Leap Frog
A green frog is sitting on a lily pad on one side of the pond. A brown frog is sitting on a lily pad on the other side of the pond.
The frogs want to swap places without getting wet.
There are three more lily pads for them to jump on.
Each frog takes a turn to jump one lily pad closer to the other side.
They can jump over each other if there's a space to land on. They can't jump backwards.
How did they swap places?
What could happen next?
How will you remember what you've done?
You might find it useful to draw five circles on a piece of paper to represent the lily pads and use two counters for the frogs.
Thank you to Samuel and Sakunthala who sent separate solutions to this problem. Samuel recorded his solution in a very clear way:
B x x x G
x B x x G
x B x G x
x x B G x
x G B x x
x G x B x
G x x B x
G x x x B
Samuel explains that they have both swapped places without getting wet. He says that at school they continued the problem up to 11 pads with 5 frogs of each colour. I wonder whether you noticed any patterns in the numbers of jumps it took each time, Samuel?
Sakunthala did it in exactly the same way but started with the green frog.
Well done both of you!