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Battleship game combinatorics

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This page is a table, reporting the number of ways to place ships as in the game "battleship". The table assumes that ships cannot be placed adjacent to one another, though not all versions of the game use this rule.
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Latest revision as of 20:03, 9 November 2012

This page is a table, reporting the number of ways to place ships as in the game "battleship". The table assumes that ships cannot be placed adjacent to one another, though not all versions of the game use this rule.

Ship sizes Number of configurations
on a 10×10 board
2 3 4 5
1
1 180
2 13952
3 614372
4 17086631
1 160
1 1 23864
2 1 1512096
3 1 53606768
4 1 1179864432
2 10124
1 2 1230092
2 2 62495628
3 2 1745117572
4 2 29650630088
3 330840
1 3 32094960
2 3 1278079616
3 3 27395120928
4 3 348892008792
1 140
1 1 20072
2 1 1219008
3 1 41283320
4 1 864647388
1 1 16896
1 1 1 1966664
2 1 1 95386968
3 1 1 2532545416
4 1 1 40721312760
2 1 786968
1 2 1 72831964
2 2 1 2755256320
3 2 1 55828223540
4 2 1 668256987440
3 1 18382184
1 3 1 1320017704
2 3 1 37880082192
3 3 1 567343768064
4 3 1 4871721743520
2 6996
1 2 779752
2 2 36085692
3 2 910464972
4 2 13847185918
1 2 619136
1 1 2 54625952
2 1 2 1961767760
3 1 2 37549258992
4 1 2 422118615240
2 2 20505284
1 2 2 1396400720
2 2 2 37804399592
3 2 2 530879625444
4 2 2 4242772005768
3 2 328511112
1 3 2 16757986408
2 3 2 330360758520
3 3 2 3268821509016
4 3 2 17707810153184
1 120
1 1 16528
2 1 961464
3 1 31086744
4 1 619268128
1 1 13808
1 1 1 1538520
2 1 1 71194112
3 1 1 1796509352
4 1 1 27329683408
2 1 610688
1 2 1 53879808
2 2 1 1935562696
3 2 1 37068246456
4 2 1 417017581256
3 1 13477504
1 3 1 918108728
2 3 1 24872048856
3 3 1 349608204104
4 3 1 2797606827136
1 1 11360
1 1 1 1211008
2 1 1 53413832
3 1 1 1279310984
4 1 1 18385007248
1 1 1 954544
1 1 1 1 80194520
2 1 1 1 2731237000
3 1 1 1 49341382288
4 1 1 1 520599890368
2 1 1 29852632
1 2 1 1 1925751392
2 2 1 1 49143133528
3 2 1 1 646677411848
4 2 1 1 4808897160408
3 1 1 448574416
1 3 1 1 21536631136
2 3 1 1 397108468832
3 3 1 1 3647432090016
4 3 1 1 18170989432520
2 1 371048
1 2 1 29660864
2 2 1 957045912
3 2 1 16298373712
4 2 1 161138941144
1 2 1 21906376
1 1 2 1 1337029984
2 1 2 1 32111473656
3 1 2 1 395146057864
4 1 2 1 2726362307664
2 2 1 462924032
1 2 2 1 20886349672
2 2 2 1 359461539224
3 2 2 1 3056118386176
4 2 2 1 13949906853080
3 2 1 4488051160
1 3 2 1 143891605904
2 3 2 1 1693472099056
3 3 2 1 9404689335808
4 3 2 1 26509655816984

[edit] References