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Why did the chicken cross the Möbius strip?

To get to the same side.

This joke might be funnier if the answer is:

To get to the other side.

(The mathematicians will know that the chicken's quest will fail. Then they'll feel sorry for the chicken...)

But the non-mathematicians will JUST give you a weird look, rather than laughing and then giving you a weird look.

I don't know. A cliche can seem funny if you add a little twist, even if the twist is incomprehensible.