saul wrote:I've just gotten hooked on kakuro recently. I've been working the medium difficulty puzzles at atksolutions.com, but this one's got me stumped. I'm sure it's correct up to here, but I don't see what to do next. All of the puzzles that I've done on this site so far have been solvable without trial and error. Do you see a way to proceed from here?

https://dl.dropbox.com/u/24746182/kakuro.png

Hi

Saul,

I've been away from any Internet access for some time and I just saw your post.

This puzzle is an easy one in the atk galaxy. It can be solved by whips of maximum length 3.

Below is the full solution given by CSP-Rules according to the theory developed in my last book "Pattern-Based Constraint Satisfaction and Logic Puzzles".

I let you find the eliminations missing in yours.

Definitions and notations (sketch):

Rows and columns are numbered from 1 to 12 (including the first totally black one).

CSP-variables hrc and vrc represent the combinations allowed in the horizontal (resp. vertical) sectors. As you know, there is a permanent interplay between the standard rc CSP-variables and the remaining allowed combinations in each sector (which are naturally represented in my approach by the hrc and vrc additional CSP-variables).

vr1c4 = 14 means that the vertical sector starting after black cell r1c4 can only contain digits 1 or 4. "14" is a shorthand for the set {1, 4}.

"cell-to-horiz-ctr" and other such rules express part of this interplay. In an advanced level puzzle, these should normally be considered as obvious and should not be displayed.

But this interplay also appears in the combined presence of both types of variables in whips.

***** KakuRules 1.2 based on CSP-Rules 1.2, config: W *****

horizontal magic sector 34-in-5, starting in r2c2, unique combination: 46789

horizontal pseudo magic sector 13-in-4, starting in r3c8, for digits: (1)

horizontal magic sector 4-in-2, starting in r4c1, unique combination: 13

horizontal pseudo magic sector 25-in-6, starting in r4c4, for digits: (1 2)

horizontal magic sector 22-in-6, starting in r6c1, unique combination: 123457

horizontal magic sector 30-in-4, starting in r7c2, unique combination: 6789

horizontal magic sector 11-in-4, starting in r7c7, unique combination: 1235

horizontal magic sector 23-in-3, starting in r9c1, unique combination: 689

horizontal magic sector 21-in-6, starting in r10c3, unique combination: 123456

horizontal magic sector 11-in-4, starting in r11c1, unique combination: 1235

horizontal magic sector 34-in-5, starting in r11c6, unique combination: 46789

horizontal magic sector 30-in-4, starting in r12c1, unique combination: 6789

horizontal magic sector 35-in-5, starting in r12c6, unique combination: 56789

vertical magic sector 17-in-2, starting in r7c2, unique combination: 89

vertical magic sector 42-in-8, starting in r1c3, unique combination: 12456789

vertical magic sector 37-in-8, starting in r4c4, unique combination: 12345679

vertical pseudo magic sector 38-in-7, starting in r1c5, for digits: (7 8 9)

vertical magic sector 24-in-3, starting in r1c6, unique combination: 789

vertical magic sector 16-in-5, starting in r1c7, unique combination: 12346

vertical magic sector 28-in-7, starting in r5c9, unique combination: 1234567

vertical magic sector 43-in-8, starting in r1c10, unique combination: 13456789

vertical magic sector 17-in-2, starting in r10c10, unique combination: 89

vertical magic sector 44-in-8, starting in r4c11, unique combination: 23456789

vertical magic sector 7-in-3, starting in r7c12, unique combination: 124

naked singles: r11c2 = 5, r10c6 = 6, r9c12 = 4, r10c12 = 2, r8c12 = 1, r8c2 = 8, r9c2 = 9, r9c4 = 6, r9c3 = 8, r7c8 = 5, r7c6 = 6, r4c3 = 1, r4c2 = 3, r2c4 = 4, r2c7 = 6, vr1c4 = 14, r3c4 = 1, vr5c6 = 16, r6c6 = 1, vr6c8 = 58, r8c8 = 8, hr8c1 = 1238, r8c3 = 2, hr10c10 = 29, r10c11 = 9, hr9c8 = 4689, r9c9 = 6, r9c11 = 8, r9c10 = 9, vr8c6 = 69, r9c6 = 9, hr9c5 = 39

naked-single ==> r9c7 = 3, vr10c2 = 59, r12c2 = 9, r12c4 = 7, r7c4 = 9, r7c3 = 7, r2c3 = 9, r7c5 = 8, r2c5 = 7, r2c6 = 8, r12c5 = 6, r12c3 = 8, vr10c3 = 18, r11c3 = 1, vr9c5 = 136, r11c5 = 3, r11c4 = 2, r10c5 = 1

hidden-single-in-magic-horiz-sector ==> r6c2 = 7

naked-singles ==> vr3c2 = 137, r5c2 = 1

hidden-single-in-magic-verti-sector ==> r8c4 = 1

naked-single ==> r8c5 = 3

cell-to-horiz-ctr ==> hr5c1 <> 1269

cell-to-horiz-ctr ==> hr5c1 <> 1278

ctr-to-horiz-sector ==> r5c5 <> 2

cell-to-horiz-ctr ==> hr4c4 <> 123568

cell-to-horiz-ctr ==> hr3c8 <> 1345

ctr-to-horiz-sector ==> r3c9 <> 5

ctr-to-horiz-sector ==> r3c10 <> 5

ctr-to-horiz-sector ==> r3c12 <> 5

cell-to-verti-ctr ==> vr7c7 <> 13679

horiz-sector-to-ctr ==> hr5c1 <> 1368

horiz-sector-to-ctr ==> hr5c1 <> 1458

horiz-sector-to-ctr ==> hr5c1 <> 1467

naked-singles ==> hr5c1 = 1359, r5c4 = 3, r5c5 = 9, r6c3 = 4, r3c3 = 6, r6c4 = 5, r6c5 = 2, r6c7 = 3, r10c4 = 4, vr1c5 = 2345789

cell-to-horiz-ctr ==> hr3c2 <> 13678

cell-to-horiz-ctr ==> hr5c6 <> 36

ctr-to-horiz-sector ==> r5c8 <> 3

cell-to-horiz-ctr ==> hr3c2 <> 12679

naked-singles ==> hr3c2 = 14569, r3c7 = 4, r3c5 = 5, r4c5 = 4, r3c6 = 9, r4c6 = 7

ctr-to-horiz-sector ==> r4c8 <> 9

cell-to-horiz-ctr ==> hr5c6 <> 45

ctr-to-horiz-sector ==> r5c8 <> 4

ctr-to-horiz-sector ==> r5c8 <> 5

cell-to-verti-ctr ==> vr3c8 <> 39

ctr-to-verti-sector ==> r4c8 <> 3

cell-to-verti-ctr ==> vr9c8 <> 479

ctr-to-verti-sector ==> r11c8 <> 4

horiz-sector-to-ctr ==> hr5c9 <> 289

ctr-to-horiz-sector ==> r5c11 <> 2

ctr-to-horiz-sector ==> r5c12 <> 2

horiz-sector-to-ctr ==> hr5c9 <> 379

ctr-to-horiz-sector ==> r5c10 <> 3

ctr-to-horiz-sector ==> r5c11 <> 3

ctr-to-horiz-sector ==> r5c12 <> 3

horiz-sector-to-ctr ==> hr5c9 <> 469

verti-sector-to-ctr ==> vr3c8 <> 48

naked-singles ==> vr3c8 = 57, r4c8 = 5, r5c8 = 7, hr5c6 = 27, r5c7 = 2, r4c7 = 1, hr4c4 = 124567, r4c10 = 6, r4c9 = 2

ctr-to-verti-sector ==> r2c9 <> 6

ctr-to-verti-sector ==> r3c9 <> 6

ctr-to-verti-sector ==> r2c9 <> 4

ctr-to-verti-sector ==> r3c9 <> 4

verti-sector-to-ctr ==> vr7c7 <> 13589

biv-chain[2]: vr1c11{n69 n78} - r3c11{n6 n7} ==> r2c11 <> 7

biv-chain[2]: hr3c8{n1237 n1246} - r3c11{n7 n6} ==> r3c12 <> 6

biv-chain[2]: r3c11{n6 n7} - vr1c11{n69 n78} ==> r2c11 <> 6

cell-to-horiz-ctr ==> hr2c8 <> 4567

whip[2]: r3c11{n7 n6} - hr3c8{n1237 .} ==> r3c10 <> 7, r3c9 <> 7

biv-chain[2]: r3c9{n1 n3} - vr1c9{n127 n235} ==> r2c9 <> 1

cell-to-horiz-ctr ==> hr2c8 <> 1489

biv-chain[2]: vr1c9{n127 n235} - r3c9{n1 n3} ==> r2c9 <> 3

cell-to-horiz-ctr ==> hr2c8 <> 3469

cell-to-horiz-ctr ==> hr2c8 <> 2389

whip[2]: r2c11{n8 n9} - hr2c8{n3568 .} ==> r2c10 <> 8

whip[2]: r10c8{n5 n3} - vr9c8{n578 .} ==> r12c8 <> 5

whip[2]: r2c10{n7 n5} - r2c9{n5 .} ==> hr2c8 <> 2569

whip[2]: hr5c9{n568 n478} - r5c12{n5 .} ==> r5c11 <> 7, r5c10 <> 7

whip[2]: hr5c9{n568 n478} - r5c11{n5 .} ==> r5c10 <> 4

whip[2]: vr1c12{n16 n25} - r3c12{n1 .} ==> r2c12 <> 2

horiz-sector-to-ctr ==> hr2c8 <> 2578

horiz-sector-to-ctr ==> hr2c8 <> 2479

whip[2]: vr1c12{n25 n16} - r3c12{n2 .} ==> r2c12 <> 1

whip[2]: vr4c12{n17 n26} - r5c12{n5 .} ==> r6c12 <> 6

whip[2]: vr4c12{n17 n35} - r5c12{n6 .} ==> r6c12 <> 5

whip[2]: vr4c12{n26 n17} - r5c12{n5 .} ==> r6c12 <> 7

whip[3]: r2c9{n7 n5} - hr2c8{n1678 n1579} - r2c12{n3 .} ==> r2c10 <> 7

whip[3]: r2c9{n5 n7} - hr2c8{n3568 n1579} - r2c12{n3 .} ==> r2c10 <> 5

naked-triplets-in-a-column c10{r2 r3 r7}{n1 n4 n3} ==> r8c10 <> 4

whip[2]: hr8c6{n124789 n134689} - r8c10{n7 .} ==> r8c11 <> 3, r8c9 <> 3

naked-triplets-in-a-column c10{r2 r3 r7}{n1 n4 n3} ==> r8c10 <> 3

cell-to-horiz-ctr ==> hr8c6 <> 134689

naked-triplets-in-a-column c10{r2 r3 r7}{n1 n4 n3} ==> r6c10 <> 4, r6c10 <> 3, r6c10 <> 1

cell-to-horiz-ctr ==> hr6c8 <> 1346

whip[2]: hr6c8{n1238 n1247} - r6c10{n8 .} ==> r6c9 <> 7, r6c11 <> 7

biv-chain[3]: c11n3{r6 r7} - r7n2{c11 c9} - c9n1{r7 r6} ==> r6c9 <> 3

whip[3]: r3c9{n1 n3} - r3c10{n3 n4} - hr3c8{n1237 .} ==> r3c12 <> 1

cell-to-verti-ctr ==> vr1c12 <> 16

ctr-to-verti-sector ==> r2c12 <> 6

cell-to-horiz-ctr ==> hr2c8 <> 1678

horiz-sector-to-ctr ==> hr2c8 <> 3568

whip[2]: hr2c8{n3478 n1579} - r2c12{n3 .} ==> r2c9 <> 5

naked-singles ==> r2c9 = 7, vr1c9 = 127, r3c9 = 1

biv-chain[2]: r3c10{n3 n4} - hr3c8{n1237 n1246} ==> r3c12 <> 3

biv-chain[2]: vr1c12{n25 n34} - r3c12{n2 n4} ==> r2c12 <> 4

biv-chain[2]: hr2c8{n1579 n3478} - r2c12{n5 n3} ==> r2c10 <> 3

biv-chain[2]: hr3c8{n1237 n1246} - r3c10{n3 n4} ==> r3c12 <> 4

naked-singles ==> r3c12 = 2, vr1c12 = 25, r2c12 = 5, hr2c8 = 1579, r2c10 = 1, r7c10 = 3, r3c10 = 4, r7c11 = 2, r7c9 = 1, r2c11 = 9, vr1c11 = 69, r3c11 = 6, hr3c8 = 1246

hidden-single-in-magic-verti-sector ==> r10c9 = 3

naked-singles ==> r10c8 = 5, r10c7 = 2

hidden-single-in-magic-verti-sector ==> r6c11 = 3

ctr-to-horiz-sector ==> r6c10 <> 7

hidden-single-in-magic-verti-sector ==> r8c10 = 7

cell-to-verti-ctr ==> vr4c12 <> 35

ctr-to-verti-sector ==> r5c12 <> 5

biv-chain[2]: r6c10{n5 n8} - hr6c8{n2345 n1238} ==> r6c9 <> 5

biv-chain[2]: c9n7{r11 r12} - c11n7{r12 r11} ==> r11c8 <> 7, r11c7 <> 7

biv-chain[2]: hr5c9{n478 n568} - r5c12{n7 n6} ==> r5c11 <> 6

biv-chain[2]: hr5c9{n478 n568} - r5c11{n4 n5} ==> r5c10 <> 5

singles to the end

GRID SOLVED. rating-type = W, MOST COMPLEX RULE = Whip[3]

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