Word problems - the pigeon hole Principle?

Question

91 five digit numbers are written on a blackboard. Prove that one can find three numbers on the blackboard such that the sums of their digits are equal.

Luv your responses guys...

cn u hv da working for this aswell....sweet...

xx

Answer 1

Ugh, long time since statistics and combinatorics but I'll take a stab.

In 5 digit numbers, the sum of the five digits is between 1 (10000) and 45 (99999) - that's assuming that starting 0 aren't allowed (00025 isn't a real 5 digit number as the value wolld be 25, which is a two digit number)

With 46 numbers you're certain that at least one sum will be shown twice (45+1), with 91 numbers you're certain that at least one sum will be shown three times (45+45+1).

Answer 2

The only way I would know to do this is to visually scan for three numbers that contain the same five digits.

You didn't say if there's anything special about the five-digit numbers.  Are they consecutive or random? do they contain the same digit twice or more (like 33444 for example)? or each digit only once?