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.
yes, they do
