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### Number and algebra

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# Frogs

Imagine two red frogs and two blue frogs sitting on lily pads, with a spare lily pad in between them.

Frogs can slide onto adjacent lily pads or jump over a frog; frogs can't jump over more than one frog.

**Can we swap the red frogs with the blue frogs?**
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Age 11 to 14

Challenge Level

Watch the video below.

*If you can't see the video, reveal the hidden text which describes the video*

Imagine two red frogs and two blue frogs sitting on lily pads, with a spare lily pad in between them.

Frogs can slide onto adjacent lily pads or jump over a frog; frogs can't jump over more than one frog.

Experiment with different numbers of red and blue frogs.

Can you always swap the frogs over without having to move any frogs backwards?

Can you predict how many moves it will take you?

Can you swap the frogs over when the number of red and blue frogs is not the same?

Can you predict how many moves it will take you?

You can use the interactive environment below or explore with counters.

Full Screen and tablet version

Can you see any patterns in the sequence of moves that it takes to swap the frogs over?

Can you explain why those patterns occur?

**Can you describe a method for swapping all the frogs over in the minimum number of moves?**

Printable NRICH Roadshow resource.

Imagine you are suspending a cube from one vertex and allowing it to hang freely. What shape does the surface of the water make around the cube?

Given the nets of 4 cubes with the faces coloured in 4 colours, build a tower so that on each vertical wall no colour is repeated, that is all 4 colours appear.