Five red-eye frogs and five orange frogs line up in a row with a space between them.

They have to change places but they can only hop, one frog over another frog or slide to an empty space next to them.

Red-eye frogs can only move to the right and orange frogs can only move to the left and never in the other directions.

How can they change places following these rules?

How many moves will it take?

Try the puzzle with 2 frogs on each side first, then with 3 frogs on each side …

FROGS GAME  Start with 3 frogs on each side and act out the frogs puzzle. You need 7 chairs and 3 people from each team on each side with an empty chair in the middle. If the players get blocked then start again. If there are more players in the teams then the extras can advise the active players. This is not a competitive game, rather a collaborative activity to solve the problem.

Triangle and Tribar variants of the Frogs Puzzle have been invented by Toni and Alan Beardon for the book ‘Lets Play Mathematically AIMING HIGH Family Games. In these puzzles the frogs slide and hop as in the standard puzzle. In the Triangle Puzzle there are 12 cells, 3 on each edge and one at each vertex that is empty at the start. For example, the A and B frogs at the top can change places as follows:

1. Frog A slides into the empty rhombus shaped cell leaving an empty space.

2. Frog B hops over Frog A and lands in the empty cell.

There are 3 different possible starting layouts with 3 frogs on each edge discounting other layouts arising from rotating the triangle or tribar with the frogs ‘riding’ on their edges. Work out how to start from one layout and move to another and how many moves it would take.