Solving technique
How to Solve Number Elimination Puzzles Without Guessing
Guessing is tempting when two candidates look alike. A more dependable method is to identify the exact clue that separates them and keep both until that clue has been tested.
Choose an efficient order
A broad filter such as odd/even or a range can remove many numbers quickly. Then use more specific digit and remainder clues on the survivors. The clue order does not change the answer, so begin with the rule you can check most confidently.
- Cross out only candidates that fail a stated rule.
- Finish testing one clue against all survivors before moving on.
- On a tablet, tap a used clue to mark your place.
Write down why a number was removed
For a paper puzzle, write a small clue number beside a cross if the register is crowded. In the online sampler, the clue and number marks can be changed as you solve. If you find a contradiction later, you can retrace the decision instead of restarting the whole puzzle.
- Never eliminate a candidate because it 'seems wrong'.
- Check multi-digit numbers digit by digit.
- Recalculate remainders rather than doing them from memory.
When you are stuck with two survivors
Compare the two numbers directly. Which properties do they share, and which differ? For example, 42 and 48 are both even and begin with 4, but they have different last digits and digit sums. Re-read the clues that test those differences. One of them should exclude one candidate.
- Look for the first differing digit.
- Compare their digit sums.
- Check any remainder condition on both.