Alice: Pick a 5-digit number.
Bob: Got it.
Alice: Now reverse it and subtract the lesser from the greater.
Bob: Done.
Alice: Now pick one of the five digits of the result and circle it (but don't choose a zero). Tell me the other digits, in some random order.
Bob: Sure; they are 1, 1, 0, and 8.
Alice: Then the circled digit is....

Alice does indeed correctly give the circled digit. How did she do it?

(In reply to How it works- a spoiler by Ady TZIDON)

In this case, the digits are 1, 1, 0, and 8. Since 1+1+0+8=10, the next multiple of 9 is 18. Therefore, the missing digit is 18-10=8.

Posted by Math Man on 2012-11-07 11:46:08