Copyright © University of Cambridge. All rights reserved.

## 'Number Pyramids' printed from http://nrich.maths.org/

Choose three single-digit numbers and write them in the bottom
row of the pyramid.

This text is usually replaced by the Flash movie.

Try some different numbers.

Can you work out how the numbers in the upper layers are
generated?

Here are some questions to
consider:

- Given the numbers on the bottom layer in order, can you find a
quick way to work out the number at the top?
- If you change the order of the numbers on the bottom layer,
will the top number change?
- If you can rearrange the numbers on the bottom layer, can you
find a quick way to work out the largest possible number that
could go at the top?
- Given the number at the top, how can you come up with possible
numbers to go at the bottom?

Test out your observations and insights. You could use big numbers,
small numbers, negative numbers, decimals...

Can you explain
what is happening?

Can you explain why it is happening?

Can you explain it algebraically?

Can you adapt your insights so
that they apply to pyramids with more than three
layers?
Here is a number pyramid with four layers so that you can test
some of your ideas:

Full Screen
Version

This text is usually replaced by the Flash movie.

To experiment with 5 and 6 layer pyramids, you may find

this
spreadsheet useful.

You could adapt it to work on even larger pyramids!

For other problems that use this idea go to

More Number
Pyramids.