### Euler's Squares

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

### Odd Differences

The diagram illustrates the formula: 1 + 3 + 5 + ... + (2n - 1) = n² Use the diagram to show that any odd number is the difference of two squares.

### Peeling the Apple or the Cone That Lost Its Head

How much peel does an apple have?

# Peaches in General

##### Stage: 4 Challenge Level:

Obviously start by doing the original problem, that's plenty hard enough as a first challenge if you haven't seen anything like it before, but after that ask yourself the question:

• What things might generalise?

Perhaps the fraction taken each day, or the number of days , or the 'plus one more', or something else, but take those possibilities one at a time.

If you use a spreadsheet (and there are really strong reasons for doing that in this type of problem), what do you need to calculate in each column of the sheet? You can have as many columns as you want, so do simple calculations, then calculations further along the row that use those answers, rather than complicated calculations in single cells.

Will you make your first column a number of peaches before any eating happens? It might be better to have the number of peaches in the final column, making your row a calculation trail that deduces the number at the start?