4
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Can you place thirteen mines on a Minesweeper grid such that they create seven 5s? The size of the grid can be arbitrary. The mines may create numbers other than 5s, but those are irrelevant.

A similar question about 4s is here:

Twelve Minesweeper mines that make twelve 4s

Good luck!

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3
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How about (another horrible ascii depiction):

.**.**.
.55555.
*******
..55...
..**...

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  • $\begingroup$ Correct and great work! Different from my solution, but it works. You are very good at these puzzles. $\endgroup$ – Dmitry Kamenetsky Sep 18 at 2:30
  • 1
    $\begingroup$ @DmitryKamenetsky I spent a while on the last one. For this one, I just took the solution to 4 and tweaked it a little. $\endgroup$ – JS1 Sep 18 at 2:31
3
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I brute forced an answer using my minesweeper library at https://github.com/bradmarder/MSEngine

I apologize if this is considered cheating. Here is the snippet of code I used to calculate the answer.

private static void Test()
{
    var watch = System.Diagnostics.Stopwatch.StartNew();
    var iteration = 0;

    while (true)
    {
        var board = Engine.Instance.GenerateBoard(5, 8, 13);
        var count = board.Tiles.Count(x => !x.HasMine && x.AdjacentMineCount == 5);

        if (count == 7)
        {
            var failBoard = BoardStateMachine.GetFailedBoard(board);
            Console.WriteLine(GetBoardAsciiArt(failBoard));
            break;
        }

        Interlocked.Increment(ref iteration);
        Console.SetCursorPosition(0, Console.CursorTop);
        Console.Write($"Iteration = {iteration}, and ellapsed MS = {watch.ElapsedMilliseconds}");
    }
}

012x2
02x5x
14x5x
x5x52
x5x5x
14x5x
02x31
01110

This code took 2,031,528 iterations to find a board that satisfied the criteria. On a side note, I played around with this code to find answers to some of your other Minesweeper questions, but the solutions are exceptionally rare. I stopped running the code after 100+ million failed iterations.

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0
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The solution to this problem and its generalizations (more mines on larger grids) can be found in my integer sequence:

https://oeis.org/A302929/

The actual solutions are here:

https://oeis.org/A302929/a302929.txt

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