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This puzzle consists of 36 tiles. Each tile has a digit and may or may not have a mine.

The goal is to assemble a 6×6 Minesweeper grid — in other words, each digit must equal the number of mines adjacent to it (including diagonals). Unlike in traditional Minesweeper, the mines themselves have digits on them, but they only count the surrounding mines, not themselves. It’s therefore possible to have a mine with a 0 on it.

Two example puzzles and a possible solution for each are shown below. The solutions may unfortunately may not be unique (even beyond just rotation and reflection).

Puzzle 1 Solution 1

Puzzle 2 Solution 2

Here’s what we found so far:

  • There are 𝑐 mines in the corners, each of which is seen by 3 tiles
  • There are 𝑒 mines on the edges, each seen by 5 tiles
  • There are 𝑖 mines on the inside, each seen by 8 tiles
  • Therefore, 3𝑐 + 5𝑒 + 8𝑖 = 𝑠, where 𝑠 is the sum of all digits on all tiles
  • Also, 𝑐 + 𝑒 + 𝑖 = 𝑛, where 𝑛 is the number of mines
  • This gives rise to a set of Diophantine equations, which usually have only 1 or 2 solutions because 0 ≤ 𝑐 ≤ 4.

Beyond this, we haven’t found much else to go by. Is there a way to approach this puzzle that doesn’t amount to literal trial and error?

Any additional deductions would be helpful, even if they don’t solve the whole puzzle.

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    $\begingroup$ Looks like it's from an interactive game. Can you share the source? $\endgroup$
    – Bubbler
    Dec 7 '20 at 7:25
  • $\begingroup$ @Bubbler It’s a mod for KTANE and the mod is Mineswapper. You need the game on Steam in order to play it. $\endgroup$
    – Timwi
    Dec 7 '20 at 7:27
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Will not solve the puzzle, but will assist in trial and error:

An edge and an adjacent corner cannot have a difference greater than 3

An edge and an adjacent edge cannot have a difference greater than 3

An edge and an adjacent inside cannot have a difference greater than 4

A corner and an adjacent inside cannot have a difference greater than 6

An inside and an adjacent inside cannot have a difference greater than 4

This leads to some if statements that count as a logical deduction.

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