How to Solve Mine Finder Puzzles: Beginner Strategies Step by Step

To solve a Mine Finder puzzle you need three ideas, and each one is a way of counting. This page teaches them one at a time and then uses all three on a real Medium grid, move by move. If you do not know the rules yet, read the Mine Finder puzzle rules first.

Before you start

Use a pencil and two marks: draw a small mine where you are sure there is one, and put a dot where you are sure there is none. Every deduction below turns an empty square into one of those two marks, and each new mark helps the numbers around it. Remember that a number counts all 8 squares around it, diagonals included, and that a numbered square is never a mine.

Here is the grid we will use. It is a Medium puzzle (10 x 10, 16 mines) made by the LogikLand generator.

Rows are counted from the top and columns from the left.

Strategy 1: zeros and full numbers

Start with the numbers that decide everything about their neighbours.

A 0 makes every empty neighbour safe

The 0 in row 2, column 1 touches the empty squares at row 1 columns 1 and 2, and row 3 columns 1 and 2. None of them is a mine, so put a dot in each.

A number with exactly as many empty neighbours as mines

The 2 in the top right corner (row 1, column 10) has only three neighbours. One of them, row 1 column 9, is a number. That leaves two empty squares, row 2 columns 9 and 10, for two mines: both are mines. The same reading works for the 2 in row 2, column 2: once the four dots from the 0 are in, only row 2 column 3 and row 3 column 3 are still empty, so they are both mines.

A number that already has all its mines

The 2 in row 1, column 9 touches the two mines we just found, in row 2 columns 9 and 10. It needs no more, so its other empty neighbours, row 1 column 8 and row 2 column 8, are safe.

Strategy 2: count what is left

Both moves above are the same calculation: mines left = the number minus the mines already found around it. Then compare it with the empty squares around the number.

Do this for every number on the grid, then do it again: every new mark changes the count of the numbers around it. In this grid the nearby zeros (row 5 column 6, row 7 columns 6 and 10, and row 8 column 8) put a dot on every neighbour of the 1 in row 7, column 8 except one, row 6 column 8. The 1 needs one mine and has one empty square left: that is a mine.

Strategy 3: compare two numbers

Sooner or later every number is in the third line of the table above, and you need to look at two numbers together. This is the idea that the Medium level asks for. Take two numbers that are next to each other. If the empty squares around the first one are all among the empty squares around the second one, then the extra squares of the second number hold the difference of their mines.

A safe square from two numbers

Look at the 1 in row 4, column 8 and the 2 in row 5, column 9. At this point of the solution the 1 in row 4 column 8 has two empty neighbours, row 4 column 9 and row 5 column 8, and needs one mine. The 2 in row 5 column 9 already touches the mine in row 6 column 8, so it needs one more mine among three empty squares: row 4 column 9, row 5 column 8 and row 4 column 10. Two of those three are the empty squares of the 1, and they hold exactly one mine. The 2 needs only one mine in all, so the third square, row 4 column 10, is safe.

A mine from two numbers

The same idea can place a mine. The 2 in row 9 column 4 has three empty neighbours and needs one mine (it already touches the mine in row 9 column 3). The 2 in row 9 column 5 needs two mines among those same three squares and one more, row 9 column 6. The three shared squares hold exactly one mine, so the second mine of the 2 in row 9 column 5 must be in the extra square: row 9 column 6 is a mine.

Working through a Medium grid

This is the order in which a logical solver finds the squares of the grid above. We solved the same grid with a separate program written for this article, which uses only the three strategies of this page, and it reached the solution with no guess: 19 of its 32 deductions are the "everything around it is safe" reading (a 0, or a number that already has all its mines), 9 are mines found by counting the empty neighbours, and the remaining 4 compare two numbers.

1. The 2 in the top right corner: two mines (row 2, columns 9 and 10).
2. The 2 beside it (row 1, column 9): row 1 column 8 and row 2 column 8 are safe.
3. The 0 in row 2, column 1: its four empty neighbours are safe.
4. The 2 in row 2, column 2: mines in row 2 column 3 and row 3 column 3.
5. The zeros in the middle of the grid (row 4 column 5, row 5 column 6, row 7 column 6, row 7 column 10) clear large areas at once.
6. The 1 in row 7, column 8: its one empty neighbour, row 6 column 8, is a mine.
7. Two comparisons, described above, finish the middle and the bottom: row 4 column 10 is safe, row 9 column 6 is a mine.

The grid has 16 mines. When your drawn mines reach 16 and every number agrees with the mines around it, the puzzle is solved.

When you are stuck

• Go through the numbers again from the top. A mark you added ten minutes ago may have finished a number you skipped.
• Look for pairs of touching numbers that share most of their empty squares.
• Count the mines you have drawn. The total under the grid tells you how many are left to find.
• Check your marks. One wrong dot makes a number look impossible; if a number has no solution, a mark near it is wrong.

Practice

Easy puzzles need only the first two strategies, which is why they are the right place to begin. Medium puzzles add the comparison of two numbers; Hard and Expert grids go further, as described in advanced Mine Finder techniques. Beginners can also print a few grids from our printable easy Mine Finder puzzles.

Questions