MathDB
A flea jumps n times from origin

Source:

February 23, 2012
combinatorics unsolvedcombinatorics

Problem Statement

A flea is initially at the point (0,0)(0, 0) in the Cartesian plane. Then it makes nn jumps. The direction of the jump is taken in a choice of the four cardinal directions. The first step is of length 11, the second of length 22, the third of length 44, and so on. The nthn^{th}-jump is of length 2nāˆ’12^{n-1}. Prove that, if you know the final position flea, then it is possible to uniquely determine its position after each of the nn jumps.