1. Minefield study 4
9 steps in the included checked route. Study the given safe opening, then reveal one cell at a time.
PRACTICE COLLECTION
Compare what two clues share
Work with overlapping neighbourhoods and subtract only when one unresolved set contains the other. Notice which extra squares are settled and which shared squares remain unknown.
Print these three studies with answers
Start with a decision
TRY IT 1 · mines-subset-1
| 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 R5C6? Treat the displayed starting marks as established facts, except flags, which the explanation must justify from revealed clues.
Written explanation
Step 1: clue 1 at R1C4 still requires 1 mine among R2C5 after the established safe cells and proved mines are accounted for. Player flags are not used as evidence. Therefore R2C5 is a mine.
Step 2: clue 1 at R1C5 still requires 0 mines among R1C6, R2C6 after the established safe cells and proved mines are accounted for. Player flags are not used as evidence. Therefore R2C6 is safe.
Step 3: clue 2 at R3C5 requires 1 mines in {R3C6, R4C6}; clue 1 at R4C5 requires 1 in its superset {R4C6, R3C6, R5C6}. Subtracting leaves 0 mines in the 1 extra square. Therefore R5C6 is safe.
TRY IT 2 · mines-all-mines-1
| 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 R1C1? Treat the displayed starting marks as established facts, except flags, which the explanation must justify from revealed clues.
Written explanation
clue 1 at R1C2 still requires 1 mine among R1C1 after the established safe cells and proved mines are accounted for. Player flags are not used as evidence. Therefore R1C1 is a mine.
TRY IT 3 · mines-all-safe-1
| 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 R2C5? Treat the displayed starting marks as established facts, except flags, which the explanation must justify from revealed clues.
Written explanation
clue 0 at R1C5 still requires 0 mines among R2C5, R1C6, R2C6 after the established safe cells and proved mines are accounted for. Player flags are not used as evidence. Therefore R2C5 is safe.
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 5
13 steps in the included checked route. Study the given safe opening, then reveal one cell at a time.
3. Minefield study 6
17 steps in the included checked route. Study the given safe opening, then reveal one cell at a time.