1 is 8 by naked-single. pending={o1}
m1 is 2 by naked-single. pending={m1}
p1 is 11 by naked-single. pending={p1}

deduce.grid31: hidden-singles

deduce.grid31.rowe. e7 is 8 by hidden-single.

deduce.grid31.rowe. e16 is 4 by hidden-single.

pending={e7, e16}

deduce.grid31: naked-singles

deduce.grid31: hidden-singles

deduce.grid31.rowj. j6 is 7 by hidden-single.

pending={j6}

deduce.grid31: naked-singles

deduce.grid31: hidden-singles

deduce.grid31.rowp. p13 is 12 by hidden-single.

pending={p13}

deduce.grid31: naked-singles

deduce.grid31: hidden-singles

deduce.grid31.rowp. p11 is 5 by hidden-single.

pending={p11}

deduce.grid31: naked-singles

o11 is 14 by naked-single. pending={o11}
n11 is 16 by naked-single. pending={n11}
i11 is 10 by naked-single. pending={i11}
l11 is 4 by naked-single. pending={l11}

deduce.grid31: hidden-singles

deduce.grid31.rowl. l4 is 10 by hidden-single.

pending={l4}

deduce.grid31: naked-singles

deduce.grid31: hidden-singles

deduce.grid31.rowo. o13 is 5 by hidden-single.

pending={o13}

deduce.grid31: naked-singles

deduce.grid31: hidden-singles

deduce.grid31.col5. d5 is 16 by hidden-single.

pending={d5}

deduce.grid31: naked-singles

deduce.grid31: hidden-singles

deduce.grid31.col14. p14 is 13 by hidden-single.

pending={p14}

deduce.grid31: naked-singles

p10 is 7 by naked-single. pending={p10}
p9 is 8 by naked-single. pending={p9}

deduce.grid31: hidden-singles

deduce.grid31.rowi. i9 is 7 by hidden-single.

pending={i9}

deduce.grid31: naked-singles

deduce.grid31: hidden-singles

deduce.grid31.rowp. p7 is 2 by hidden-single.

pending={p7}

deduce.grid31: naked-singles

deduce.grid31: hidden-singles

deduce.grid31.col3. d3 is 7 by hidden-single.

pending={d3}

deduce.grid31: naked-singles

d4 is 14 by naked-single. pending={d4}
p4 is 4 by naked-single. pending={p4}
p15 is 9 by naked-single. pending={p15}
p8 is 16 by naked-single. pending={p8}
p3 is 14 by naked-single. pending={p3}
m3 is 16 by naked-single. pending={m3}

deduce.grid31: hidden-singles

deduce.grid31.rowm. m13 is 14 by hidden-single.

pending={m13}

deduce.grid31: naked-singles

i13 is 2 by naked-single. pending={i13}
i14 is 14 by naked-single. pending={i14}
l13 is 3 by naked-single. pending={l13}

deduce.grid31: hidden-singles

deduce.grid31.rowl. l9 is 14 by hidden-single.

pending={l9}

deduce.grid31: naked-singles

deduce.grid31: hidden-singles

deduce.grid31.rowm. m8 is 8 by hidden-single.

pending={m8}

deduce.grid31: naked-singles

deduce.grid31: hidden-singles

deduce.grid31.rown. n7 is 14 by hidden-single.

deduce.grid31.rown. n16 is 2 by hidden-single.

pending={n7, n16}

deduce.grid31: naked-singles

c16 is 10 by naked-single. pending={c16}
c15 is 8 by naked-single. pending={c15}
c14 is 2 by naked-single. pending={c14}
j16 is 6 by naked-single. pending={j16}
j14 is 8 by naked-single. pending={j14}
j13 is 4 by naked-single. pending={j13}
j15 is 10 by naked-single. pending={j15}
m16 is 1 by naked-single. pending={m16}
m9 is 6 by naked-single. pending={m9}
n13 is 8 by naked-single. pending={n13}
o16 is 7 by naked-single. pending={o16}
o4 is 6 by naked-single. pending={o4}
n4 is 7 by naked-single. pending={n4}
o15 is 4 by naked-single. pending={o15}
n15 is 6 by naked-single. pending={n15}

deduce.grid31: hidden-singles

deduce.grid31.rown. n5 is 4 by hidden-single.

pending={n5}

deduce.grid31: naked-singles

deduce.grid31: hidden-singles

deduce.grid31.rown. n9 is 13 by hidden-single.

pending={n9}

deduce.grid31: naked-singles

o9 is 1 by naked-single. pending={o9}
o5 is 13 by naked-single. pending={o5}
o6 is 15 by naked-single. pending={o6}
o8 is 9 by naked-single. pending={o8}

deduce.grid31: hidden-singles

deduce.grid31.rowj. j4 is 13 by hidden-single.

pending={j4}

deduce.grid31: naked-singles

i4 is 1 by naked-single. pending={i4}
i6 is 16 by naked-single. pending={i6}
i10 is 13 by naked-single. pending={i10}
l6 is 6 by naked-single. pending={l6}
e6 is 1 by naked-single. pending={e6}
e14 is 6 by naked-single. pending={e14}
f5 is 3 by naked-single. pending={f5}
f7 is 6 by naked-single. pending={f7}
d7 is 3 by naked-single. pending={d7}
d8 is 6 by naked-single. pending={d8}
f14 is 1 by naked-single. pending={f14}
j5 is 1 by naked-single. pending={j5}
j8 is 3 by naked-single. pending={j8}
l7 is 13 by naked-single. pending={l7}
l8 is 15 by naked-single. pending={l8}
l10 is 16 by naked-single. pending={l10}
n6 is 3 by naked-single. pending={n6}
n8 is 1 by naked-single. pending={n8}

deduce.grid31. Solved.

grid31
	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16
a	3	4	6	2	10	12	1	11	9	8	7	16	13	15	5	14
b	15	12	8	5	2	13	9	14	11	4	6	10	1	7	16	3
c	13	9	11	16	5	4	15	7	12	14	3	1	6	2	8	10
d	1	10	7	14	16	8	3	6	15	5	2	13	9	4	11	12
e	14	16	13	11	9	1	8	5	10	3	12	2	15	6	7	4
f	4	5	12	15	3	14	6	13	16	11	9	7	10	1	2	8
g	7	2	1	3	15	11	4	10	5	6	8	14	16	9	12	13
h	10	6	9	8	7	2	16	12	4	1	13	15	11	3	14	5
i	5	8	3	1	11	16	12	4	7	13	10	6	2	14	15	9
j	16	14	15	13	1	7	5	3	2	12	11	9	4	8	10	6
k	6	11	4	12	14	9	10	2	3	15	1	8	7	5	13	16
l	9	7	2	10	8	6	13	15	14	16	4	5	3	12	1	11
m	2	13	16	9	12	5	7	8	6	10	15	4	14	11	3	1
n	12	15	5	7	4	3	14	1	13	9	16	11	8	10	6	2
o	8	3	10	6	13	15	11	9	1	2	14	12	5	16	4	7
p	11	1	14	4	6	10	2	16	8	7	5	3	12	13	9	15

grid31. Copying solution to raw grid.

	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16
a	3	4	6	2	10	12	1	11	9	8	7	16	13	15	5	14
b	15	12	8	5	2	13	9	14	11	4	6	10	1	7	16	3
c	13	9	11	16	5	4	15	7	12	14	3	1	6	2	8	10
d	1	10	7	14	16	8	3	6	15	5	2	13	9	4	11	12
e	14	16	13	11	9	1	8	5	10	3	12	2	15	6	7	4
f	4	5	12	15	3	14	6	13	16	11	9	7	10	1	2	8
g	7	2	1	3	15	11	4	10	5	6	8	14	16	9	12	13
h	10	6	9	8	7	2	16	12	4	1	13	15	11	3	14	5
i	5	8	3	1	11	16	12	4	7	13	10	6	2	14	15	9
j	16	14	15	13	1	7	5	3	2	12	11	9	4	8	10	6
k	6	11	4	12	14	9	10	2	3	15	1	8	7	5	13	16
l	9	7	2	10	8	6	13	15	14	16	4	5	3	12	1	11
m	2	13	16	9	12	5	7	8	6	10	15	4	14	11	3	1
n	12	15	5	7	4	3	14	1	13	9	16	11	8	10	6	2
o	8	3	10	6	13	15	11	9	1	2	14	12	5	16	4	7
p	11	1	14	4	6	10	2	16	8	7	5	3	12	13	9	15

	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16
a	3	4	6	2	10	12	1	11	9	8	7	16	13	15	5	14
b	15	12	8	5	2	13	9	14	11	4	6	10	1	7	16	3
c	13	9	11	16	5	4	15	7	12	14	3	1	6	2	8	10
d	1	10	7	14	16	8	3	6	15	5	2	13	9	4	11	12
e	14	16	13	11	9	1	8	5	10	3	12	2	15	6	7	4
f	4	5	12	15	3	14	6	13	16	11	9	7	10	1	2	8
g	7	2	1	3	15	11	4	10	5	6	8	14	16	9	12	13
h	10	6	9	8	7	2	16	12	4	1	13	15	11	3	14	5
i	5	8	3	1	11	16	12	4	7	13	10	6	2	14	15	9
j	16	14	15	13	1	7	5	3	2	12	11	9	4	8	10	6
k	6	11	4	12	14	9	10	2	3	15	1	8	7	5	13	16
l	9	7	2	10	8	6	13	15	14	16	4	5	3	12	1	11
m	2	13	16	9	12	5	7	8	6	10	15	4	14	11	3	1
n	12	15	5	7	4	3	14	1	13	9	16	11	8	10	6	2
o	8	3	10	6	13	15	11	9	1	2	14	12	5	16	4	7
p	11	1	14	4	6	10	2	16	8	7	5	3	12	13	9	15

	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16
a	3	4	6	2	10	12	1	11	9	8	7	16	13	15	5	14
b	15	12	8	5	2	13	9	14	11	4	6	10	1	7	16	3
c	13	9	11	16	5	4	15	7	12	14	3	1	6	2	8	10
d	1	10	7	14	16	8	3	6	15	5	2	13	9	4	11	12
e	14	16	13	11	9	1	8	5	10	3	12	2	15	6	7	4
f	4	5	12	15	3	14	6	13	16	11	9	7	10	1	2	8
g	7	2	1	3	15	11	4	10	5	6	8	14	16	9	12	13
h	10	6	9	8	7	2	16	12	4	1	13	15	11	3	14	5
i	5	8	3	1	11	16	12	4	7	13	10	6	2	14	15	9
j	16	14	15	13	1	7	5	3	2	12	11	9	4	8	10	6
k	6	11	4	12	14	9	10	2	3	15	1	8	7	5	13	16
l	9	7	2	10	8	6	13	15	14	16	4	5	3	12	1	11
m	2	13	16	9	12	5	7	8	6	10	15	4	14	11	3	1
n	12	15	5	7	4	3	14	1	13	9	16	11	8	10	6	2
o	8	3	10	6	13	15	11	9	1	2	14	12	5	16	4	7
p	11	1	14	4	6	10	2	16	8	7	5	3	12	13	9	15