# Given a number of items, how many sets of three are there where no two sets are two thirds similar?

Sorry if the title isn't proper math-talk. Hopefully I can explain it better here.

So let's say we have a set. 1, 2, 3, 4, 5, 6, 7, 8, 9. I want to know how many groups of three can be made where no two sets have two items in common.

If (1,2,3) is one group, then no other group can have (1,2), (1,3), or (2,3).

So for nine items we can make:

123
145
167
189
246
258
269
348
379
478


Ten groups that follow those rules.