Embarassed to say that I didn't realize it was a problem in finite projective geometry until seeing Joel's post. Kept thinking graph theory.
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Anyway, housemate got about half of the idea from that post, then we spent a lovely evening going over the math by hand on the kids' easel.
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Nice side effect for me is that I understand concretely & not just abstractly why you use spaces over Z/p and not arbitrary Z/n.
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Say n is composite = pq. Then the line y = px intersects the line y = 0 q times, and y = 1 never! (and projectivizing doesn't fix that).
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oops, intersects p times I mean. i.e.: look at y = 3x mod 15. equals zero for x = 0, 5, 10.
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OBVIOUSLY Rev why u so dum
End of conversation
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. Banned in Sweden. SubGenius, Zhuangist, white-hat troll. Defrocked mathematician. Brain problems.