Cantor

Too bad the matching rules seem ridiculous too me. Sometimes the obvious match is not accepted but some very different looking stones are considered the correct matchup.

I don't understand the rules. The tutorial made it seem like you have to select three things and they either have to share a color, shape, or texture or they all have to have a different color, shape, or texture, but that isn't working.

@xXNoPPeXx Eh? You've got a bunch of sets in there. Just picking an arbitrary one off the bat: {(1,1,1), (2,3,1), (3,2,1)}. First coord is all different, second coord is all different, third coord is all same.

@Kenaron 13 elements and I can't find a set. (1,1,1) (1,2,1) (2,1,1) (3,3,1) (2,3,1) (3,2,1) Next layer is the same. (1,1,2) (1,2,2) (2,1,2) (3,3,2) (2,3,2) (3,2,2) and last layer (2,2,3)

@galmacky I looked over that article and it shows the opposite. Suppose you rank your elements as just 3 numbers each 1-3. So one element can be 1-1-1, then 1-1-2, etc. Lets say you have 8 elements that represent every combination of 1 and 2. You don't have a match yet. But whatever the 9th element is must have a 3 in it somwehre. And it makes a match. Replace all 3's in your element with 1 and that's the second element. Replace the 3's with 2 for your second. Match had.

Any other attempt to make in impossible set is fundamentally isomorphic to the situation described above. You literally can not get stuck in this version, though in higher dimensions it becomes possible. If there are N different characteristics, with 3 characteristics each, you need 2^n +1 objects to guarantee a set.