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PostPosted: Tue Sep 25, 2018 5:16 pm 
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I've started working my way through the Gentle killer series on sudoku.org.uk. I finished the first one, now working on the second (bombed the first try). For those who are not aware, I'm a pencil-and-paper solver. I'm looking for some tips on how to keep track of possible cage combinations for each cage and eliminating them as they are ruled out. The 2-cell cages are easy enough, but cages with more than that are beyond my skill in keeping them in my head.


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PostPosted: Wed Sep 26, 2018 8:07 pm 
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Location: Lethbridge, Alberta, Canada
I have a Cage Combinations file which I refer to for anything longer than 3 cells, which I've got to learn over time.

For very large cages, it's often easier to think about which numbers are missing.

2-cell cages

3(2) = {12}
4(2) = {13}
5(2) = {14/23}
6(2) = {15/24}
7(2) = {16/25/34}, no 7,8,9
8(2) = {17/26/35}, no 4,8,9
9(2) = {18/27/36/45}, no 9
10(2) = {19/28/37/46}, no 5
11(2) = {29/38/47/56}, no 1
12(2) = {39/48/57}, no 1,2,6
13(2) = {49/58/67}, no 1,2,3
14(2) = {59/68}
15(2) = {69/78}
16(2) = {79}
17(2) = {89}

3-cell cages

6(3) = {123}
7(3) = {124}
8(3) = {125/134}
9(3) = {126/135/234}, no 7,8,9
10(3) = {127/136/145/235}, no 8,9
11(3) = {128/137/146/236/245}, no 9
12(3) = {129/138/147/156/237/246/345}
13(3) = {139/148/157/238/247/256/346}
14(3) = {149/158/167/239/248/257/347/356}
15(3) = {159/168/249/258/267/348/357/456}
16(3) = {169/178/259/268/349/358/367/457}
17(3) = {179/269/278/359/368/458/467}
18(3) = {189/279/369/378/459/468/567}
19(3) = {289/379/469/478/568}, no 1
20(3) = {389/479/569/578}, no 1,2
21(3) = {489/579/678}, no 1,2,3
22(3) = {589/679}
23(3) = {689}
24(3) = {789}

4-cell cages

10(4) = {1234}
11(4) = {1235}
12(4) = {1236/1245}, no 7,8,9
13(4) = {1237/1246/1345}, no 8,9
14(4) = {1238/1247/1256/1346/2345}, no 9
15(4) = {1239/1248/1257/1347/1356/2346}
16(4) = {1249/1258/1267/1348/1357/1456/2347/2356}
17(4) = {1259/1268/1349/1358/1367/1457/2348/2357/2456}
18(4) = {1269/1278/1359/1368/1458/1467/2349/2358/2367/2457/3456}
19(4) = {1279/1369/1378/1459/1468/1567/2359/2368/2458/2467/3457}
20(4) = {1289/1379/1469/1478/1568/2369/2378/2459/2468/2567/3458/3467}
21(4) = {1389/1479/1569/1578/2379/2469/2478/2568/3459/3468/3567}
22(4) = {1489/1579/1678/2389/2479/2569/2578/3469/3478/3568/4567}
23(4) = {1589/1679/2489/2579/2678/3479/3569/3578/4568}
24(4) = {1689/2589/2679/3489/3579/3678/4569/4578}
25(4) = {1789/2689/3589/3679/4579/4678}
26(4) = {2789/3689/4589/4679/5678}, no 1
27(4) = {3789/4689/5679}, no 1,2
28(4) = {4789/5689}, no 1,2,3
29(4) = {5789}
30(4) = {6789}

5-cell cages

15(5) = {12345}
16(5) = {12346}
17(5) = {12347/12356}, no 8,9
18(5) = {12348/12357/12456}, no 9
19(5) = {12349/12358/12367/12457/13456}
20(5) = {12359/12368/12458/12467/13457/23456}
21(5) = {12369/12378/12459/12468/12567/13458/13467/23457}
22(5) = {12379/12469/12478/12568/13459/13468/13567/23458/23467}
23(5) = {12389/12479/12569/12578/13469/13478/13568/14567/23459/23468/23567}
24(5) = {12489/12579/12678/13479/13569/13578/14568/23469/23478/23568/24567}
25(5) = {12589/12679/13489/13579/13678/14569/14578/23479/23569/23578/24568/34567}
26(5) = {12689/13589/13679/14579/14678/23489/23579/23678/24569/24578/34568}
27(5) = {12789/13689/14589/14679/15678/23589/23679/24579/24678/34569/34578}
28(5) = {13789/14689/15679/23689/24589/24679/25678/34579/34678}
29(5) = {14789/15689/23789/24689/25679/34589/34679/35678}
30(5) = {15789/24789/25689/34689/35679/45678}
31(5) = {16789/25789/34789/35689/45679}
32(5) = {26789/35789/45689}, no 1
33(5) = {36789/45789}, no 1,2
34(5) = {46789}
35(5) = {56789}

6-cell cages

21(6) = {123456}
22(6) = {123457}
23(6) = {123458/123467}, no 9
24(6) = {123459/123468/123567}
25(6) = {123469/123478/123568/124567}
26(6) = {123479/123569/123578/124568/134567}
27(6) = {123489/123579/123678/124569/124578/134568/234567}
28(6) = {123589/123679/124579/124678/134569/134578/234568}
29(6) = {123689/124589/124679/125678/134579/134678/234569/234578}
30(6) = {123789/124689/125679/134589/134679/135678/234579/234678}
31(6) = {124789/125689/134689/135679/145678/234589/234679/235678}
32(6) = {125789/134789/135689/145679/234689/235679/245678}
33(6) = {126789/135789/145689/234789/235689/245679/345678}
34(6) = {136789/145789/235789/245689/345679}
35(6) = {146789/236789/245789/345689}
36(6) = {156789/246789/345789}
37(6) = {256789/346789}, no 1
38(6) = {356789}
39(6) = {456789}

7-cell cages

28(7) = {1234567}
29(7) = {1234568}
30(7) = {1234569/1234578}
31(7) = {1234579/1234678}
32(7) = {1234589/1234679/1235678}
33(7) = {1234689/1235679/1245678}
34(7) = {1234789/1235689/1245679/1345678}
35(7) = {1235789/1245689/1345679/2345678}
36(7) = {1236789/1245789/1345689/2345679}
37(7) = {1246789/1345789/2345689}
38(7) = {1256789/1346789/2345789}
39(7) = {1356789/2346789}
40(7) = {1456789/2356789}
41(7) = {2456789}
42(7) = {3456789}

8-cell cages

36(8) = {12345678}
37(8) = {12345679}
38(8) = {12345689}
39(8) = {12345789}
40(8) = {12346789}
41(8) = {12356789}
42(8) = {12456789}
43(8) = {13456789}
44(8) = {23456789}

and finally

45(9) = {123456789}


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PostPosted: Wed Sep 26, 2018 10:17 pm 
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Thanks, Andrew! I do have that list (that I got from you, I believe), as well as Trevor Butler's (trevor45) killer calculator app. Those are both immensely helpful in making the initial eliminations. I'm looking more for something to help me keep track of each cage's remaining combination possibilities as I solve the puzzle. Any suggestions or best practices?


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