## 24 x 14 Kakuro Challenge

For fans of Kakuro

### 24 x 14 Kakuro Challenge

A sample puzzle from my catalog - it is challenging, but it is still definitely P&P solvable.

Due to the size and nature of the grid, you will probably need some hours to complete it (and lots of tea!).

Hopefully someone will enjoy puzzles like this, as I do. If so I can keep them coming.

Puzzle image: Show
RB0000_1.png (178.94 KiB) Viewed 462 times

RB0000_1 Solution: Show
Code: Select all
95.598.745.98
89.7523698.21
7498.918.4879
215473.471236
16.1548296.14
6359.695.2143
57869...13265
421.38974.957
..38.271.98..
842631.957624
97.7942513.13
73.4756321.98
42.9867435.79
619253.876935
..13.986.28..
126.37529.574
56891...52346
4172.974.1687
34.5823174.32
758391.387259
8796.896.3125
98.4837216.98
63.794.968.13

Mathimagics
2017 Supporter

Posts: 1762
Joined: 27 May 2015
Location: Canberra

### Re: 24 x 14 Kakuro Challenge

Hi Mathimagics,

I don't have time to solve so large puzzles manually. Most large puzzles have many obvious elementary steps, which makes them very boring. This is no exception.
Some preliminary analysis of the data shows a great number of magic sectors:
Hidden Text: Show
Code: Select all
horizontal-magic-sector: hr24c12 = 13
horizontal-magic-sector: hr24c8 = 689
horizontal-magic-sector: hr23c12 = 89
horizontal-magic-sector: hr23c1 = 89
horizontal-magic-sector: hr22c10 = 1235
horizontal-magic-sector: hr22c6 = 689
horizontal-magic-sector: hr22c1 = 6789
horizontal-magic-sector: hr16c6 = 689
horizontal-magic-sector: hr16c3 = 13
horizontal-magic-sector: hr15c8 = 356789
horizontal-magic-sector: hr14c12 = 79
horizontal-magic-sector: hr14c4 = 3456789
horizontal-magic-sector: hr13c12 = 89
horizontal-magic-sector: hr13c4 = 1234567
horizontal-magic-sector: hr12c12 = 13
horizontal-magic-sector: hr12c1 = 79
horizontal-magic-sector: hr10c10 = 89
horizontal-magic-sector: hr9c1 = 124
horizontal-magic-sector: hr8c1 = 56789
horizontal-magic-sector: hr7c10 = 1234
horizontal-magic-sector: hr5c1 = 123457
horizontal-magic-sector: hr3c12 = 12
horizontal-magic-sector: hr3c1 = 89
horizontal-magic-sector: hr2c12 = 89
vertical-magic-sector: vr16c14 = 23456789
vertical-magic-sector: vr1c14 = 13456789
vertical-magic-sector: vr16c13 = 12345789
vertical-magic-sector: vr1c13 = 12345679
vertical-magic-sector: vr20c12 = 12
vertical-magic-sector: vr1c11 = 1234568
vertical-magic-sector: vr4c10 = 79
vertical-magic-sector: vr8c9 = 123456789
vertical-magic-sector: vr21c8 = 79
vertical-magic-sector: vr8c8 = 79
vertical-magic-sector: vr5c8 = 89
vertical-magic-sector: vr2c8 = 13
vertical-magic-sector: vr8c7 = 123456789
vertical-magic-sector: vr22c6 = 89
vertical-magic-sector: vr19c6 = 89
vertical-magic-sector: vr16c6 = 13
vertical-magic-sector: vr20c4 = 89
vertical-magic-sector: vr16c3 = 12345678
vertical-magic-sector: vr1c3 = 12345679
vertical-magic-sector: vr16c2 = 13456789
vertical-magic-sector: vr10c2 = 46789
vertical-magic-sector: vr1c2 = 12456789

Here is now KakuRules pure logic solution.
The resolution rules used are the general whips and g-whips defined in my book "Pattern-Based Constraint Satisfaction and Logic Puzzles (available at https://arxiv.org/abs/1304.1628). The resolution strategy is the default "simple-first" one.
This puzzle is one more example of the power of g-whips in Kakuro.
In my rating system, it is in gW8.

Hidden Text: Show
Code: Select all
***********************************************************************************************
***  KakuRules 2.0.s based on CSP-Rules 2.0.s, config = gW+S
***  using CLIPS 6.31-r738
***********************************************************************************************
Uppermost (black) row and leftmost (black) column have index 1
naked-single ==> r24c14 = 3
naked-single ==> r24c13 = 1
naked-single ==> r24c10 = 6
naked-single ==> r23c3 = 8
naked-single ==> r23c2 = 9
naked-single ==> r22c8 = 9
naked-single ==> r23c8 = 7
naked-single ==> r14c2 = 4
naked-single ==> r12c3 = 7
naked-single ==> r12c2 = 9
naked-single ==> r10c8 = 7
naked-single ==> r9c8 = 9
naked-single ==> r5c10 = 7
naked-single ==> r6c10 = 9
naked-single ==> r6c8 = 8
naked-single ==> r7c8 = 9
naked-single ==> r5c4 = 5
naked-single ==> r3c14 = 1
naked-single ==> r3c13 = 2
naked-single ==> r3c3 = 9
naked-single ==> r3c2 = 8
naked-single ==> r2c13 = 9
naked-single ==> r2c14 = 8
naked-single ==> vr3c4 = 59
naked-single ==> r4c4 = 9
naked-single ==> hr5c8 = 123467
naked-single ==> hr10c6 = 127
naked-single ==> vr10c3 = 12347
naked-single ==> hr14c1 = 24
naked-single ==> r14c3 = 2
naked-single ==> vr22c10 = 16
naked-single ==> r23c10 = 1
hidden-single-for-magic-digit-in-horiz-sector ==> r4c5 = 8
cell-to-horiz-ctr  ==> hr13c1 ≠ 28
ctr-to-horiz-sector  ==> r13c2 ≠ 8
cell-to-horiz-ctr  ==> hr13c1 ≠ 19
ctr-to-horiz-sector  ==> r13c3 ≠ 1
cell-to-horiz-ctr  ==> hr11c1 ≠ 123459
ctr-to-horiz-sector  ==> r11c4 ≠ 9
ctr-to-horiz-sector  ==> r11c5 ≠ 9
ctr-to-horiz-sector  ==> r11c6 ≠ 9
ctr-to-horiz-sector  ==> r11c7 ≠ 9
cell-to-horiz-ctr  ==> hr4c6 ≠ 279
ctr-to-horiz-sector  ==> r4c7 ≠ 2
ctr-to-horiz-sector  ==> r4c9 ≠ 2
cell-to-horiz-ctr  ==> hr4c6 ≠ 459
cell-to-horiz-ctr  ==> hr4c6 ≠ 468
ctr-to-horiz-sector  ==> r4c9 ≠ 4
ctr-to-horiz-sector  ==> r4c7 ≠ 4
cell-to-horiz-ctr  ==> hr4c6 ≠ 567
ctr-to-horiz-sector  ==> r4c9 ≠ 5
ctr-to-horiz-sector  ==> r4c7 ≠ 5
cell-to-horiz-ctr  ==> hr17c5 ≠ 24569
cell-to-horiz-ctr  ==> hr17c5 ≠ 24578
cell-to-horiz-ctr  ==> hr18c1 ≠ 24689
cell-to-horiz-ctr  ==> hr18c1 ≠ 25679
cell-to-horiz-ctr  ==> hr21c8 ≠ 345679
cell-to-verti-ctr  ==> vr18c7 ≠ 123579
cell-to-verti-ctr  ==> vr18c9 ≠ 124567
cell-to-verti-ctr  ==> vr10c14 ≠ 24689
cell-to-verti-ctr  ==> vr10c14 ≠ 25679
cell-to-verti-ctr  ==> vr10c13 ≠ 13567
cell-to-verti-ctr  ==> vr10c13 ≠ 23467
cell-to-verti-ctr  ==> vr10c13 ≠ 12568
cell-to-verti-ctr  ==> vr10c13 ≠ 13468
cell-to-verti-ctr  ==> vr10c13 ≠ 23458
cell-to-verti-ctr  ==> vr14c4 ≠ 25789
ctr-to-verti-sector  ==> r15c4 ≠ 2
ctr-to-verti-sector  ==> r17c4 ≠ 2
ctr-to-verti-sector  ==> r18c4 ≠ 2
ctr-to-verti-sector  ==> r19c4 ≠ 2
cell-to-verti-ctr  ==> vr14c4 ≠ 45679
horiz-sector-to-ctr  ==> hr2c1 ≠ 68
naked-single ==> hr2c1 = 59
naked-single ==> r2c3 = 5
naked-single ==> r2c2 = 9
horiz-sector-to-ctr  ==> hr6c12 ≠ 23
naked-single ==> hr6c12 = 14
naked-single ==> r6c14 = 4
naked-single ==> r7c14 = 3
naked-single ==> r5c14 = 6
naked-single ==> r6c13 = 1
naked-single ==> r7c13 = 4
naked-single ==> r5c13 = 3
cell-to-horiz-ctr  ==> hr9c11 ≠ 489
ctr-to-horiz-sector  ==> r9c12 ≠ 4
cell-to-verti-ctr  ==> vr3c12 ≠ 37
ctr-to-verti-sector  ==> r4c12 ≠ 7
cell-to-verti-ctr  ==> vr6c12 ≠ 34568
horiz-sector-to-ctr  ==> hr20c12 ≠ 14
naked-single ==> hr20c12 = 23
naked-single ==> r20c14 = 2
naked-single ==> r22c14 = 5
naked-single ==> r20c13 = 3
naked-single ==> r22c13 = 2
naked-single ==> r22c12 = 1
naked-single ==> r22c11 = 3
naked-single ==> r21c12 = 2
ctr-to-horiz-sector  ==> r21c11 ≠ 1
ctr-to-horiz-sector  ==> r21c9 ≠ 1
hidden-single-for-magic-digit-in-verti-sector ==> r20c9 = 1
hidden-single-for-magic-digit-in-verti-sector ==> r23c9 = 2
verti-sector-to-ctr  ==> vr18c8 ≠ 19
ctr-to-verti-sector  ==> r19c8 ≠ 9
ctr-to-verti-sector  ==> r20c8 ≠ 9
verti-sector-to-ctr  ==> vr4c6 ≠ 48
ctr-to-verti-sector  ==> r5c6 ≠ 4
ctr-to-verti-sector  ==> r6c6 ≠ 4
verti-sector-to-ctr  ==> vr4c6 ≠ 39
naked-single ==> vr4c6 = 57
naked-single ==> r5c6 = 7
naked-single ==> r6c6 = 5
naked-pairs-in-horiz-sector: r21{c4 c6}{n8 n9} ==> r21c7 ≠ 9
naked-pairs-in-horiz-sector: r21{c4 c6}{n8 n9} ==> r21c7 ≠ 8
naked-pairs-in-horiz-sector: r21{c4 c6}{n8 n9} ==> r21c5 ≠ 9
naked-pairs-in-horiz-sector: r21{c4 c6}{n8 n9} ==> r21c5 ≠ 8
naked-pairs-in-horiz-sector: r21{c4 c6}{n8 n9} ==> r21c2 ≠ 8
x-wing-in-horiz-sectors: n9{r13 r14}{c13 c14} ==> r15c14 ≠ 9
x-wing-in-horiz-sectors: n9{r13 r14}{c13 c14} ==> r15c13 ≠ 9
x-wing-in-horiz-sectors: n9{r13 r14}{c13 c14} ==> r11c14 ≠ 9
x-wing-in-horiz-sectors: n9{r13 r14}{c13 c14} ==> r11c13 ≠ 9
biv-chain[2]: r13n9{c13 c14} - r14n9{c14 c13} ==> vr10c13 ≠ 12478
ctr-to-verti-sector  ==> r11c13 ≠ 8
ctr-to-verti-sector  ==> r13c13 ≠ 8
naked-single ==> r13c13 = 9
naked-single ==> r14c13 = 7
naked-single ==> r14c14 = 9
naked-single ==> r13c14 = 8
naked-single ==> vr10c13 = 12379
naked-single ==> r15c13 = 3
naked-single ==> r12c13 = 1
naked-single ==> r12c14 = 3
naked-single ==> r11c13 = 2
ctr-to-verti-sector  ==> r11c14 ≠ 6
ctr-to-verti-sector  ==> r15c14 ≠ 6
ctr-to-verti-sector  ==> r11c14 ≠ 1
verti-sector-to-ctr  ==> vr10c14 ≠ 23789
naked-single ==> vr10c14 = 34589
naked-single ==> r15c14 = 5
naked-single ==> r11c14 = 4
ctr-to-horiz-sector  ==> r11c9 ≠ 1
ctr-to-horiz-sector  ==> r11c10 ≠ 1
ctr-to-horiz-sector  ==> r11c11 ≠ 1
ctr-to-horiz-sector  ==> r11c12 ≠ 1
biv-chain[2]: c10n2{r13 r12} - c10n1{r12 r13} ==> r13c10 ≠ 3
biv-chain[2]: c10n2{r13 r12} - c10n1{r12 r13} ==> r13c10 ≠ 4
biv-chain[2]: c10n2{r13 r12} - c10n1{r12 r13} ==> r13c10 ≠ 5
biv-chain[2]: c10n2{r13 r12} - c10n1{r12 r13} ==> r13c10 ≠ 6
biv-chain[2]: c10n2{r13 r12} - c10n1{r12 r13} ==> r13c10 ≠ 7
biv-chain[2]: c10n1{r12 r13} - c10n2{r13 r12} ==> r12c10 ≠ 3
biv-chain[2]: c10n1{r12 r13} - c10n2{r13 r12} ==> r12c10 ≠ 4
biv-chain[2]: c10n1{r12 r13} - c10n2{r13 r12} ==> r12c10 ≠ 5
biv-chain[2]: c10n1{r12 r13} - c10n2{r13 r12} ==> r12c10 ≠ 6
biv-chain[2]: c10n1{r12 r13} - c10n2{r13 r12} ==> r12c10 ≠ 7
biv-chain[2]: c10n1{r12 r13} - c10n2{r13 r12} ==> r12c10 ≠ 8
biv-chain[2]: vr17c11{n1234579 n1234678} - r24c11{n9 n8} ==> r18c11 ≠ 8
biv-chain[2]: vr17c11{n1234579 n1234678} - r24c11{n9 n8} ==> r19c11 ≠ 8
biv-chain[2]: vr17c11{n1234579 n1234678} - r24c11{n9 n8} ==> r20c11 ≠ 8
biv-chain[2]: vr17c11{n1234579 n1234678} - r24c11{n9 n8} ==> r21c11 ≠ 8
biv-chain[2]: vr17c11{n1234579 n1234678} - r24c11{n9 n8} ==> r23c11 ≠ 8
biv-chain[2]: vr17c11{n1234678 n1234579} - r24c11{n8 n9} ==> r18c11 ≠ 9
biv-chain[2]: vr17c11{n1234678 n1234579} - r24c11{n8 n9} ==> r19c11 ≠ 9
biv-chain[2]: vr17c11{n1234678 n1234579} - r24c11{n8 n9} ==> r20c11 ≠ 9
biv-chain[2]: vr17c11{n1234678 n1234579} - r24c11{n8 n9} ==> r21c11 ≠ 9
biv-chain[2]: vr17c11{n1234678 n1234579} - r24c11{n8 n9} ==> r23c11 ≠ 9
biv-chain[2]: hr3c4{n1456789 n2356789} - r3c8{n1 n3} ==> r3c5 ≠ 3
biv-chain[2]: hr3c4{n1456789 n2356789} - r3c8{n1 n3} ==> r3c7 ≠ 3
biv-chain[2]: hr3c4{n1456789 n2356789} - r3c8{n1 n3} ==> r3c9 ≠ 3
biv-chain[2]: hr3c4{n1456789 n2356789} - r3c8{n1 n3} ==> r3c11 ≠ 3
biv-chain[2]: hr3c4{n2356789 n1456789} - r3c8{n3 n1} ==> r3c5 ≠ 1
biv-chain[2]: hr3c4{n2356789 n1456789} - r3c8{n3 n1} ==> r3c7 ≠ 1
biv-chain[2]: hr3c4{n2356789 n1456789} - r3c8{n3 n1} ==> r3c9 ≠ 1
biv-chain[2]: hr3c4{n2356789 n1456789} - r3c8{n3 n1} ==> r3c11 ≠ 1
biv-chain[2]: hr8c9{n12347 n12356} - r8c14{n7 n5} ==> r8c11 ≠ 5
biv-chain[2]: hr8c9{n12347 n12356} - r8c14{n7 n5} ==> r8c12 ≠ 5
biv-chain[2]: hr8c9{n12347 n12356} - r8c14{n7 n5} ==> r8c13 ≠ 5
biv-chain[2]: r8c13{n7 n6} - hr8c9{n12347 n12356} ==> r8c12 ≠ 7
biv-chain[2]: r8c13{n7 n6} - hr8c9{n12347 n12356} ==> r8c14 ≠ 7
naked-single ==> r8c14 = 5
naked-single ==> hr8c9 = 12356
naked-single ==> r8c13 = 6
verti-sector-to-ctr  ==> vr6c12 ≠ 24578
verti-sector-to-ctr  ==> vr6c12 ≠ 24569
verti-sector-to-ctr  ==> vr6c12 ≠ 23489
verti-sector-to-ctr  ==> vr6c12 ≠ 14678
verti-sector-to-ctr  ==> vr6c12 ≠ 14579
x-wing-in-verti-sectors: n7{c13 c14}{r4 r9} ==> r9c12 ≠ 7
biv-chain[2]: c13n7{r4 r9} - c14n7{r9 r4} ==> hr4c10 ≠ 5689
naked-single ==> hr4c10 = 4789
naked-single ==> r4c13 = 7
naked-single ==> r9c13 = 5
naked-single ==> r4c14 = 9
naked-single ==> r9c14 = 7
naked-single ==> hr9c11 = 579
naked-single ==> r9c12 = 9
naked-single ==> r10c12 = 8
naked-single ==> r10c11 = 9
ctr-to-verti-sector  ==> r11c12 ≠ 7
cell-to-verti-ctr  ==> vr3c12 ≠ 19
ctr-to-verti-sector  ==> r5c12 ≠ 1
verti-sector-to-ctr  ==> vr3c12 ≠ 46
naked-single ==> vr3c12 = 28
naked-single ==> r5c12 = 2
naked-single ==> r4c12 = 8
naked-single ==> r4c11 = 4
naked-single ==> r5c11 = 1
naked-single ==> r7c11 = 2
naked-single ==> r8c11 = 3
naked-single ==> r6c11 = 6
naked-single ==> r7c12 = 1
naked-single ==> r8c12 = 2
naked-single ==> r8c10 = 1
naked-single ==> r5c9 = 4
naked-single ==> vr7c10 = 14
naked-single ==> r9c10 = 4
naked-single ==> vr6c12 = 12689
naked-single ==> r11c12 = 6
naked-single ==> hr11c8 = 245679
naked-single ==> hr6c4 = 1245689
ctr-to-horiz-sector  ==> r9c7 ≠ 2
ctr-to-horiz-sector  ==> r9c9 ≠ 2
ctr-to-horiz-sector  ==> r9c7 ≠ 1
ctr-to-horiz-sector  ==> r9c9 ≠ 1
cell-to-horiz-ctr  ==> hr2c8 ≠ 169
cell-to-horiz-ctr  ==> hr2c8 ≠ 367
cell-to-horiz-ctr  ==> hr2c8 ≠ 349
cell-to-verti-ctr  ==> vr9c11 ≠ 1234689
naked-single ==> vr9c11 = 1235679
cell-to-verti-ctr  ==> vr10c10 ≠ 12348
ctr-to-verti-sector  ==> r14c10 ≠ 8
ctr-to-verti-sector  ==> r15c10 ≠ 8
verti-sector-to-ctr  ==> vr7c6 ≠ 48
ctr-to-verti-sector  ==> r8c6 ≠ 8
hidden-single-in-magic-horiz-sector ==> r8c4 = 8
naked-single ==> vr6c4 = 12358
ctr-to-verti-sector  ==> r9c6 ≠ 8
cell-to-horiz-ctr  ==> hr10c3 ≠ 47
ctr-to-horiz-sector  ==> r10c5 ≠ 4
ctr-to-horiz-sector  ==> r10c5 ≠ 7
horiz-sector-to-ctr  ==> hr7c1 ≠ 4568
horiz-sector-to-ctr  ==> hr7c1 ≠ 3578
horiz-sector-to-ctr  ==> hr7c1 ≠ 2678
horiz-sector-to-ctr  ==> hr7c1 ≠ 2489
horiz-sector-to-ctr  ==> hr7c1 ≠ 1589
naked-pairs-in-horiz-sector: r15{c10 c11}{n6 n7} ==> r15c12 ≠ 7
naked-pairs-in-horiz-sector: r15{c10 c11}{n6 n7} ==> r15c12 ≠ 6
naked-pairs-in-horiz-sector: r15{c10 c11}{n6 n7} ==> r15c9 ≠ 7
naked-pairs-in-horiz-sector: r15{c10 c11}{n6 n7} ==> r15c9 ≠ 6
naked-pairs-in-horiz-sector: r11{c10 c11}{n5 n7} ==> r11c9 ≠ 7
naked-pairs-in-horiz-sector: r11{c10 c11}{n5 n7} ==> r11c9 ≠ 5
naked-single ==> r11c9 = 9
naked-single ==> r15c9 = 8
naked-single ==> r16c9 = 6
naked-single ==> r15c12 = 9
cell-to-verti-ctr  ==> vr15c8 ≠ 67
ctr-to-verti-sector  ==> r17c8 ≠ 6
ctr-to-verti-sector  ==> r17c8 ≠ 7
horiz-sector-to-ctr  ==> hr16c10 ≠ 19
ctr-to-horiz-sector  ==> r16c11 ≠ 1
ctr-to-horiz-sector  ==> r16c12 ≠ 1
x-wing-in-verti-sectors: n1{c10 c11}{r12 r13} ==> r13c9 ≠ 1
x-wing-in-verti-sectors: n1{c10 c11}{r12 r13} ==> r13c8 ≠ 1
x-wing-in-verti-sectors: n1{c10 c11}{r12 r13} ==> r13c7 ≠ 1
x-wing-in-verti-sectors: n1{c10 c11}{r12 r13} ==> r13c5 ≠ 1
x-wing-in-verti-sectors: n1{c10 c11}{r12 r13} ==> r12c9 ≠ 1
x-wing-in-verti-sectors: n1{c10 c11}{r12 r13} ==> r12c8 ≠ 1
verti-sector-to-ctr  ==> vr11c8 ≠ 159
verti-sector-to-ctr  ==> vr11c8 ≠ 168
x-wing-in-verti-sectors: n1{c10 c11}{r12 r13} ==> r12c7 ≠ 1
x-wing-in-verti-sectors: n1{c10 c11}{r12 r13} ==> r12c5 ≠ 1
biv-chain[2]: r16c8{n9 n8} - vr15c8{n49 n58} ==> r17c8 ≠ 9
cell-to-horiz-ctr  ==> hr17c5 ≠ 13679
biv-chain[2]: vr15c8{n49 n58} - r16c8{n9 n8} ==> r17c8 ≠ 8
cell-to-horiz-ctr  ==> hr17c5 ≠ 12689
cell-to-horiz-ctr  ==> hr17c5 ≠ 23678
biv-chain[2]: vr10c10{n12456 n12357} - r15c10{n6 n7} ==> r11c10 ≠ 7
naked-single ==> r11c10 = 5
naked-single ==> r11c11 = 7
naked-single ==> r15c11 = 6
naked-single ==> r15c10 = 7
naked-single ==> vr10c10 = 12357
naked-single ==> r14c10 = 3
naked-single ==> r14c11 = 5
cell-to-horiz-ctr  ==> hr16c10 ≠ 46
ctr-to-horiz-sector  ==> r16c12 ≠ 4
ctr-to-horiz-sector  ==> r16c12 ≠ 6
biv-chain[2]: r16c11{n3 n2} - hr16c10{n37 n28} ==> r16c12 ≠ 3
biv-chain[2]: hr16c10{n37 n28} - r16c11{n3 n2} ==> r16c12 ≠ 2
biv-chain[2]: hr20c4{n1234569 n1234578} - r20c6{n9 n8} ==> r20c5 ≠ 8
biv-chain[2]: hr20c4{n1234569 n1234578} - r20c6{n9 n8} ==> r20c7 ≠ 8
biv-chain[2]: hr20c4{n1234569 n1234578} - r20c6{n9 n8} ==> r20c8 ≠ 8
biv-chain[2]: hr20c4{n1234569 n1234578} - r20c6{n9 n8} ==> r20c10 ≠ 8
biv-chain[2]: hr20c4{n1234578 n1234569} - r20c6{n8 n9} ==> r20c5 ≠ 9
biv-chain[2]: hr20c4{n1234578 n1234569} - r20c6{n8 n9} ==> r20c7 ≠ 9
biv-chain[2]: hr20c4{n1234578 n1234569} - r20c6{n8 n9} ==> r20c10 ≠ 9
biv-chain[2]: r20c10{n7 n6} - vr19c10{n78 n69} ==> r21c10 ≠ 7
biv-chain[2]: r20c10{n7 n6} - hr20c4{n1234578 n1234569} ==> r20c5 ≠ 7
biv-chain[2]: r20c10{n7 n6} - hr20c4{n1234578 n1234569} ==> r20c7 ≠ 7
biv-chain[2]: r20c10{n7 n6} - hr20c4{n1234578 n1234569} ==> r20c8 ≠ 7
biv-chain[2]: r20c10{n7 n6} - hr20c4{n1234578 n1234569} ==> r20c11 ≠ 7
biv-chain[2]: hr20c4{n1234578 n1234569} - r20c10{n7 n6} ==> r20c5 ≠ 6
biv-chain[2]: hr20c4{n1234578 n1234569} - r20c10{n7 n6} ==> r20c7 ≠ 6
biv-chain[2]: hr20c4{n1234578 n1234569} - r20c10{n7 n6} ==> r20c8 ≠ 6
biv-chain[2]: hr20c4{n1234578 n1234569} - r20c10{n7 n6} ==> r20c11 ≠ 6
biv-chain[2]: vr19c10{n78 n69} - r20c10{n7 n6} ==> r21c10 ≠ 6
biv-chain[2]: hr23c4{n1234579 n1234678} - r23c6{n9 n8} ==> r23c5 ≠ 8
biv-chain[2]: hr23c4{n1234579 n1234678} - r23c6{n9 n8} ==> r23c7 ≠ 8
biv-chain[2]: hr23c4{n1234678 n1234579} - r23c6{n8 n9} ==> r23c5 ≠ 9
biv-chain[2]: hr23c4{n1234678 n1234579} - r23c6{n8 n9} ==> r23c7 ≠ 9
biv-chain[2]: r21c4{n8 n9} - r21c6{n9 n8} ==> hr21c1 ≠ 245679
biv-chain[2]: r21c4{n9 n8} - r21c6{n8 n9} ==> hr21c1 ≠ 345678
biv-chain[2]: r22c9{n6 n8} - r24c9{n8 n9} ==> vr18c9 ≠ 123478
ctr-to-verti-sector  ==> r19c9 ≠ 7
ctr-to-verti-sector  ==> r21c9 ≠ 7
biv-chain[2]: vr18c9{n123568 n123469} - r24c9{n8 n9} ==> r19c9 ≠ 9
biv-chain[2]: vr18c9{n123568 n123469} - r24c9{n8 n9} ==> r21c9 ≠ 9
biv-chain[2]: r24c9{n8 n9} - vr18c9{n123568 n123469} ==> r19c9 ≠ 8
biv-chain[2]: r24c9{n8 n9} - vr18c9{n123568 n123469} ==> r21c9 ≠ 8
biv-chain[2]: r24c9{n8 n9} - vr18c9{n123568 n123469} ==> r22c9 ≠ 8
naked-single ==> r22c9 = 6
naked-single ==> r22c7 = 8
whip[2]: r18c6{n3 n1} - hr18c1{n23789 .} ==> r18c5 ≠ 3
whip[2]: r18c6{n1 n3} - hr18c1{n14789 .} ==> r18c5 ≠ 1
whip[2]: r18c6{n3 n1} - hr18c1{n23789 .} ==> r18c4 ≠ 3
whip[2]: r18c6{n1 n3} - hr18c1{n14789 .} ==> r18c4 ≠ 1
whip[2]: r18c6{n3 n1} - hr18c1{n23789 .} ==> r18c3 ≠ 3
whip[2]: r18c6{n1 n3} - hr18c1{n14789 .} ==> r18c3 ≠ 1
whip[2]: r18c6{n3 n1} - hr18c1{n23789 .} ==> r18c2 ≠ 3
whip[2]: r18c6{n1 n3} - hr18c1{n14789 .} ==> r18c2 ≠ 1
whip[2]: r4c8{n3 n1} - hr4c6{n369 .} ==> r4c9 ≠ 3
whip[2]: r4c8{n1 n3} - hr4c6{n189 .} ==> r4c9 ≠ 1
whip[2]: r4c8{n3 n1} - hr4c6{n369 .} ==> r4c7 ≠ 3
whip[2]: r4c8{n1 n3} - hr4c6{n189 .} ==> r4c7 ≠ 1
whip[2]: r16c4{n3 n1} - vr14c4{n34789 .} ==> r19c4 ≠ 3
whip[2]: r16c4{n3 n1} - vr14c4{n34789 .} ==> r17c4 ≠ 3
whip[2]: r16c4{n1 n3} - vr14c4{n16789 .} ==> r19c4 ≠ 1
whip[2]: r16c4{n1 n3} - vr14c4{n16789 .} ==> r17c4 ≠ 1
whip[2]: r16c4{n3 n1} - vr14c4{n34789 .} ==> r15c4 ≠ 3
whip[2]: r16c4{n1 n3} - vr14c4{n16789 .} ==> r15c4 ≠ 1
whip[2]: r6c9{n2 n1} - vr1c9{n234689 .} ==> r3c9 ≠ 2
whip[2]: r6c9{n2 n1} - vr1c9{n234689 .} ==> r2c9 ≠ 2
horiz-sector-to-ctr  ==> hr2c8 ≠ 259
ctr-to-horiz-sector  ==> r2c10 ≠ 9
ctr-to-horiz-sector  ==> r2c9 ≠ 9
horiz-sector-to-ctr  ==> hr2c8 ≠ 268
ctr-to-horiz-sector  ==> r2c10 ≠ 6
ctr-to-horiz-sector  ==> r2c9 ≠ 6
whip[2]: r6c9{n1 n2} - vr1c9{n134789 .} ==> r2c9 ≠ 1
horiz-sector-to-ctr  ==> hr2c8 ≠ 178
whip[2]: hr24c1{n45 n27} - r24c2{n1 .} ==> r24c3 ≠ 7
whip[2]: hr24c1{n45 n18} - r24c3{n2 .} ==> r24c2 ≠ 1
whip[2]: hr20c1{n34 n25} - r20c2{n1 .} ==> r20c3 ≠ 5
whip[2]: hr19c6{n578 n479} - r19c9{n3 .} ==> r19c8 ≠ 4
whip[2]: hr19c6{n578 n389} - r19c9{n4 .} ==> r19c8 ≠ 3
whip[2]: hr19c6{n578 n569} - r19c8{n7 .} ==> r19c7 ≠ 6
whip[2]: hr19c6{n578 n479} - r19c9{n3 .} ==> r19c7 ≠ 4
whip[2]: hr19c6{n578 n389} - r19c9{n4 .} ==> r19c7 ≠ 3
whip[2]: hr19c1{n2345 n1238} - r19c4{n4 .} ==> r19c5 ≠ 8
whip[2]: hr19c1{n2345 n1238} - r19c4{n4 .} ==> r19c2 ≠ 8
whip[2]: hr18c9{n23456 n12359} - r18c14{n4 .} ==> r18c13 ≠ 9
whip[2]: hr18c9{n23456 n12359} - r18c14{n4 .} ==> r18c10 ≠ 9
whip[2]: r18c13{n8 n5} - r18c10{n5 .} ==> hr18c9 ≠ 12359
ctr-to-horiz-sector  ==> r18c14 ≠ 9
whip[2]: hr17c1{n234 n126} - r17c4{n4 .} ==> r17c3 ≠ 6
whip[2]: hr17c1{n234 n135} - r17c4{n4 .} ==> r17c3 ≠ 5
whip[2]: hr17c1{n135 n234} - r17c4{n5 .} ==> r17c3 ≠ 4
whip[2]: hr17c1{n234 n126} - r17c4{n4 .} ==> r17c2 ≠ 6
whip[2]: hr17c1{n234 n135} - r17c4{n4 .} ==> r17c2 ≠ 5
whip[2]: hr17c1{n135 n234} - r17c4{n5 .} ==> r17c2 ≠ 4
whip[2]: hr10c3{n38 n56} - r10c4{n2 .} ==> r10c5 ≠ 5
whip[2]: hr10c3{n56 n38} - r10c4{n2 .} ==> r10c5 ≠ 3
whip[2]: hr10c3{n56 n29} - r10c4{n3 .} ==> r10c5 ≠ 2
whip[2]: hr7c6{n569 n479} - r7c9{n3 .} ==> r7c7 ≠ 7
whip[2]: hr7c1{n3569 n1679} - r7c4{n2 .} ==> r7c5 ≠ 1
whip[2]: hr7c1{n3569 n1679} - r7c4{n2 .} ==> r7c3 ≠ 1
whip[2]: hr7c1{n3569 n1679} - r7c4{n2 .} ==> r7c2 ≠ 1
whip[2]: hr6c1{n25 n34} - r6c2{n1 .} ==> r6c3 ≠ 4
whip[2]: hr6c1{n34 n25} - r6c3{n1 .} ==> r6c2 ≠ 2
whip[2]: hr4c1{n4789 n5689} - r4c3{n4 .} ==> r4c2 ≠ 6
whip[2]: vr18c7{n134568 n123489} - r19c7{n5 .} ==> r24c7 ≠ 9
whip[2]: hr24c4{n578 n389} - r24c7{n7 .} ==> r24c5 ≠ 3
whip[2]: vr14c4{n35689 n34789} - r17c4{n5 .} ==> r19c4 ≠ 4
whip[2]: hr19c1{n2345 n1247} - r19c4{n8 .} ==> r19c5 ≠ 7
whip[2]: hr19c1{n2345 n1247} - r19c4{n8 .} ==> r19c3 ≠ 7
whip[2]: hr19c1{n2345 n1247} - r19c4{n8 .} ==> r19c2 ≠ 7
whip[2]: vr14c4{n35689 n34789} - r17c4{n5 .} ==> r18c4 ≠ 4
whip[2]: vr16c10{n68 n59} - r18c10{n6 .} ==> r17c10 ≠ 5
whip[2]: vr14c4{n35689 n34789} - r17c4{n5 .} ==> r15c4 ≠ 4
whip[2]: vr1c5{n1456789 n2356789} - r6c5{n1 .} ==> r7c5 ≠ 2
whip[2]: vr1c5{n1456789 n2356789} - r6c5{n1 .} ==> r5c5 ≠ 2
whip[2]: vr1c5{n1456789 n2356789} - r5c5{n4 .} ==> r7c5 ≠ 3
whip[2]: vr1c10{n58 n67} - r2c10{n4 .} ==> r3c10 ≠ 7
whip[2]: vr1c10{n67 n49} - r2c10{n5 .} ==> r3c10 ≠ 4
whip[2]: vr1c5{n1456789 n2356789} - r6c5{n1 .} ==> r3c5 ≠ 2
g-whip[2]: r19c9{n5 n34} - hr19c6{n578 .} ==> r19c7 ≠ 5
cell-to-verti-ctr  ==> vr18c7 ≠ 134568
whip[2]: r19c7{n7 n9} - vr18c7{n123678 .} ==> r21c7 ≠ 7
whip[2]: r19c7{n7 n9} - vr18c7{n123678 .} ==> r24c7 ≠ 7
whip[2]: hr24c4{n578 n479} - r24c7{n6 .} ==> r24c5 ≠ 4
whip[3]: r10c7{n2 n1} - c9n1{r10 r17} - hr17c5{n23489 .} ==> r17c7 ≠ 2
whip[3]: r2c11{n5 n8} - hr2c8{n457 n358} - r2c10{n4 .} ==> r2c9 ≠ 5
whip[2]: hr2c8{n358 n457} - r2c9{n8 .} ==> r2c10 ≠ 7
cell-to-verti-ctr  ==> vr1c10 ≠ 67
ctr-to-verti-sector  ==> r3c10 ≠ 6
whip[3]: r2c11{n8 n5} - r2c10{n5 n4} - hr2c8{n358 .} ==> r2c9 ≠ 8
whip[3]: r18c13{n7 n8} - r18c14{n8 n6} - r18c10{n6 .} ==> hr18c9 ≠ 12368
whip[3]: hr9c5{n34789 n45679} - r9c9{n3 n7} - r9c6{n7 .} ==> r9c7 ≠ 5
whip[3]: hr9c5{n45679 n34789} - r9c9{n5 n7} - r9c6{n7 .} ==> r9c7 ≠ 3
whip[3]: vr1c5{n2356789 n1456789} - r6c5{n2 n1} - r5c5{n1 .} ==> r7c5 ≠ 4
whip[3]: vr1c5{n2356789 n1456789} - r6c5{n2 n1} - r5c5{n1 .} ==> r3c5 ≠ 4
whip[3]: vr18c7{n124578 n123678} - r24c7{n5 n3} - r23c7{n3 .} ==> r21c7 ≠ 6
whip[3]: vr18c7{n123678 n124578} - r24c7{n6 n4} - r23c7{n4 .} ==> r20c7 ≠ 5
whip[3]: vr18c7{n123678 n124578} - r24c7{n6 n4} - r23c7{n4 .} ==> r21c7 ≠ 5
whip[4]: r17c6{n3 n1} - hr17c5{n34568 n13589} - r17c9{n7 n5} - r17c8{n5 .} ==> r17c7 ≠ 3
whip[4]: r17c6{n1 n3} - hr17c5{n14678 n13589} - r17c9{n7 n5} - r17c8{n5 .} ==> r17c7 ≠ 1
whip[4]: hr18c9{n23456 n12458} - r18c10{n6 n5} - r18c13{n5 n4} - r18c14{n4 .} ==> r18c12 ≠ 8
whip[5]: c11n8{r3 r2} - hr2c8{n457 n358} - r2c10{n4 n5} - r3c10{n5 n9} - vr1c10{n58 .} ==> r3c9 ≠ 8
whip[5]: r3c11{n8 n5} - r3c10{n5 n9} - r3c6{n9 n6} - r3c9{n6 n7} - r3c5{n7 .} ==> r3c7 ≠ 8
whip[5]: c11n8{r3 r2} - hr2c8{n457 n358} - r2c10{n4 n5} - r3c10{n5 n9} - vr1c10{n58 .} ==> r3c6 ≠ 8
whip[2]: vr1c6{n59 n68} - r3c6{n9 .} ==> r2c6 ≠ 6
whip[5]: r3c11{n5 n8} - r3c10{n8 n9} - r3c6{n9 n6} - r3c9{n6 n7} - r3c5{n7 .} ==> r3c7 ≠ 5
whip[5]: r23n3{c7 c5} - r20n3{c5 c8} - vr18c8{n46 n37} - r19c8{n8 n7} - r19c7{n7 .} ==> vr18c7 ≠ 124578
ctr-to-verti-sector  ==> r23c7 ≠ 5
ctr-to-verti-sector  ==> r24c7 ≠ 5
cell-to-horiz-ctr  ==> hr24c4 ≠ 578
whip[2]: hr24c4{n479 n569} - r24c7{n3 .} ==> r24c5 ≠ 6
whip[3]: vr18c7{n123678 n123489} - r23c7{n6 n3} - r24c7{n3 .} ==> r21c7 ≠ 4
whip[3]: vr18c7{n123678 n123489} - r23c7{n6 n3} - r24c7{n3 .} ==> r20c7 ≠ 4
whip[5]: hr23c4{n1234678 n1234579} - c6n8{r23 r24} - hr24c4{n569 n389} - r24c7{n4 n3} - r23n3{c7 .} ==> r23c5 ≠ 5
g-whip[5]: r18c10{n6 n3589} - hr18c9{n12467 n23456} - r18c14{n8 n4} - r18c13{n4 n5} - r18c10{n5 .} ==> r18c12 ≠ 6
g-whip[5]: r18c10{n6 n3589} - hr18c9{n12467 n23456} - r18c14{n8 n4} - r18c13{n4 n5} - r18c10{n5 .} ==> r18c11 ≠ 6
g-whip[5]: r17c14{n8 n124679} - hr17c11{n358 n123678} - r17c13{n4 n7} - r17c14{n7 n6} - hr17c11{n178 .} ==> r17c12 ≠ 8
whip[6]: hr21c8{n235789 n245689} - r21c9{n3 n5} - r21c11{n5 n6} - vr17c11{n1234579 n1234678} - r24n9{c11 c9} - vr18c9{n123568 .} ==> r21c14 ≠ 4
whip[6]: hr21c8{n235789 n245689} - r21c9{n3 n5} - r21c11{n5 n6} - vr17c11{n1234579 n1234678} - r24n9{c11 c9} - vr18c9{n123568 .} ==> r21c13 ≠ 4
whip[6]: hr7c1{n3569 n3479} - r7c4{n5 n3} - r7c3{n3 n7} - r8c3{n7 n6} - r4c3{n6 n4} - r9n4{c3 .} ==> r7c2 ≠ 4
whip[7]: vr18c7{n123489 n123678} - r24c7{n4 n3} - r23n3{c7 c5} - r20n3{c5 c8} - vr18c8{n46 n37} - r19c8{n8 n7} - r19c7{n7 .} ==> r23c7 ≠ 6
whip[3]: r23c7{n3 n4} - vr18c7{n123678 n123489} - r24c7{n6 .} ==> r21c7 ≠ 3
whip[3]: r23c7{n3 n4} - vr18c7{n123678 n123489} - r24c7{n6 .} ==> r20c7 ≠ 3
naked-single ==> r20c7 = 2
naked-single ==> r21c7 = 1
cell-to-verti-ctr  ==> vr18c8 ≠ 28
ctr-to-verti-sector  ==> r19c8 ≠ 8
cell-to-horiz-ctr  ==> hr19c6 ≠ 389
ctr-to-horiz-sector  ==> r19c9 ≠ 3
horiz-sector-to-ctr  ==> hr19c6 ≠ 578
biv-chain[2]: c11n2{r19 r18} - c11n1{r18 r19} ==> hr19c10 ≠ 3469
biv-chain[2]: c11n2{r19 r18} - c11n1{r18 r19} ==> hr19c10 ≠ 3478
biv-chain[2]: c11n2{r19 r18} - c11n1{r18 r19} ==> hr19c10 ≠ 3568
biv-chain[2]: c11n2{r19 r18} - c11n1{r18 r19} ==> hr19c10 ≠ 4567
biv-chain[2]: c11n2{r19 r18} - c11n1{r18 r19} ==> r19c11 ≠ 4
biv-chain[2]: c11n2{r19 r18} - c11n1{r18 r19} ==> r19c11 ≠ 5
biv-chain[2]: c11n2{r19 r18} - c11n1{r18 r19} ==> r19c11 ≠ 6
biv-chain[2]: c11n2{r19 r18} - c11n1{r18 r19} ==> r19c11 ≠ 7
biv-chain[2]: c11n1{r18 r19} - c11n2{r19 r18} ==> r18c11 ≠ 4
biv-chain[2]: c11n1{r18 r19} - c11n2{r19 r18} ==> r18c11 ≠ 5
biv-chain[2]: c11n1{r18 r19} - c11n2{r19 r18} ==> r18c11 ≠ 7
hidden-single-for-magic-digit-in-verti-sector ==> r21c11 = 7
naked-single ==> hr21c8 = 235789
naked-pairs-in-verti-sector: c14{r21 r23}{n8 n9} ==> r19c14 ≠ 9
naked-pairs-in-verti-sector: c14{r21 r23}{n8 n9} ==> r19c14 ≠ 8
cell-to-horiz-ctr  ==> hr19c10 ≠ 2389
ctr-to-horiz-sector  ==> r19c12 ≠ 3
naked-pairs-in-verti-sector: c14{r21 r23}{n8 n9} ==> r18c14 ≠ 8
naked-pairs-in-verti-sector: c14{r21 r23}{n8 n9} ==> r17c14 ≠ 9
cell-to-horiz-ctr  ==> hr17c11 ≠ 259
naked-pairs-in-verti-sector: c14{r21 r23}{n8 n9} ==> r17c14 ≠ 8
cell-to-horiz-ctr  ==> hr17c11 ≠ 358
naked-pairs-in-horiz-sector: r21{c10 c14}{n8 n9} ==> r21c13 ≠ 9
naked-pairs-in-horiz-sector: r21{c10 c14}{n8 n9} ==> r21c13 ≠ 8
naked-single ==> r21c13 = 5
naked-single ==> r21c9 = 3
biv-chain[2]: r19c8{n7 n6} - hr19c6{n479 n569} ==> r19c7 ≠ 7
naked-single ==> r19c7 = 9
naked-single ==> vr18c7 = 123489
cell-to-horiz-ctr  ==> hr24c4 ≠ 569
ctr-to-horiz-sector  ==> r24c5 ≠ 5
whip[2]: r19c11{n2 n1} - hr19c10{n2479 .} ==> r19c12 ≠ 2
whip[2]: r19c11{n1 n2} - hr19c10{n1489 .} ==> r19c12 ≠ 1
whip[3]: hr18c9{n23456 n12458} - r18c14{n6 n4} - r18c13{n4 .} ==> r18c10 ≠ 8
biv-chain[2]: r18c10{n6 n5} - vr16c10{n68 n59} ==> r17c10 ≠ 6
whip[4]: r18c10{n5 n6} - hr18c9{n12458 n23456} - r18c13{n7 n4} - r18c14{n4 .} ==> r18c12 ≠ 5
g-whip[4]: hr17c11{n457 n12356789} - r17c14{n4 n7} - hr17c11{n169 n367} - r17c13{n4 .} ==> r17c12 ≠ 6
g-whip[4]: hr17c11{n367 n12345789} - r17c14{n6 n7} - hr17c11{n169 n457} - r17c13{n8 .} ==> r17c12 ≠ 4
g-whip[4]: hr19c10{n2578 n124789} - r19c14{n6 n7} - hr19c10{n1489 n2479} - r19c12{n5 .} ==> r19c13 ≠ 4
whip[5]: r17c12{n7 n2} - vr14c12{n16789 n25789} - r18c12{n1 n7} - c13n7{r18 r19} - c14n7{r19 .} ==> hr17c11 ≠ 268
ctr-to-horiz-sector  ==> r17c12 ≠ 2
whip[5]: r17c12{n7 n1} - vr14c12{n25789 n16789} - r18c12{n2 n7} - c13n7{r18 r19} - c14n7{r19 .} ==> hr17c11 ≠ 169
g-whip[5]: r17c14{n7 n46} - hr17c11{n178 n34567} - r17c13{n9 n4} - hr17c11{n367 n457} - r17c14{n6 .} ==> r17c12 ≠ 7
whip[2]: vr14c12{n45679 n16789} - r17c12{n5 .} ==> r18c12 ≠ 1
g-whip[4]: vr14c12{n16789 n23456789} - r17c12{n1 n3} - vr14c12{n25789 n35689} - r18c12{n2 .} ==> r19c12 ≠ 5
horiz-sector-to-ctr  ==> hr19c10 ≠ 2578
horiz-sector-to-ctr  ==> hr19c10 ≠ 2569
horiz-sector-to-ctr  ==> hr19c10 ≠ 1579
g-whip[5]: hr18c9{n12458 n1234567} - r18c13{n8 n4} - r18c14{n4 n6} - hr18c9{n13457 n12467} - r18c10{n5 .} ==> r18c12 ≠ 7
cell-to-verti-ctr  ==> vr14c12 ≠ 16789
ctr-to-verti-sector  ==> r17c12 ≠ 1
cell-to-horiz-ctr  ==> hr17c11 ≠ 178
ctr-to-horiz-sector  ==> r17c13 ≠ 8
g-whip[4]: r17c12{n5 n3} - vr14c12{n25789 n3456789} - r18c12{n2 n4} - c13n4{r18 .} ==> hr17c11 ≠ 367
ctr-to-horiz-sector  ==> r17c14 ≠ 6
whip[3]: c11n2{r18 r19} - hr19c10{n1678 n2479} - c14n6{r19 .} ==> hr18c9 ≠ 13457
whip[4]: c14n6{r19 r18} - r18c10{n6 n5} - hr18c9{n12467 n23456} - c11n1{r18 .} ==> hr19c10 ≠ 2479
ctr-to-horiz-sector  ==> r19c11 ≠ 2
naked-single ==> r19c11 = 1
naked-single ==> r18c11 = 2
cell-to-verti-ctr  ==> vr14c12 ≠ 25789
horiz-sector-to-ctr  ==> hr18c9 ≠ 12467
ctr-to-horiz-sector  ==> r18c13 ≠ 7
ctr-to-horiz-sector  ==> r18c14 ≠ 7
horiz-sector-to-ctr  ==> hr18c9 ≠ 12458
naked-single ==> hr18c9 = 23456
naked-single ==> r18c13 = 4
naked-single ==> r18c14 = 6
naked-single ==> r18c10 = 5
naked-single ==> r18c12 = 3
naked-single ==> r17c12 = 5
naked-single ==> vr14c12 = 35689
naked-single ==> r16c12 = 8
naked-single ==> r19c12 = 6
naked-single ==> hr19c10 = 1678
naked-single ==> r19c14 = 7
naked-single ==> r19c13 = 8
naked-single ==> r23c13 = 9
naked-single ==> r23c14 = 8
naked-single ==> r21c14 = 9
naked-single ==> r21c10 = 8
naked-single ==> r17c13 = 7
naked-single ==> r17c14 = 4
naked-single ==> vr19c10 = 78
naked-single ==> r20c10 = 7
naked-single ==> hr20c4 = 1234578
naked-single ==> r20c6 = 8
naked-single ==> r21c6 = 9
naked-single ==> r21c4 = 8
naked-single ==> r22c4 = 9
naked-single ==> hr16c10 = 28
naked-single ==> r16c11 = 2
naked-single ==> hr17c11 = 457
naked-single ==> vr16c10 = 59
naked-single ==> r17c10 = 9
ctr-to-horiz-sector  ==> r17c7 ≠ 6
whip[4]: r17c8{n5 n4} - vr15c8{n58 n49} - r16n8{c8 c7} - r17c7{n8 .} ==> hr17c5 ≠ 23489
biv-chain[7]: r20n5{c5 c11} - c11n4{r20 r23} - r23c7{n4 n3} - r24c7{n3 n4} - hr24c4{n389 n479} - r24c6{n8 n9} - c5n9{r24 r18} ==> r18c5 ≠ 5
whip[8]: r3c11{n5 n8} - r3c10{n8 n9} - vr1c10{n58 n49} - r2c10{n8 n4} - hr2c8{n358 n457} - r2c9{n3 n7} - r3c9{n7 n6} - r3c6{n6 .} ==> r3c5 ≠ 5
whip[8]: r7c4{n5 n1} - r9c4{n1 n2} - c2n2{r9 r5} - c3n2{r5 r6} - c3n3{r6 r5} - c3n1{r5 r9} - c2n1{r9 r6} - hr6c1{n25 .} ==> hr7c1 ≠ 1679
ctr-to-horiz-sector  ==> r7c4 ≠ 1
whip[4]: hr7c1{n3479 n3569} - r7c3{n2 n3} - r7c4{n3 n5} - r7c2{n5 .} ==> r7c5 ≠ 6
g-whip[5]: r7c2{n7 n12568} - hr7c1{n3479 n2579} - r7c3{n3 n2} - r7c2{n2 n5} - r7c4{n5 .} ==> r7c5 ≠ 7
whip[8]: hr7c1{n3569 n2579} - r7c3{n6 n7} - r8c3{n7 n6} - c2n6{r8 r6} - r7c2{n6 n5} - r8c2{n5 n7} - r4c2{n7 n4} - r4c3{n4 .} ==> r7c4 ≠ 2
whip[4]: r7c4{n5 n3} - hr7c1{n2579 n3569} - r7c2{n2 n6} - r7c3{n6 .} ==> r7c5 ≠ 5
naked-single ==> r7c5 = 9
hidden-single-in-magic-horiz-sector ==> r8c6 = 9
naked-single ==> vr7c6 = 39
naked-single ==> r9c6 = 3
naked-single ==> hr9c5 = 34789
naked-single ==> r9c9 = 7
naked-single ==> r14c9 = 4
naked-single ==> r9c7 = 8
naked-single ==> r16c7 = 9
naked-single ==> r16c8 = 8
naked-single ==> vr15c8 = 58
naked-single ==> r17c8 = 5
cell-to-horiz-ctr  ==> hr17c5 ≠ 13589
biv-chain[2]: hr17c5{n23579 n14579} - r17c6{n3 n1} ==> r17c9 ≠ 1
hidden-single-in-magic-verti-sector ==> r10c9 = 1
naked-single ==> r10c7 = 2
cell-to-horiz-ctr  ==> hr17c5 ≠ 14579
naked-single ==> hr17c5 = 23579
naked-single ==> r17c7 = 7
naked-single ==> r14c7 = 6
naked-single ==> r17c6 = 3
naked-single ==> r18c6 = 1
naked-single ==> r17c9 = 2
ctr-to-horiz-sector  ==> r18c3 ≠ 2
ctr-to-horiz-sector  ==> r18c5 ≠ 2
cell-to-verti-ctr  ==> vr11c8 ≠ 456
x-wing-in-verti-sectors: n1{c3 c7}{r11 r15} ==> r15c5 ≠ 1
x-wing-in-verti-sectors: n1{c3 c7}{r11 r15} ==> r11c5 ≠ 1
x-wing-in-verti-sectors: n1{c3 c7}{r11 r15} ==> r11c4 ≠ 1
hidden-single-for-magic-digit-in-verti-sector ==> r9c4 = 1
x-wing-in-verti-sectors: n1{c2 c3}{r5 r6} ==> r5c7 ≠ 1
x-wing-in-verti-sectors: n1{c2 c3}{r5 r6} ==> r5c5 ≠ 1
biv-chain[2]: r5c5{n4 n3} - vr1c5{n1456789 n2356789} ==> r6c5 ≠ 4
naked-pairs-in-horiz-sector: r6{c5 c9}{n1 n2} ==> r6c7 ≠ 2
cell-to-verti-ctr  ==> vr1c7 ≠ 235679
naked-pairs-in-horiz-sector: r6{c5 c9}{n1 n2} ==> r6c7 ≠ 1
naked-single ==> r6c7 = 4
cell-to-horiz-ctr  ==> hr7c6 ≠ 479
ctr-to-horiz-sector  ==> r7c9 ≠ 7
cell-to-verti-ctr  ==> vr1c7 ≠ 145679
horiz-sector-to-ctr  ==> hr3c4 ≠ 1456789
naked-single ==> hr3c4 = 2356789
naked-single ==> r3c8 = 3
naked-single ==> r4c8 = 1
naked-single ==> hr4c6 = 189
verti-sector-to-ctr  ==> vr1c7 ≠ 134789
biv-chain[2]: c2n1{r6 r5} - c3n1{r5 r6} ==> hr6c1 ≠ 25
ctr-to-horiz-sector  ==> r6c2 ≠ 5
ctr-to-horiz-sector  ==> r6c3 ≠ 2
biv-chain[2]: c2n1{r6 r5} - c3n1{r5 r6} ==> hr6c1 ≠ 34
naked-single ==> hr6c1 = 16
whip[2]: hr2c4{n679 n589} - r2c5{n7 .} ==> r2c7 ≠ 5
whip[2]: hr2c4{n679 n589} - r2c5{n7 .} ==> r2c6 ≠ 5
biv-chain[2]: r2c6{n9 n8} - vr1c6{n59 n68} ==> r3c6 ≠ 9
whip[2]: vr11c8{n357 n249} - r14c8{n7 .} ==> r12c8 ≠ 9
g-whip[2]: vr11c8{n348 n234567} - r14c8{n9 .} ==> r13c8 ≠ 7
g-whip[2]: vr11c8{n357 n1234568} - r14c8{n9 .} ==> r12c8 ≠ 8
g-whip[2]: vr11c8{n348 n234567} - r14c8{n9 .} ==> r12c8 ≠ 7
x-wing-in-horiz-sectors: n7{r12 r13}{c5 c6} ==> r15c6 ≠ 7
x-wing-in-horiz-sectors: n7{r12 r13}{c5 c6} ==> r15c5 ≠ 7
x-wing-in-horiz-sectors: n7{r12 r13}{c5 c6} ==> r14c6 ≠ 7
x-wing-in-horiz-sectors: n7{r12 r13}{c5 c6} ==> r14c5 ≠ 7
hidden-single-in-magic-horiz-sector ==> r14c8 = 7
ctr-to-verti-sector  ==> r13c8 ≠ 4
ctr-to-verti-sector  ==> r12c8 ≠ 4
x-wing-in-horiz-sectors: n7{r12 r13}{c5 c6} ==> r11c6 ≠ 7
x-wing-in-horiz-sectors: n7{r12 r13}{c5 c6} ==> r11c5 ≠ 7
biv-chain[2]: r12n7{c6 c5} - r13n7{c5 c6} ==> vr10c6 ≠ 45689
ctr-to-verti-sector  ==> r11c6 ≠ 4
ctr-to-verti-sector  ==> r12c6 ≠ 4
ctr-to-verti-sector  ==> r13c6 ≠ 4
ctr-to-verti-sector  ==> r15c6 ≠ 4
x-wing-in-horiz-sectors: n4{r12 r13}{c5 c7} ==> r15c7 ≠ 4
x-wing-in-horiz-sectors: n4{r12 r13}{c5 c7} ==> r15c5 ≠ 4
x-wing-in-horiz-sectors: n4{r12 r13}{c5 c7} ==> r11c7 ≠ 4
x-wing-in-horiz-sectors: n4{r12 r13}{c5 c7} ==> r11c5 ≠ 4
biv-chain[2]: r13n4{c5 c7} - r12n4{c7 c5} ==> vr9c5 ≠ 1356789
naked-single ==> vr9c5 = 2346789
naked-single ==> r16c5 = 3
naked-single ==> r16c4 = 1
naked-single ==> vr14c4 = 16789
naked-single ==> r17c4 = 6
naked-single ==> hr17c1 = 126
naked-single ==> r17c2 = 1
naked-single ==> r17c3 = 2
cell-to-horiz-ctr  ==> hr24c1 ≠ 27
ctr-to-horiz-sector  ==> r24c2 ≠ 7
cell-to-horiz-ctr  ==> hr20c1 ≠ 25
ctr-to-horiz-sector  ==> r20c2 ≠ 5
cell-to-horiz-ctr  ==> hr19c1 ≠ 1346
cell-to-horiz-ctr  ==> hr19c1 ≠ 1256
ctr-to-horiz-sector  ==> r19c2 ≠ 6
ctr-to-horiz-sector  ==> r19c3 ≠ 6
ctr-to-horiz-sector  ==> r19c5 ≠ 6
cell-to-horiz-ctr  ==> hr19c1 ≠ 2345
ctr-to-horiz-sector  ==> r19c5 ≠ 5
ctr-to-horiz-sector  ==> r19c3 ≠ 5
ctr-to-horiz-sector  ==> r19c2 ≠ 5
biv-chain[2]: hr19c1{n1247 n1238} - r19c2{n4 n3} ==> r19c3 ≠ 3
biv-chain[2]: hr19c1{n1247 n1238} - r19c2{n4 n3} ==> r19c5 ≠ 3
biv-chain[2]: r19c2{n4 n3} - hr19c1{n1247 n1238} ==> r19c3 ≠ 4
naked-single ==> r19c3 = 1
cell-to-horiz-ctr  ==> hr24c1 ≠ 18
ctr-to-horiz-sector  ==> r24c2 ≠ 8
horiz-sector-to-ctr  ==> hr20c1 ≠ 16
naked-single ==> hr20c1 = 34
verti-sector-to-ctr  ==> vr17c5 ≠ 1345689
verti-sector-to-ctr  ==> vr17c5 ≠ 1245789
verti-sector-to-ctr  ==> vr17c5 ≠ 1236789
naked-single ==> vr17c5 = 2345679
hidden-single-in-magic-horiz-sector ==> r22c2 = 8
naked-pairs-in-verti-sector: c2{r19 r20}{n3 n4} ==> r24c2 ≠ 4
naked-pairs-in-verti-sector: c2{r19 r20}{n3 n4} ==> r24c2 ≠ 3
naked-pairs-in-verti-sector: c2{r19 r20}{n3 n4} ==> r21c2 ≠ 4
naked-pairs-in-verti-sector: c2{r19 r20}{n3 n4} ==> r21c2 ≠ 3
naked-pairs-in-verti-sector: c2{r19 r20}{n3 n4} ==> r18c2 ≠ 4
biv-chain[2]: r19c2{n4 n3} - hr19c1{n1247 n1238} ==> r19c5 ≠ 4
naked-single ==> r19c5 = 2
horiz-sector-to-ctr  ==> hr21c1 ≠ 126789
biv-chain[2]: r24c2{n6 n5} - hr24c1{n36 n45} ==> r24c3 ≠ 6
biv-chain[2]: hr24c1{n36 n45} - r24c2{n6 n5} ==> r24c3 ≠ 5
naked-pairs-in-verti-sector: c3{r20 r24}{n3 n4} ==> r21c3 ≠ 4
naked-pairs-in-verti-sector: c3{r20 r24}{n3 n4} ==> r21c3 ≠ 3
naked-pairs-in-verti-sector: c3{r20 r24}{n3 n4} ==> r18c3 ≠ 4
whip[2]: hr18c1{n15689 n14789} - r18c3{n6 .} ==> r18c2 ≠ 7
hidden-single-in-magic-verti-sector ==> r21c2 = 7
naked-single ==> hr21c1 = 135789
naked-single ==> r21c3 = 5
naked-single ==> r21c5 = 3
hidden-single-for-magic-digit-in-horiz-sector ==> r23c7 = 3
naked-single ==> r24c7 = 4
naked-single ==> hr24c4 = 479
naked-single ==> r24c6 = 9
naked-single ==> r24c5 = 7
naked-single ==> r22c5 = 6
naked-single ==> r23c5 = 4
naked-single ==> r20c5 = 5
naked-single ==> r20c11 = 4
naked-single ==> r20c8 = 3
naked-single ==> r18c5 = 9
naked-single ==> r22c3 = 7
naked-single ==> r18c3 = 6
naked-single ==> r18c2 = 5
naked-single ==> r24c2 = 6
naked-single ==> r23c6 = 8
naked-single ==> hr23c4 = 1234678
naked-single ==> r23c11 = 6
naked-single ==> vr17c11 = 1234678
naked-single ==> r24c11 = 8
naked-single ==> r24c9 = 9
naked-single ==> vr18c9 = 123469
naked-single ==> r19c9 = 4
naked-single ==> hr19c6 = 479
naked-single ==> r19c8 = 7
naked-single ==> hr24c1 = 36
naked-single ==> r24c3 = 3
naked-single ==> r20c3 = 4
naked-single ==> r20c2 = 3
naked-single ==> r19c2 = 4
naked-single ==> hr19c1 = 1247
naked-single ==> r19c4 = 7
naked-single ==> r18c4 = 8
naked-single ==> r15c4 = 9
naked-single ==> hr18c1 = 15689
naked-single ==> vr18c8 = 37
ctr-to-horiz-sector  ==> r15c6 ≠ 8
ctr-to-horiz-sector  ==> r15c5 ≠ 8
ctr-to-horiz-sector  ==> r15c2 ≠ 8
hidden-single-in-magic-verti-sector ==> r11c2 = 8
naked-single ==> hr11c1 = 123468
naked-pairs-in-verti-sector: c5{r11 r15}{n2 n6} ==> r13c5 ≠ 6
naked-pairs-in-verti-sector: c5{r11 r15}{n2 n6} ==> r13c5 ≠ 2
naked-pairs-in-verti-sector: c5{r11 r15}{n2 n6} ==> r12c5 ≠ 6
naked-pairs-in-verti-sector: c5{r11 r15}{n2 n6} ==> r12c5 ≠ 2
naked-pairs-in-verti-sector: c5{r11 r15}{n2 n6} ==> r10c5 ≠ 6
cell-to-horiz-ctr  ==> hr10c3 ≠ 56
ctr-to-horiz-sector  ==> r10c4 ≠ 5
naked-pairs-in-verti-sector: c4{r10 r11}{n2 n3} ==> r7c4 ≠ 3
naked-single ==> r7c4 = 5
ctr-to-horiz-sector  ==> r7c3 ≠ 4
naked-pairs-in-verti-sector: c5{r10 r14}{n8 n9} ==> r12c5 ≠ 9
naked-pairs-in-verti-sector: c5{r10 r14}{n8 n9} ==> r12c5 ≠ 8
biv-chain[2]: c6n8{r12 r14} - c6n9{r14 r12} ==> r12c6 ≠ 2
biv-chain[2]: c6n8{r12 r14} - c6n9{r14 r12} ==> r12c6 ≠ 3
biv-chain[2]: c6n8{r12 r14} - c6n9{r14 r12} ==> r12c6 ≠ 5
biv-chain[2]: c6n8{r12 r14} - c6n9{r14 r12} ==> r12c6 ≠ 6
biv-chain[2]: c6n8{r12 r14} - c6n9{r14 r12} ==> r12c6 ≠ 7
hidden-single-for-magic-digit-in-horiz-sector ==> r12c5 = 7
naked-single ==> r13c5 = 4
hidden-single-in-magic-verti-sector ==> r12c7 = 4
hidden-single-in-magic-horiz-sector ==> r13c6 = 7
hidden-single-in-magic-horiz-sector ==> r13c8 = 6
naked-single ==> vr11c8 = 267
naked-single ==> r12c8 = 2
naked-single ==> r12c10 = 1
naked-single ==> r13c10 = 2
naked-single ==> r12c11 = 3
naked-single ==> r13c11 = 1
naked-single ==> r12c9 = 5
naked-single ==> r13c9 = 3
naked-single ==> r13c7 = 5
naked-single ==> hr12c4 = 1234579
naked-single ==> r12c6 = 9
naked-single ==> r14c6 = 8
naked-single ==> r14c5 = 9
naked-single ==> r10c5 = 8
naked-single ==> hr10c3 = 38
naked-single ==> r10c4 = 3
naked-single ==> r11c4 = 2
naked-single ==> r11c5 = 6
naked-single ==> r15c5 = 2
naked-single ==> r11c6 = 3
naked-single ==> r11c7 = 1
naked-single ==> r15c7 = 3
naked-single ==> r11c3 = 4
naked-single ==> r15c3 = 1
naked-single ==> r13c3 = 3
naked-single ==> hr13c1 = 37
naked-single ==> r13c2 = 7
naked-single ==> r15c2 = 6
naked-single ==> r15c6 = 5
naked-single ==> hr15c1 = 123569
naked-single ==> vr10c6 = 35789
whip[2]: hr7c1{n2579 n3569} - r7c2{n2 .} ==> r7c3 ≠ 6
whip[4]: r5n1{c2 c3} - c3n3{r5 r7} - c3n2{r7 r9} - r9c2{n2 .} ==> r5c2 ≠ 4
whip[4]: c2n5{r8 r4} - hr4c1{n4789 n5689} - r4c3{n4 n6} - r8c3{n6 .} ==> r8c2 ≠ 7
biv-chain[5]: c3n3{r5 r7} - hr7c1{n2579 n3569} - c2n7{r7 r4} - c2n4{r4 r9} - r9c3{n4 n2} ==> r5c3 ≠ 2
whip[5]: c3n3{r5 r7} - hr7c1{n2579 n3569} - c3n2{r7 r9} - c2n2{r9 r5} - r5c7{n2 .} ==> r5c5 ≠ 3
naked-single ==> r5c5 = 4
naked-single ==> vr1c5 = 1456789
naked-single ==> r6c5 = 1
naked-single ==> r6c9 = 2
biv-chain[2]: c2n4{r4 r9} - c3n4{r9 r4} ==> hr4c1 ≠ 5689
naked-single ==> hr4c1 = 4789
hidden-single-in-magic-verti-sector ==> r8c2 = 5
hidden-single-for-magic-digit-in-verti-sector ==> r2c5 = 5
naked-single ==> hr2c4 = 589
naked-pairs-in-verti-sector: c7{r2 r4}{n8 n9} ==> r7c7 ≠ 8
naked-pairs-in-verti-sector: c7{r2 r4}{n8 n9} ==> r3c7 ≠ 9
biv-chain[2]: r2c7{n9 n8} - r4c7{n8 n9} ==> vr1c7 ≠ 245678
naked-single ==> vr1c7 = 234689
biv-chain[2]: r7c7{n6 n3} - hr7c6{n569 n389} ==> r7c9 ≠ 6
biv-chain[2]: hr7c6{n569 n389} - r7c7{n6 n3} ==> r7c9 ≠ 3
biv-chain[2]: r2c9{n7 n3} - vr1c9{n245678 n234689} ==> r3c9 ≠ 7
hidden-single-for-magic-digit-in-horiz-sector ==> r3c5 = 7
naked-single ==> r8c5 = 6
naked-single ==> r8c3 = 7
naked-single ==> r4c3 = 4
naked-single ==> r9c3 = 2
naked-single ==> r9c2 = 4
naked-single ==> r7c3 = 3
naked-single ==> r5c3 = 1
naked-single ==> r6c3 = 6
naked-single ==> r6c2 = 1
naked-single ==> r5c2 = 2
naked-single ==> r5c7 = 3
naked-single ==> r7c7 = 6
naked-single ==> r3c7 = 2
naked-single ==> r4c2 = 7
naked-single ==> r7c2 = 6
naked-single ==> hr7c6 = 569
naked-single ==> r7c9 = 5
naked-single ==> vr1c9 = 245678
naked-single ==> r4c9 = 8
naked-single ==> r4c7 = 9
naked-single ==> r2c7 = 8
naked-single ==> r2c6 = 9
naked-single ==> r3c9 = 6
naked-single ==> r3c6 = 5
naked-single ==> r3c11 = 8
naked-single ==> r3c10 = 9
naked-single ==> r2c11 = 5
naked-single ==> r2c9 = 7
naked-single ==> hr2c8 = 457
naked-single ==> r2c10 = 4
PUZZLE SOLVED. rating-type = gW+S, MOST COMPLEX RULE TRIED = W[8]

------------------------
-95-598-745-98----------
-89-7523698-21----------
-7498-918-4879----------
-215473-471236----------
-16-1548296-14----------
-6359-695-2143----------
-57869---13265----------
-421-38974-957----------
---38-271-98------------
-842631-957624----------
-97-7942513-13----------
-73-4756321-98----------
-42-9867435-79----------
-619253-876935----------
---13-986-28------------
-126-37529-574----------
-56891---52346----------
-4172-974-1687----------
-34-5823174-32----------
-758391-387259----------
-8796-896-3125----------
-98-4837216-98----------
-63-794-968-13----------

***********************************************************************************************
***  KakuRules 2.0.s based on CSP-Rules 2.0.s, config = gW+S
***  using CLIPS 6.31-r738
***********************************************************************************************

(The 10 ending "-" at the end of each line in the solution puzzle are due to the fact that KakuRules requires squares puzzles - a limitation I should correct some day.)

You proposed this puzzle as a challenge, but the challenge is now for you: write a fully detailed, simpler, pure logic solution (i.e. one in which no chain of length greater than 8 will be required).
denis_berthier
2010 Supporter

Posts: 2465
Joined: 19 June 2007
Location: Paris

### Re: 24 x 14 Kakuro Challenge

Hi Denis,

I only meant a challenge for P&P solvers. It is not intended to be challenge for software - actually, with grids of this size and cell density, for P&P solving I only generate puzzles that are solvable by my "linear solver", without recursion.

Your challenge is interesting, but I am not sure exactly what you mean by a "chain" here?

Cheers
MM

Mathimagics
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### Re: 24 x 14 Kakuro Challenge

I meant the universal types of chains used in my resolution path: bivalue-chains, whips, g-whips, or any other type of chain people prefer. I don't know what your linear solver does, but it sounds much like T&E(1). If so, this should allow the mentioned chains to solve these puzzles.

But the challenge is not about how you solve it (hand or computer), it's about the patterns you use. If you don't like "my" chains, you can still use different ones.
denis_berthier
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### Re: 24 x 14 Kakuro Challenge

Solved with my solver using only singles and calculations in 1.8 seconds.
creint

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### Re: 24 x 14 Kakuro Challenge

creint wrote:Solved with my solver using only singles and calculations in 1.8 seconds.

What do you mean by "calculations"? T&E ?
denis_berthier
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### Re: 24 x 14 Kakuro Challenge

denis_berthier wrote:I don't know what your linear solver does, but it sounds much like T&E(1).

Indeed, my simple Kakuro solver (SKS) uses only simple candidate eliminations based on testing "Can cell (R, C) = D?". The test looks only at the intersecting runs, H & V, to see if both runs can still be completed with (R, C) = D given current domains.

The solution path produced (if the puzzle is solved) is simply a list of individual candidate eliminations + naked singles.

An elementary Kakuro puzzle "triage" classification might be:

• solvable by SKS
• T&E required

Mathimagics
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### Re: 24 x 14 Kakuro Challenge

denis_berthier wrote:
creint wrote:Solved with my solver using only singles and calculations in 1.8 seconds.

What do you mean by "calculations"? T&E ?

Digit cannot be placed in a cell because sum value would be different than expected. All within one constraint. Some solvers can check combinations in multiple constraints.
creint

Posts: 305
Joined: 20 January 2018

### Re: 24 x 14 Kakuro Challenge

creint wrote:Digit cannot be placed in a cell because sum value would be different than expected. All within one constraint. Some solvers can check combinations in multiple constraints.

So, your "calculations" include an unrestricted number of combination checks, right?
denis_berthier
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### Re: 24 x 14 Kakuro Challenge

For every constraint for every cell in constraint for every digit in cell: if there is no combination containing this digit in this cell then exclude. Only restricted to a single calculation constraint.
creint

Posts: 305
Joined: 20 January 2018

### Re: 24 x 14 Kakuro Challenge

creint wrote:For every constraint for every cell in constraint for every digit in cell: if there is no combination containing this digit in this cell then exclude. Only restricted to a single calculation constraint.

I don't understand how you can solve this puzzle that way. It can't be solved by only such local constraints. Some form or another of chain is required.
denis_berthier
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Location: Paris

### Re: 24 x 14 Kakuro Challenge

denis_berthier wrote:
creint wrote:For every constraint for every cell in constraint for every digit in cell: if there is no combination containing this digit in this cell then exclude. Only restricted to a single calculation constraint.

I don't understand how you can solve this puzzle that way. It can't be solved by only such local constraints. Some form or another of chain is required.

Sum 17 in 2 cells then only 8 and 9 are possible in a cell. 8+9 or 9+8
Sum 14 in 2 cell then only 5689 are possible in a cell. 5+9, 6+8, 8+6, 9+5

Sum 14 in 2 cells digits 569, 56 then only 9+5 is possible.
Sum 28 in 4 cells digits 4567, 467, 9, 45678 then -6, _, _, -4567
-6 because 6, 47, 9, 4578 has no combination of sum 28. Same for the other exclusions.
creint

Posts: 305
Joined: 20 January 2018

### Re: 24 x 14 Kakuro Challenge

Hi creint
I see what you mean, but those are only local exclusions for the easiest cells, based only on local constraints. This type of reasoning is not enough for this puzzle. You must have harder steps for some eliminations, involving several sectors.
denis_berthier
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Location: Paris

### Re: 24 x 14 Kakuro Challenge

No, my solver used only singles and calculations, how do you want to debug this?
I could give a screenshot of each step, or pencilmarks like these.

First step of calculations
Hidden Text: Show
Code: Select all
5689      569                 56789     5689      56789               123456789 456789    1234568             9         89
89        9                   123456789 5689      123456789 13        123456789 456789    1234568             12        1
456789    45679     5689      456789              123456789 13        123456789           4568      46789     45679     456789
12457     123457    5         123457    3457      123457              12345678  7         1234568   1234678   1234567   1345678
12456     123456              123456789 345789    123456789 89        123456789 79        1234568             1234      134
12456789  12345679  123456789 123456789           3456789   89        3456789             1234      1234      1234      134
56789     5679      56789     56789     5789                                    1234      123456    1234567   1234567   134567
124       124       124                 345789    123456789 79        123456789 1234                456789    45679     456789
23456789  23456789            1234567   7         1234567             89        89
46789     1234567   123456789 123456789 23456789  123456789           123456789 12345678  123456789 123456789 123456789 123456789
79        7                   123456789 23456789  123456789 123456789 123456789 12345678  123456789           13        13
46789     123467              1234567   234567    1234567   1234567   1234567   1234567   1234567             89        89
4         1245                3456789   3456789   3456789   3456789   3456789   345678    3456789             79        79
46789     1234567   123456789 123456789 23456789  123456789           356789    35678     356789    356789    356789    356789
13        13                  689       689       689                 12346789  12346789
13456     123456    123456              13        123456789 456789    123456789 5689                123456789 12345789  23456789
13456789  12345678  123456789 123456789 13                                      5689      123456789 123456789 12345789  23456789
1345678   12345678  12345678  12345678            3456789   346789    3456789             123456789 123456789 12345789  23456789
13456     123456              123456789 89        123456789 12346789  123456789 6789      123456789           1234      234
13456789  12345678  89        123456789 89        123456789           123456789 6789      123456789 12        12345789  23456789
6789      678       89        6789                689       9         689                 1235      12        1235      235
89        8                   123456789 89        123456789 79        123456789 123456    123456789           89        89
1345678   12345678            3456789   89        3456789             689       6         689                 13        3

After singles, second step of calculations
Hidden Text: Show
Code: Select all
9         5                   56789     5689      56789               123456789 456789    1234568             9         8
8         9                   2456789   5689      2456789   13        2456789   456789    24568               2         1
45679     4567      9         456789              6789      13        6789                4568      46789     4567      5679
1247      12347     5         12347     7         12347               12346     7         12346     12346     1346      6
12456     12356               1234567   5         1234567   8         1234567   9         123456              1         4
1245679   1234567   12345678  123456789           345678    9         345678              1234      1234      134       34
5679      567       56789     56789     5789                                    1234      123456    1234567   134567    567
124       124       124                 3457      345678    9         345678    1234                5789      4567      5679
2345678   23456789            12        7         12                  89        89
678       1234      12345678  12345678  2345678   12345678            123456789 12345678  123456789 123456789 2         2456
9         7                   123456789 23456789  123456789 123456789 123456789 12345678  123456789           1         13
678       234                 1234567   234567    1234567   1234567   1234567   1234567   1234567             9         89
4         2                   3456789   3456789   3456789   3456789   3456789   345678    3456789             7         79
678       1234      56789     123456789 23456789  123456789           356789    35678     356789    356789    3         56789
13        13                  689       689       689                 12346789  12346789
13456     123456    456                 13        123456789 457       123456789 5689                123456789 2345789   2456789
45678     24567     56789     2456789   13                                      5689      1234567   123456789 2345789   2456789
1345678   1234567   5678      12345678            3456789   346789    345                 1234567   123456789 2345789   2456789
13456     12346               12345     89        12345     1234      12345     67        12345               3         2
134567    1234567   89        1234567   89        1234567             345       6789      34567     12        345789    456789
678       67        89        6789                68        9         6                   1235      12        235       25
9         8                   123456    89        123456    7         12345     1         123456              89        89
345678    123456              3456789   89        3456789             89        6         89                  1         3
creint

Posts: 305
Joined: 20 January 2018

### Re: 24 x 14 Kakuro Challenge

creint wrote:Sum 17 in 2 cells then only 8 and 9 are possible in a cell. 8+9 or 9+8
Sum 14 in 2 cell then only 5689 are possible in a cell. 5+9, 6+8, 8+6, 9+5

Sum 14 in 2 cells digits 569, 56 then only 9+5 is possible.
Sum 28 in 4 cells digits 4567, 467, 9, 45678 then -6, _, _, -4567
-6 because 6, 47, 9, 4578 has no combination of sum 28. Same for the other exclusions.

After your last post, I understand better what you meant above.
Each elimination combines knowledge from several sectors.

Even for your own purposes, I think you could make your output more explicit.
denis_berthier
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