Problem of the Week 1103

Missing Digit

Alice: Pick a 5-digit number.

Bob: Got it.

Alice: Now reverse it and subtract it from the original.

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 four 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?

Suggested by Bill Owens, Macalester '01.

© Copyright 2008 Stan Wagon. Reproduced with permission.

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