This is a well known puzzle but even if you have met it before you may find more mathematics in it this time round. You can solve it on the computer below or use a line of coloured counters or act it out getting some friends to play the roles of frogs and toads.

Start with some frogs in a line on one side and some toads on the other and some spaces in between. The frogs and toads have to change places taking as few moves as possible. They can SLIDE to an adjacent empty space or HOP over one other frog or toad to an empty space on the other side.

Can you swap them over without moving any frogs or toads backwards? With 3 frogs and 3 toads and one space between how many moves does it take? How many hops? How many slides? Now vary the numbers of frogs and toads and find how many moves are needed each time. Can you find a formula?

Try playing this with some friends and you'll see whether they pull together as a team, or not. Usually people get in a muddle at first and enjoy solving this puzzle together. Divide the group into frogs and toads. Set out a row of chairs and sit the frogs on one side and the toads on the other. Explain what they have to do and tell them when to start.

To move a frog or a toad, just click on it. There's no need to click and drag to the space into which you want to move (why?). If the piece cannot move, then nothing will happen. If it can, then it moves into the empty space. In this version of the game, the toads cannot move to the left, and the frogs cannot move to the right, so think carefully before you move.

When you have solved the problem (or when you are stuck), you can click "Play Again!" to start the game over. After mastering 3 frogs and 3 toads, try changing the numbers before you select "Play Again". Any numbers for the frogs and toads will work provided that there is at least one frog and one toad, but not more than twenty total critters at a time.