A flea jumps in a straight numbered line. It jumps first from point 0 to point 1. Afterwards, if its last jump was from A to B, then the next jump is from B to one of the points B+(B−A)−1, B+(B−A), B+(B−A)+1.
Prove that if the flea arrived twice at the point n, n positive integer, then it performed at least ⌈2n⌉ jumps. ceiling functionanalytic geometrygeometryrectanglegraphing linesslopecombinatorics unsolved