TITLE: riddle that involves elementary geometry
QUESTION [10 upvotes]: $3$ frogs are positioned at the vertices of an equilateral triangle whos sides are of length $1$. We have $1$ frog on each vertex.
The frogs are able to "leap" one over another. When they do, they will land in the symmetric spot to where they jumped from as shown on this drawing.

they can jump in any order they want and also any number of times they want.
Is it possible to arrange the frogs such that they are on the vertices of an equialteral triangle whos sides are equal to $2$?

REPLY [8 votes]: It seems that it is imposiible because in the following coloring of a triangle (with side 1) grid we see that grid vertices of each triangle with side $1$ are 3-colored, 
grid vertices of each triangle with side $2$ are 1-colored, and a jump doesn't change the color of the jumping frog place.