Reducing Minesweeper Clues | minesweeperpatterns

See the pattern step by step

Three covered squares sit above 2-3-2. A known mine below the middle 3 touches all three clues. The bottom corner squares show 1s. Subtract the known mine from each clue: 2 − 1 = 1, 3 − 1 = 2, and 2 − 1 = 1. The remaining counts above form 1-2-1. Both ends of the top row have flags. Its middle square is open and shows 2. The known mine below stays flagged. The clue row stays 2-3-2. — Download image

Board example

The row shows 2-3-2. One known mine sits below the middle number. It touches all three numbers. Only the three squares above the row are left to check. Subtract 1 from each number: 2−1=1, 3−1=2 and 2−1=1.

Before

Three covered squares sit above 2-3-2. A known mine below the middle 3 touches all three clues. The bottom corner squares show 1s.

After

Both ends of the top row have flags. Its middle square is open and shows 2. The known mine below stays flagged. The clue row stays 2-3-2.

Why it works

The remaining counts are 1-2-1. Apply that pattern to the three squares above. Both ends have mines, and the middle is safe. The known mine below stays in place. In the picture, the safe middle square opens to show 2.

Subtract the known mine from each clue: 2 − 1 = 1, 3 − 1 = 2, and 2 − 1 = 1. The remaining counts above form 1-2-1.

The rule

For each number, count the known mines that touch it. Subtract that count from the number. The result is the number of mines in its remaining unknown squares. Keep those squares in the same places.

What to check

Count known mines for each number. Include a mine only if it touches that number. Check all unknown squares, including the corners. Count a flag as a known mine once the numbers prove it.

Keep the board numbers and remaining counts distinct

A flag counts as a known mine when the numbers prove it. Subtract that mine only from clues that touch it, including at a corner. In 2-3-2, the mine below the middle touches all three clues, leaving 1-2-1 for the three squares above. The printed numbers stay 2-3-2; the smaller counts are notes. A flag placed on an assumed mine gives the wrong starting count. Check its proof before you use it in another deduction.

Read the board, then choose

Each flag marks a known mine. Subtract it from every number it touches: 2 − 1 = 1, 3 − 1 = 2, 2 − 1 = 1. The remaining counts are 1-2-1. In the covered row, both ends have mines and the middle is safe.

A three-row, three-column board places covered A, B and C above a row of 2, 3 and 2. Below them are 1, a known mine with a flag, and 1. The flag touches each middle clue, so their remaining counts are 1, 2 and 1. Applying those counts proves both top ends mined and the top middle safe. The visible numbers stay 2-3-2, and the top squares stay covered.

Subtract the known mines2 − 1 = 3 − 1 = 2 − 1 =

Choose a covered square. Then decide whether it is safe, has a mine, or needs more information.

Why this answer is correct

A: Mine · B: Safe · C: Mine

The shown covered squares are the only unknown squares around these numbers. Gaps stand for open squares or the board edge. Check every nearby square before you apply the result. Flags in these examples mark known mines.