Pick four integers. Calculate their six pairwise differences. Multiply all those differences. Prove that the result is a multiple of 12.

1. Out of any 4 numbers at least two are equal modulo 3

2. The following table presents the quantity of even differences

for any number of even numbers in the chosen set of four:

0 EVEN NUMBERS...............6 EVEN differences

1........................................3

2........................................2

3 .......................................3

4..........................................6

this .shows that the PRODUCT will include factors 3 and 2^2

i.e. will be a multiple of 12.