Two mentalists and the digit that was crossed out
Two performers rehearse a routine. On stage, performer A hands a volunteer these instructions:
- Write down any whole number you like.
- Add up its digits, and subtract that sum from your number.
- From the result, cross out any one nonzero digit.
- Read the remaining digits aloud, in any order you please.
Performer B, blindfolded the whole time, then names the crossed-out digit exactly. No signaling passes between A and B during the act.
What is the secret, and why does it always work?
Your answer
This one is open-ended. Work it through, then check your reasoning against the full solution.