Battleship game combinatorics
Jump to navigation
Jump to search
The printable version is no longer supported and may have rendering errors. Please update your browser bookmarks and please use the default browser print function instead.
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 |
References
- Haskell program that computes the table