Calculator Interrogation: rules and deduction strategies
The challenge is deciding what to ask, rather than calculating faster. Learn what swapped keys and each piece of evidence mean.
What are you trying to find?
Four distinct digits from 0 to 9 are swapped in two pairs. With 1↔7 and 3↔8, typing 12+34 makes the calculator read 72+84 and return 156. Output digits are not swapped again. The remaining six digit keys work normally.
Three questions, one accusation
Each question accepts two integers from 0 to 99. Negative numbers, decimals and three-digit numbers are excluded. You can accuse a wiring before using all three questions, but submission ends the round. Enter four different digits in two pairs. There is no time limit; paper and pencil are welcome.
Why can an ordinary answer still hide a fault?
The answer 12+34=46 does not prove the keys are normal. Swapping 7↔8 and 0↔9 changes none of the digits in that question, so the same answer remains possible. Changes can also cancel each other in a sum. Separate a normal-looking answer from proof of a particular wiring.
How does the calculator escape?
There is no fixed culprit at the start. For each question it groups the wirings consistent with all earlier answers, then chooses the answer retaining the largest group. Ties use the lowest answer. It never discards earlier evidence. You must force a unique wiring and correctly name it to win.
Design a useful question
Repeating a sum adds no evidence. Simply including many digits is not enough either: addition can give the same result for different wirings when positions or operands are exchanged. Change place values and digit combinations so that your remaining hypotheses produce different answers.
Where do the 630 wirings come from?
There are 10×9×8×7÷24=210 ways to choose four digits. Those four digits can form two unordered pairs in three ways, giving 210×3=630 wirings. We checked a strategy that distinguishes every possible answer branch within three questions. This does not mean any three sums will work.
Read a failed round
A wiring that contradicts any answer is wrong. Even a consistent wiring loses if another wiring still fits: the calculator can escape using that alternative. Compare each line of the revealed calculations. Look for untested digits or different swaps that produced the same sum.
Scores and privacy
This is not an IQ test or a verified population ranking. We do not invent percentiles. Inputs and deduction run in your browser. Shared text contains only the outcome and question count. Restarting begins under the same rules.