AUSTRIAN-POLISH 1996 Problem 9

For any triple $(a, b, c)$ of positive integers, not all equal, We are given sufficiently many rectangular blocks of size $a \times b \times c$ . We use these blocks to fill up a cubic box of edge $10$ . (a) Assume we have used at least $100$ blocks. Show that there are two blocks, one of which is a translate of the other. (b) Find a number smaller than $100$ (the smaller, the better) for which the above statement still holds.