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Here's a neat problem I solved in 8th grade during the preparation for the high school entrance exam:

Let A~1~ B~1~C~1~D~1~A~2~B~2~C~2~D~2~ be a cube with A~1~B~1~C~1~D~1~ being the bottom face and A~2~B~2~C~2~D~2~ the four corners of the top face. Given that A~1~A~2~ is of length 1 what's the distance between D~2~A~1~ and A~2~B~1~.

Let A1B1C1D1A2B2C2D2 be a cube with A1B1C1D1 being the bottom face and A2B2C2D2 the four corners of the top face. Given that A1A2 is of length 1 what's the distance between D2A1 and A2B1.

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