Frogs have a saying: "The Other Lilly Pad Is Always Greener". Some green and yellow frogs were arguing about this until they agreed that they should switch Lilly Pads.

• The green frogs can only be moved to the right and the yellow frogs can only be moved to the left.
• A frog can jump onto an empty Lilly Pad if it is beside it.
• A frog can also jump over a different coloured frog as long as there is an empty Lilly Pad to land on.
• A frog cannot jump over two or more frogs.

Can the frogs switch Lilly Pads?

Extensions:

How many ways are there for the frogs to do this?

How many moves does it take?

What if there were four frogs on both sides?

Can you find the formula that gives the number of moves if there are N frogs on both sides?

Jillian! and Amy! from Bishop Pinkham found that it was still possible to solve if there were 2 frogs on one side and 3 frogs on the other side. How many ways are there to do this?

Same problem with jumping dogs and horses.

Is it possible for all the frogs in the 3 by 3 square below to move to a different Lilly Pad? Frogs can only jump or move horizontally or diagonally. Again frogs can jump over at most one frog of a different colour and only if there is a free Lilly Pad to land on.

I don't particularly like this 3 by 3 extension. Create your own problem and email it to me and I will replace this problem with yours. Please include your first name and school so I can credit you properly. The problem must, of course, be an excellent one.

Credits:

This is a classic problem.

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