If you play Minesweeper on Cool Math Games, this independent guide offers practice with minesweeper safe squares. Its exercises distinguish a proved local deduction from an estimate that depends on additional assumptions.
Sometimes a clue has already accounted for all of its mines. In that situation, its other covered neighbours can be safe under the stated assumptions. The important work is checking those assumptions.
A practical starting point
Subtract only confirmed mines from the clue. If the remaining requirement is zero, the remaining neighbours of that clue need no mines. If it equals the number of covered neighbours, every one of those neighbours must be a mine.
Two exact conclusions from subtraction
If the confirmed mines already satisfy a clue, the remaining neighbouring cells are safe under those assumptions. If the remaining mine requirement equals the number of still-covered neighbours, all of those neighbours are mines. Intermediate counts generally leave several possible assignments. Keep the set boundary visible: a square merely near the clue may lie outside its neighbourhood. Before acting on the conclusion, recheck that each supposedly confirmed flag is actually supported and that no neighbouring cell was omitted.
A mistake to watch for
Do not extend a conclusion beyond the set of squares constrained by the clue. A nearby covered square that is not a neighbour belongs to a different calculation.
Worked examples and practice decisions
Try each question before reading its explanation. These examples are deliberately limited to the information they state. They separate a rule or calculation from a broader judgement about a complete game.
1. Clue exercise 1: check the unknown set
The clue is 2. It has 0 already confirmed neighbouring mines and 2 other covered neighbours. Only these covered neighbours are included in this exercise. Before reading the calculation, separate the covered-cell set from any nearby square that is not part of it. All confirmed mines in this exercise are assumptions stated in the question, not guesses represented by flags.
The remaining mine requirement is 2 − 0 = 2. There are 1 ways to place exactly 2 mines within the 2 unknown neighbours. Every listed unknown neighbour must contain a mine under these assumptions.
Countercheck: the subtraction used 0 confirmed mines, leaving 2 among 2 unknown neighbours. If one flag were only a guess, this conclusion would need to be revisited. Do not silently change a confirmed assumption into an uncertain one while keeping the same answer. Sketch the neighbour set and label exactly which information is established.
2. Clue exercise 2: check the unknown set
The clue is 7. It has 6 already confirmed neighbouring mines and 1 other covered neighbours. Only these covered neighbours are included in this exercise. Before reading the calculation, separate the covered-cell set from any nearby square that is not part of it. All confirmed mines in this exercise are assumptions stated in the question, not guesses represented by flags.
The remaining mine requirement is 7 − 6 = 1. There are 1 ways to place exactly 1 mines within the 1 unknown neighbours. Every listed unknown neighbour must contain a mine under these assumptions.
Countercheck: the subtraction used 6 confirmed mines, leaving 1 among 1 unknown neighbours. If one flag were only a guess, this conclusion would need to be revisited. Do not silently change a confirmed assumption into an uncertain one while keeping the same answer. Sketch the neighbour set and label exactly which information is established.
3. Clue exercise 3: check the unknown set
The clue is 1. It has 1 already confirmed neighbouring mines and 6 other covered neighbours. Only these covered neighbours are included in this exercise. Before reading the calculation, separate the covered-cell set from any nearby square that is not part of it. All confirmed mines in this exercise are assumptions stated in the question, not guesses represented by flags.
The remaining mine requirement is 1 − 1 = 0. There are 1 ways to place exactly 0 mines within the 6 unknown neighbours. Every listed unknown neighbour is safe under these assumptions.
Countercheck: the subtraction used 1 confirmed mines, leaving 0 among 6 unknown neighbours. If one flag were only a guess, this conclusion would need to be revisited. Do not silently change a confirmed assumption into an uncertain one while keeping the same answer. Sketch the neighbour set and label exactly which information is established.
4. Clue exercise 4: check the unknown set
The clue is 6. It has 1 already confirmed neighbouring mines and 5 other covered neighbours. Only these covered neighbours are included in this exercise. Before reading the calculation, separate the covered-cell set from any nearby square that is not part of it. All confirmed mines in this exercise are assumptions stated in the question, not guesses represented by flags.
The remaining mine requirement is 6 − 1 = 5. There are 1 ways to place exactly 5 mines within the 5 unknown neighbours. Every listed unknown neighbour must contain a mine under these assumptions.
Countercheck: the subtraction used 1 confirmed mines, leaving 5 among 5 unknown neighbours. If one flag were only a guess, this conclusion would need to be revisited. Do not silently change a confirmed assumption into an uncertain one while keeping the same answer. Sketch the neighbour set and label exactly which information is established.
5. Clue exercise 5: check the unknown set
The clue is 6. It has 3 already confirmed neighbouring mines and 3 other covered neighbours. Only these covered neighbours are included in this exercise. Before reading the calculation, separate the covered-cell set from any nearby square that is not part of it. All confirmed mines in this exercise are assumptions stated in the question, not guesses represented by flags.
The remaining mine requirement is 6 − 3 = 3. There are 1 ways to place exactly 3 mines within the 3 unknown neighbours. Every listed unknown neighbour must contain a mine under these assumptions.
Countercheck: the subtraction used 3 confirmed mines, leaving 3 among 3 unknown neighbours. If one flag were only a guess, this conclusion would need to be revisited. Do not silently change a confirmed assumption into an uncertain one while keeping the same answer. Sketch the neighbour set and label exactly which information is established.
6. Clue exercise 6: check the unknown set
The clue is 8. It has 3 already confirmed neighbouring mines and 5 other covered neighbours. Only these covered neighbours are included in this exercise. Before reading the calculation, separate the covered-cell set from any nearby square that is not part of it. All confirmed mines in this exercise are assumptions stated in the question, not guesses represented by flags.
The remaining mine requirement is 8 − 3 = 5. There are 1 ways to place exactly 5 mines within the 5 unknown neighbours. Every listed unknown neighbour must contain a mine under these assumptions.
Countercheck: the subtraction used 3 confirmed mines, leaving 5 among 5 unknown neighbours. If one flag were only a guess, this conclusion would need to be revisited. Do not silently change a confirmed assumption into an uncertain one while keeping the same answer. Sketch the neighbour set and label exactly which information is established.
7. Clue exercise 7: check the unknown set
The clue is 3. It has 2 already confirmed neighbouring mines and 1 other covered neighbours. Only these covered neighbours are included in this exercise. Before reading the calculation, separate the covered-cell set from any nearby square that is not part of it. All confirmed mines in this exercise are assumptions stated in the question, not guesses represented by flags.
The remaining mine requirement is 3 − 2 = 1. There are 1 ways to place exactly 1 mines within the 1 unknown neighbours. Every listed unknown neighbour must contain a mine under these assumptions.
Countercheck: the subtraction used 2 confirmed mines, leaving 1 among 1 unknown neighbours. If one flag were only a guess, this conclusion would need to be revisited. Do not silently change a confirmed assumption into an uncertain one while keeping the same answer. Sketch the neighbour set and label exactly which information is established.
8. Clue exercise 8: check the unknown set
The clue is 6. It has 4 already confirmed neighbouring mines and 2 other covered neighbours. Only these covered neighbours are included in this exercise. Before reading the calculation, separate the covered-cell set from any nearby square that is not part of it. All confirmed mines in this exercise are assumptions stated in the question, not guesses represented by flags.
The remaining mine requirement is 6 − 4 = 2. There are 1 ways to place exactly 2 mines within the 2 unknown neighbours. Every listed unknown neighbour must contain a mine under these assumptions.
Countercheck: the subtraction used 4 confirmed mines, leaving 2 among 2 unknown neighbours. If one flag were only a guess, this conclusion would need to be revisited. Do not silently change a confirmed assumption into an uncertain one while keeping the same answer. Sketch the neighbour set and label exactly which information is established.
9. Clue exercise 9: check the unknown set
The clue is 1. It has 1 already confirmed neighbouring mines and 1 other covered neighbours. Only these covered neighbours are included in this exercise. Before reading the calculation, separate the covered-cell set from any nearby square that is not part of it. All confirmed mines in this exercise are assumptions stated in the question, not guesses represented by flags.
The remaining mine requirement is 1 − 1 = 0. There are 1 ways to place exactly 0 mines within the 1 unknown neighbours. Every listed unknown neighbour is safe under these assumptions.
Countercheck: the subtraction used 1 confirmed mines, leaving 0 among 1 unknown neighbours. If one flag were only a guess, this conclusion would need to be revisited. Do not silently change a confirmed assumption into an uncertain one while keeping the same answer. Sketch the neighbour set and label exactly which information is established.
10. Clue exercise 10: check the unknown set
The clue is 8. It has 2 already confirmed neighbouring mines and 6 other covered neighbours. Only these covered neighbours are included in this exercise. Before reading the calculation, separate the covered-cell set from any nearby square that is not part of it. All confirmed mines in this exercise are assumptions stated in the question, not guesses represented by flags.
The remaining mine requirement is 8 − 2 = 6. There are 1 ways to place exactly 6 mines within the 6 unknown neighbours. Every listed unknown neighbour must contain a mine under these assumptions.
Countercheck: the subtraction used 2 confirmed mines, leaving 6 among 6 unknown neighbours. If one flag were only a guess, this conclusion would need to be revisited. Do not silently change a confirmed assumption into an uncertain one while keeping the same answer. Sketch the neighbour set and label exactly which information is established.
Use the guide in your next session
Draw a boundary around the cells you are reasoning about. A simple set label prevents you from applying a correct subtraction to the wrong group of covered squares.
Begin with one observation connected to minesweeper safe squares. After checking an example, close the answer and reconstruct the reasoning in your own words. If a step is uncertain, return to that step rather than repeating a result you cannot explain. A small, specific correction provides a clearer next aim than trying to improve every part of a game at once.
Frequently asked questions
Does a flag prove a mine is present?
A flag records a choice. Subtract it from a clue only when the reasoning has actually established that mine.
Are diagonal cells neighbours?
Yes. Interior clues can refer to eight adjacent cells, while edges and corners have fewer neighbours.
Does a local probability give exact full-board risk?
Only if its assumptions match all relevant information. Other clues or a known total mine count can alter the possible assignments.
More cool math games guides
- Minesweeper Beginner Guide: Read the Eight Neighbours
- Minesweeper Subset Patterns: Compare Two Clues
- Open the relevant game or guide page
Sources and scope
This is an independent, AI-assisted editorial guide. The worked examples and diagrams are original teaching material, not official game screenshots or a claim of personal live-game testing. Game interfaces can change; check the current instructions when controls or rules differ.
