MathDB
Jumping flea

Source: Iberoamerican 2005

September 28, 2005
ceiling functionanalytic geometrygeometryrectanglegraphing linesslopecombinatorics unsolved

Problem Statement

A flea jumps in a straight numbered line. It jumps first from point 00 to point 11. Afterwards, if its last jump was from AA to BB, then the next jump is from BB to one of the points B+(B−A)−1B + (B - A) - 1, B+(B−A)B + (B - A), B+(B−A)+1B + (B-A) + 1. Prove that if the flea arrived twice at the point nn, nn positive integer, then it performed at least ⌈2n⌉\lceil 2\sqrt n\rceil jumps.
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