Frogs

How many moves does it take to swap over some red and blue frogs? Do you have a method?
Exploring and noticing Working systematically Conjecturing and generalising Visualising and representing Reasoning, convincing and proving
Being curious Being resourceful Being resilient Being collaborative

Problem

Frogs printable sheet



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.

Image
Frogs


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?

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.