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Basic Techniques and Cage Combinations http://www.rcbroughton.co.uk/sudoku/forum/viewtopic.php?f=8&t=649 |
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Author: | Andrew [ Wed Nov 18, 2009 4:48 am ] |
Post subject: | Basic Techniques and Cage Combinations |
There are several excellent solving guides available on the internet so, rather than trying to explain these techniques, here are links to three of them. nd's tips Ruud's solving guide Sudopedia Two of the most important techniques are the 45 rule and combination analysis. It is very useful to have access to a combination calculator. The one I use regularly is Ruud's combination calculator which is very useful because one can specify required and forbidden numbers which reduces the number of possible combinations. I've also compiled my own Cage Combinations table, which is listed below. 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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