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.

Each digit: a(10^n) = a +9a(10^[n-1])+9a(10^[n-2])+...+9a(10^1)+9a(10^0)

Entire number:A= Σa(10^a)=Σa+Σ(9aÓ10^n)

Therefore A-Σa is divisible by 9 => A and Σa leave the same remainder when divided by nine.

Examples:

123 = 100(1)+10(2)+3=99(1)+1+9(2)+2+3 = 1+2+3+99(1)+9(2)=(1+2+3)+9(1+11[2])

4567 = 1000(4)+100(5)+10(6)+7 = 4+4(999)+5+5(99)+6+6(9)+7 = 4+5+6+7+4(999)+5(99)+6(9) = (4+5+6+7)+9[4(111)+5(11)+6)

Edited on March 11, 2004, 11:36 am

Posted by TomM on 2004-03-11 11:32:39