MathDB

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.

Problem Statement