A flea jumps n times from origin
Source:
February 23, 2012
combinatorics unsolvedcombinatorics
Problem Statement
A flea is initially at the point in the Cartesian plane. Then it makes jumps. The direction of the jump is taken in a choice of the four cardinal directions. The first step is of length , the second of length , the third of length , and so on. The -jump is of length . Prove that, if you know the final position flea, then it is possible to uniquely determine its position after each of the jumps.