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In a Super™ Minesweeper grid each cell is either a mine or a value. A value in row $𝑟$ and column $𝑐$ represents the total number of mines located in row $𝑟$ or column $𝑐$.

What is the most number of 5s that can occur in a 5x5 Super™ Minesweeper grid? Good luck!

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  • $\begingroup$ Would [optimization] be an appropriate tag? $\endgroup$ – bobble Nov 9 '20 at 0:59
  • $\begingroup$ Yes I suppose it is an optimization. $\endgroup$ – Dmitry Kamenetsky Nov 9 '20 at 1:02
  • $\begingroup$ Shouldn't it be "the total number of mines located in row r AND column c."? $\endgroup$ – Kruga Nov 9 '20 at 8:26
  • $\begingroup$ it depends how you interpret it. We are counting mines that are either in the same row or same column, they can't be in both. $\endgroup$ – Dmitry Kamenetsky Nov 9 '20 at 10:47
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Number of fives:

Twelve

One such grid:

 X 5 X 5 X
 5 X 5 X 5
 X 5 X 5 X
 5 X 5 X 5
 X 5 X 5 X

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    $\begingroup$ Via integer linear programming, this value is optimal. $\endgroup$ – RobPratt Nov 9 '20 at 1:32
  • $\begingroup$ @RobPratt I expected it would be. Thanks for confirmation. $\endgroup$ – Daniel Mathias Nov 9 '20 at 1:33
  • $\begingroup$ Well done! Pretty solution. $\endgroup$ – Dmitry Kamenetsky Nov 9 '20 at 2:29

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