Minesweeper Pyramid Patterns

A 2 sits above a 1. One covered square forms the top point, with three covered squares along the bottom. The top point has a mine. The bottom row is safe.

See the pattern step by step

A 2 sits above a 1. A is the covered top point. B, C, D and E form the four covered side squares. F, G and H are the covered bottom row. The 2 counts A plus the four shared squares. The 1 counts the shared squares plus F, G and H. Subtraction gives A − (F + G + H) = 1. A flag marks the mine at the top point, A. Circles mark F, G and H along the bottom as safe. The four shared side squares remain unknown and contain one mine. — Download image

Board example

The upper clue gives A + B + C + D + E = 2. The lower clue gives B + C + D + E + F + G + H = 1. Subtracting gives A − (F + G + H) = 1.

Before

A 2 sits above a 1. A is the covered top point. B, C, D and E form the four covered side squares. F, G and H are the covered bottom row.

After

A flag marks the mine at the top point, A. Circles mark F, G and H along the bottom as safe. The four shared side squares remain unknown and contain one mine.

Why it works

A can hold at most one mine. The equation therefore requires a mine in A and no mines in F, G or H. One mine remains among the four shared squares. A 3 above a 2 gives the same top and bottom results, with two mines in the shared group.

The 2 counts A plus the four shared squares. The 1 counts the shared squares plus F, G and H. Subtraction gives A − (F + G + H) = 1.

The rule

Both clues touch the same four unknown squares at their sides. The 2 also touches A at the top point. The 1 also touches F, G and H in the bottom row.

What to check

There must be just one unknown square that touches the upper clue alone: the top point. The four side squares touch both clues. The three bottom squares touch only the lower clue. Check all three groups.

Try this board

Read the board, then choose

Both clues touch the same four unknown squares at their sides. The 2 also touches A at the top point. The 1 also touches F, G and H in the bottom row.

A four-row, three-column board has covered A at the top middle, with omitted open space or board edge beside it. A 2 sits above a 1 in the middle column. Four covered side squares touch both clues; three covered squares form the bottom row. The upper clue counts A plus the shared group, while the lower counts that group plus the bottom. Their difference proves A mined and the bottom safe. One mine remains unresolved among the four side squares.

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: Not enough information · C: Not enough information · D: Not enough information · E: Not enough information · F: Safe · G: Safe · H: Safe

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.

Try the same idea with other numbers

Read the board, then choose

Try the same idea with other numbers

A four-row, three-column board places covered A at the top middle between two omitted open spaces or board edges. A 3 sits above a 2 in the middle column. Four covered side squares touch both numbers; the three bottom squares touch only the 2. Subtracting the shared group leaves A minus the bottom-row mine count equal to one. Therefore A must have a mine and all three bottom squares are safe. Two mines remain unresolved among the side squares.

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: Not enough information · C: Not enough information · D: Not enough information · E: Not enough information · F: Safe · G: Safe · H: Safe

See the pattern step by step

Board example

Before

After

Why it works

The rule

What to check

Read the board, then choose

Try the same idea with other numbers

Read the board, then choose

Privacy