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Basic Techniques and Cage Combinations
http://www.rcbroughton.co.uk/sudoku/forum/viewtopic.php?f=8&t=649		 Page 1 of 1
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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