A302928 Maximum number of 4's possible in an infinite Minesweeper grid with n mines.

0, 0, 0, 2, 2, 4, 6, 6, 7, 8, 10, 12, 12, 13, 14, 16, 18, 18, 19, 21, 22, 24, 24, 26, 28, 30, 30, 31, 33, 34, 36, 36

Offset: 1

Author

Dmitry Kamenetsky, Apr 16 2018

Keywords

• nonn
• more

Comments

Question: what is the maximum value possible for (a(n) - n)? The current record is 5, which occurs at n=31.

There is no maximum. We can take k copies of the 17-mine configuration and place them sufficiently far apart to get 18k fours. So a(17k) - 17k >= 18k - 17k = k can get arbitrarily large. A possibly more interesting question is to ask about the maximum ratio a(n)/n. - Yevhenii Diomidov, Jan 19 2022

Links

• Dmitry Kamenetsky, The first 32 solutions
• Wikipedia, Minesweeper.

Crossrefs

Cf. A047345, A302929, A302930, A302931.