Pick any number with at least three different digits. Jumble the digits however you want to create a different number. Take these two numbers and find their difference. Their difference is your new number. Pick a non-zero digit in your new number and remove it. Give me the rest of the digits in any order you please. From this, I can work out what digit you removed.

How do I find your digit? Why does this work? Prove it.

The idea for this puzzle was taken from a mindreading program here.

(In reply to proof by ramu)

The difference will be a multiple of 9; not necessarily a multiple of 99. Neither is the sum of the digits in a multiple of 99 always 18; but similarly, the sum of digits in a multiple of 99 is a multiple of 9.

Posted by DJ on 2004-03-13 02:44:59