Cat and Mouse

The problem

A mouse is at the centre of a circular pond. A cat who wants to eat the mouse is at the edge. The mouse can run faster than the cat, but can only swim at ¼ of the speed the cat can run. The cat will not enter the water.

Can the mouse escape the cat? How?

What path should it take to escape most quickly?

The solution

There’s no physical model with this puzzle, but lower down is a link to a model in GeoGebra that illustrates the solution. I particularly like the puzzle as it is solvable without using anything other than basic maths, but to find the optimum escape path uses a mix of techniques that is a nice challenge for A level maths students.

To see the escape path in action Click here

And to see the calculations that show how the path is determined Click here