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Think of classic Minesweeper game, with the following list of restrictions on the placement of mines:

  • C (Connected): All mines are connected via 8-way neighborhood (orthogonal and diagonal).
  • Q (Quad): Every 2x2 subgrid contains at least one mine.
  • T (Triplet): No three mines are adjacent on a line (row, column, or diagonal). Think of Tic-Tac-Toe.
  • O (Outside): All mines are connected to the outside via 4-way neighborhood (orthogonal), and all non-mine cells are connected via 4-way neighborhood.

Here are some examples under each restriction: (X are mines, and . are cells without mines)

C Q T O
XXX..
...X.
.XX..
..X..
.X.XX
.X..X
..X..
.X..X
.X.X.
.XX.X
X...X
X..X.
.X..X
XX...
...XX
.XX.X
....X
.X...
XXXX.
X....

Now, find the unique combination of two restrictions that allow you to open a cell with 100% certainty on a large enough grid. What kind of cell(s) can you open, and what is the minimum size of such a grid?


Note: The answer to this puzzle spoils how to get a specific achievement in 14 Minesweeper Variants (2022) by Artless Games.

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  • $\begingroup$ Are you saying there is only one unique combination of restrictions? And one specific grid size? $\endgroup$ Feb 20 at 9:40

1 Answer 1

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A grid that satisfies the condition is

a 7x7 grid with Triplet and Outside restrictions.

We can click on

the center cell.

Indeed, if it was a mine, then we would need to connect it to the outside border. To progress towards the border from the center mine, we must do some sort of S shape in any direction:

enter image description here

As we can see, we end up being stuck because of the triplet rule. Hence, the center cell cannot be a mine, so it's safe to click on it!

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  • 2
    $\begingroup$ That was quick. Have you already played the 14 Minesweeper Variants? $\endgroup$ Feb 19 at 6:29

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