1. Minefield study 7
15 steps in the included checked route. Study the given safe opening, then reveal one cell at a time.
PRACTICE COLLECTION
Prove a move or keep it undecided
Choose among local counting, subset comparison and an honest uncertainty result. The goal is a justified classification, not a lucky selection from the hidden answer.
Print these three studies with answers
Start with a decision
TRY IT 1 · mines-all-mines-2
| C1 | C2 | C3 | C4 | C5 | C6 | |
|---|---|---|---|---|---|---|
| R1 | ||||||
| R2 | ||||||
| R3 | ||||||
| R4 | ||||||
| R5 | ||||||
| R6 |
What can you justify?
Use the all remaining neighbours must be mines technique. What does it prove about R1C2? Treat the displayed starting marks as established facts, except flags, which the explanation must justify from revealed clues.
Written explanation
clue 2 at R2C3 still requires 2 mines among R1C3, R1C2 after the established safe cells and proved mines are accounted for. Player flags are not used as evidence. Therefore R1C2 is a mine.
TRY IT 2 · mines-all-safe-2
| C1 | C2 | C3 | C4 | C5 | C6 | |
|---|---|---|---|---|---|---|
| R1 | ||||||
| R2 | ||||||
| R3 | ||||||
| R4 | ||||||
| R5 | ||||||
| R6 |
What can you justify?
Use the a satisfied clue makes its other neighbours safe technique. What does it prove about R5C6? Treat the displayed starting marks as established facts, except flags, which the explanation must justify from revealed clues.
Written explanation
clue 0 at R6C6 still requires 0 mines among R5C6, R5C5 after the established safe cells and proved mines are accounted for. Player flags are not used as evidence. Therefore R5C6 is safe.
TRY IT 3 · mines-subset-2
| C1 | C2 | C3 | C4 | C5 | C6 | |
|---|---|---|---|---|---|---|
| R1 | ||||||
| R2 | ||||||
| R3 | ||||||
| R4 | ||||||
| R5 | ||||||
| R6 |
What can you justify?
Use the compare overlapping clues by subtracting shared squares technique. What does it prove about R4C1? Treat the displayed starting marks as established facts, except flags, which the explanation must justify from revealed clues.
Written explanation
clue 1 at R6C2 requires 1 mines in {R6C1, R5C1}; clue 2 at R5C2 requires 2 in its superset {R5C1, R4C1, R6C1}. Subtracting leaves 1 mines in the 1 extra square. Therefore R4C1 is a mine.
TRY IT 4 · mines-uncertainty-2
A ?B ?C ?
Exactly 2 mines in these squares; no other constraints.
What can you justify?
This local exercise contains only A, B, C and exactly 2 mines. Is A proved safe or proved mined?
Written explanation
Arrangements with mines at A/B, A/C and B/C all satisfy the count. A is mined in two and safe in one, so the count does not force its value. No probability model is specified.
Apply the ideas to a complete board
These are fixed original studies, not new daily puzzles. The three study links below and this collection’s printable pack use identical starting positions. Their checked solution routes are included on each practice page. A collection’s technique drills may also appear in its lessons.
2. Minefield study 8
21 steps in the included checked route. Study the given safe opening, then reveal one cell at a time.
3. Minefield study 9
21 steps in the included checked route. Study the given safe opening, then reveal one cell at a time.