in an inventory consisting of a list of 100 items, each is marked available or unavailable. there are 55 available items. show that there are at least two available items in the list that are exactly four items apart.
Say this is what part of the list looks like (a=available, n= not available):
a
n
n
n
n
a
n
n
n
n
a
that satisfies the original claim that there's at least two with four between them
note that this takes up 11 lines of 3 a's and 8 n's
100-11=89 (remaining lines)
55-3=52 (remaining a's)
(100-55)-8=37 (remaining n's)
add 52 and 37 to get 89
well, what do you know? 89 is the exact amount of lines you have left! perfecto!