TECHNIQUE 4 OF 4
Recognise when the clues do not settle a square
A useful solver must sometimes stop short of choosing a cell. Understanding what remains uncertain prevents a guess from spreading through later deductions as if it were a fact.
The rule
A square is forced safe or forced mined only when every arrangement consistent with all the constraints under consideration agrees about it. If two such arrangements give it different values, those constraints do not settle it. Look for other clues or relevant total-count information before concluding that the full board requires a guess.
A common mistake
Two visible alternatives do not automatically mean a fifty-fifty chance: there may be other arrangements, differently constrained regions or information not yet considered. Being correct after a guess does not retroactively make the guess a proof.
TRY IT 1 · mines-uncertainty-1
Exactly 1 mine in these squares; no other constraints.
What can you justify?
This local exercise contains only A, B and exactly 1 mine. Is A proved safe or proved mined?
Written explanation
A mined/B safe and A safe/B mined both satisfy the only clue. Neither square is forced. These two arrangements establish ambiguity, not a probability claim.
TRY IT 2 · mines-uncertainty-2
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.
A locally unresolved pair can be resolved elsewhere
One local clue says hidden squares A and B contain exactly one mine. A second independent, valid deduction establishes that A is a mine.
The tempting move
Continue calling B an unavoidable guess because the first clue originally allowed two arrangements.
Why it fails
The additional fact removes the arrangement with A safe and B mined. Uncertainty was relative to the earlier information, not a permanent property of B.
What is actually justified
B is now proved safe. Recompute possibilities when new evidence arrives, and distinguish 'this local clue cannot decide' from 'the entire current board cannot decide'.
Transfer the idea
The only information in a local exercise is that A and B contain exactly one mine. One legal arrangement puts it at A, and another at B. Is either square proved safe? What is the strongest justified statement?
Check your reasoning
Neither square is proved safe or proved mined. Exactly one is a mine, but the local information does not identify which. This statement does not assign probabilities or prove that the rest of a full game board could not resolve the choice.