1d packing mini-challenge

a programming challenge

You have an unlimited supply of black and red checkers.

You stack checkers next to each other into two piles on a level table.

In the first pile, you stack N red checkers, then M black checkers,
then P red checkers, and then (possibly) repeat M black/P red checkers for
a total of X times.

In the second pile you do the same, with (possibly) different values
of N,M,P, and X.

Without examining the stacks checker by	checker, for any given set of
values N,M,P,X,N',M',P',X', say	whether	or not two black checkers are side-by-side.
Or in	other words, solve it in less than O(min(@stack_heights)).