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# Peaches in General

There's a problem which goes like this :

By the time you reach Stage 4 you will start to feel that problems like this are examples or instances of something more general.

Try this problem as it is and then generalise your solution as far as you think you can.

Using a spreadsheet may be a help, but you can judge that for yourself.

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Age 14 to 16

Challenge Level

There's a problem which goes like this :

A monkey had some peaches.

He ate half of them plus one
more.

On the second day, he ate half of
the rest plus one more.

On the third day, he ate half of
the rest plus one more again.

On the fourth day, he found there
was only one left.

How many did he have at the
beginning?

By the time you reach Stage 4 you will start to feel that problems like this are examples or instances of something more general.

Try this problem as it is and then generalise your solution as far as you think you can.

Using a spreadsheet may be a help, but you can judge that for yourself.

Euler found four whole numbers such that the sum of any two of the numbers is a perfect square...

The diagram illustrates the formula: 1 + 3 + 5 + ... + (2n - 1) = nÂ² Use the diagram to show that any odd number is the difference of two squares.

Can you make sense of information about trees in order to maximise the profits of a forestry company?