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This Pied Piper of Hamelin

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2



"The Pied Piper of Hamelin'' is a story you may have heard or read. This man, who is often dressed in very bright colours, drives the many rats out of town by his pipe playing -  and the children follow his tune.

Suppose that there were $100$ children  and $100$ rats. Supposing they all have the usual number of legs, there will be $600$ legs in the town belonging to people and rats.

But now, what if you were only told that there were $600$ legs belonging to people and rats but you did not know how many children/rats there were?

The challenge is to investigate how many children/rats there could be if the number of legs was $600$. To start you off, it is not too hard to see that you could have $100$ children and $100$ rats; or you could have had $250$ children and $25$ rats. See what other numbers you can come up with.
Remember that you have to have $600$ legs altogether and rats will have $4$ legs and children will have $2$ legs.

When it's time to have a look at all the results that you have got and see what things you notice you might write something like this:

a) $100$ Children and $100$ Rats  - the same number of both,
b) $150$ Children and $75$ Rats - twice as many Children as rats,
c) $250$ Children and $25$ Rats -   ten times as many Children as Rats.

This seems as if it could be worth looking at more deeply. I guess there are other things which will "pop up'', to explore.

Then there is the chance to put the usual question "I wonder what would happen if ...?''