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Feb 12, 2016 at 19:03 comment added Max Alekseyev This somewhat reminded me the AMM problem 11666 of Fon-Der-Flaass and myself.
Feb 12, 2016 at 2:18 comment added Tony Huynh I know the Oddtown theorem, but I do not know a non-(linear algebra) proof of it. I am not sure my example is what you are looking for either since the second proof still uses linear algebra. But it certainly is a 'counting' proof I feel.
Feb 12, 2016 at 1:32 comment added domotorp You're proving the wrong theorem: exwiki.org/mw/index.php?title=The_Oddtown_theorem
Feb 11, 2016 at 23:25 history answered Tony Huynh CC BY-SA 3.0