Department of Mathematics
Undergraduate Problem Solving Competition

Problem 5 (2/10 - 2/24) - Left-handed clocks

A "left-handed" clock has its numbers printed counter-clockwise and runs counter-clockwise to point at them, effectively performing as a mirror image to a normal clock. Besides noon, midnight and 6:00:

a) Considering only the hour and minute hands, which we consider indistinguishable, are there any times at which the hands of a left-handed clock point in exactly the same directions as those of a regular clock?

b) Are there any such times when we consider all three hands of the clock (again, postulating that they are indistinguishable)?

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