A very easy riddle. Four frogs are sitting on the corners of the unit square (i.e. they have coordinates (0,0), (0,1), (1,1) and (1,0) ). Each turn, a frog can jump over any other frog, thereby transferring itself to the symmetrical point on the other side of the static frog. For example, if the frog at (0,0) jumps over the frog at (1,1) it will land on (2,2).

Prove that the frogs cannot transfer themselves to a square with a side of length 2.

I know of two different solutions to this one (both easy ).

Thanks to Nadav Sherman for asking me this riddle.

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