Puzzle fairness
Why a Number Puzzle Needs One Provable Answer
A good elimination puzzle does more than point toward a likely number. Every other candidate must fail a stated clue, and the answer must satisfy them all.
What 'one answer' means
Imagine a register containing 42, 47 and 48. A clue that the answer is even removes 47 but leaves 42 and 48. It has narrowed the search, yet it has not solved the puzzle. Add a clue that the digit sum is greater than 10: 42 has sum 6 and 48 has sum 12. Only 48 survives both rules.
- The answer must be in the register.
- It must satisfy every clue.
- Every other registered number must fail at least one clue.
Why each clue should have a job
In The Hidden Number Files, the generator checks that removing any one clue would leave more than one possible number. That means each clue contributes to the uniqueness of that puzzle. You can solve in a different order, but you should be able to see why the complete set is necessary.
- A clue can still eliminate several candidates.
- A useful clue may only become decisive after other clues.
- An extra decorative statement is not needed to identify the answer.
Audit your own solution
After finding the survivor, test it against each clue. Then pick another number from the register and identify at least one condition it breaks. That second check explains why the answer is proved rather than simply plausible. If the published clue seems ambiguous, follow its exact wording and recalculate before revealing the answer.
- Check the survivor against all clues.
- Check excluded numbers against at least one failing clue.
- Correct mistaken crosses before pressing Check answer.