If you play Minesweeper on Cool Math Games, this independent guide offers practice with minesweeper beginner guide. Its exercises distinguish a proved local deduction from an estimate that depends on additional assumptions.
A numbered square describes its surrounding neighbours, including diagonals. It does not describe only the squares above, below, left and right. Missing that detail changes every later deduction.
A practical starting point
Separate a clue’s total from the mines you have already confirmed around it. The remaining requirement applies to the still-covered neighbours. That subtraction is the starting point for the examples.
Describe the clue as a neighbour count
A Minesweeper clue counts mines among its adjacent squares, including diagonals. At an edge there are fewer neighbours than in the interior. Separate already confirmed mines from still-covered neighbours, then subtract the confirmed count from the clue. The resulting requirement applies only to those remaining neighbours. A flag is not automatically a proof, so every subtraction in these exercises clearly states which mines are assumed confirmed. No first-click safety guarantee is implied for an unspecified version.
A mistake to watch for
A flag records a belief unless the position has proved it. Do not subtract an uncertain flag as if it were established fact. The worked examples clearly label which flagged neighbours are assumed confirmed.
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 5. It has 4 already confirmed neighbouring mines and 4 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 5 − 4 = 1. There are 4 ways to place exactly 1 mines within the 4 unknown neighbours. The clue alone does not identify which of the listed neighbours contains a mine.
Countercheck: the subtraction used 4 confirmed mines, leaving 1 among 4 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 4. 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 4 − 2 = 2. There are 15 ways to place exactly 2 mines within the 6 unknown neighbours. The clue alone does not identify which of the listed neighbours contains a mine.
Countercheck: the subtraction used 2 confirmed mines, leaving 2 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.
3. Clue exercise 3: check the unknown set
The clue is 5. It has 0 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 5 − 0 = 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 0 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.
4. Clue exercise 4: check the unknown set
The clue is 8. It has 7 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 8 − 7 = 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 7 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.
5. Clue exercise 5: check the unknown set
The clue is 6. It has 6 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 − 6 = 0. There are 1 ways to place exactly 0 mines within the 2 unknown neighbours. Every listed unknown neighbour is safe under these assumptions.
Countercheck: the subtraction used 6 confirmed mines, leaving 0 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.
6. Clue exercise 6: check the unknown set
The clue is 4. It has 0 already confirmed neighbouring mines and 7 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 4 − 0 = 4. There are 35 ways to place exactly 4 mines within the 7 unknown neighbours. The clue alone does not identify which of the listed neighbours contains a mine.
Countercheck: the subtraction used 0 confirmed mines, leaving 4 among 7 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 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.
8. Clue exercise 8: 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.
9. Clue exercise 9: check the unknown set
The clue is 1. It has 0 already confirmed neighbouring mines and 4 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 − 0 = 1. There are 4 ways to place exactly 1 mines within the 4 unknown neighbours. The clue alone does not identify which of the listed neighbours contains a mine.
Countercheck: the subtraction used 0 confirmed mines, leaving 1 among 4 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 6. It has 2 already confirmed neighbouring mines and 4 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 − 2 = 4. There are 1 ways to place exactly 4 mines within the 4 unknown neighbours. Every listed unknown neighbour must contain a mine under these assumptions.
Countercheck: the subtraction used 2 confirmed mines, leaving 4 among 4 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
Before opening another square, describe the clue in a sentence. State how many neighbours remain and how many mines must still be among them. This makes the difference between a deduction and a guess visible.
Begin with one observation connected to minesweeper beginner guide. 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 Safe Squares: Subtract Confirmed Flags
- 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.
