MathDB

There are

n

fleas on an infinite sheet of triangulated paper. Initially the fleas are in different small triangles, all of which are inside some equilateral triangle consisting of

n^2

small triangles. Once a second each flea jumps from its original triangle to one of the three small triangles having a common vertex but no common side with it. For which natural numbers

n

does there exist an initial configuration such that after a finite number of jumps all the

n

fleas can meet in a single small triangle?

Problem Statement