NRICH: More Number Pyramids

In the number pyramid below, the number in the bottom left hand corner determines all the other numbers.

Try entering some different numbers.
What patterns do you notice?Here are some questions to consider:


  • If I give you the number in the bottom left hand corner, can you work out the top number without working out the middle layers?
  • Can you explain why some numbers are impossible to get at the top, if you start with a whole number in the bottom left hand corner?
  • If I give you the number at the top, can you find a quick way of working out the number in the bottom left hand corner?

Do your insights still apply if you use negative numbers or decimals?

Can you justify any generalisations that you have reached?
Perhaps you could use algebra to explain your thinking.

Can you adapt what you discovered about 4-layer pyramids to larger pyramids?


What if the numbers on the bottom layer go up in 2s? Or 3s?

Here is an interactive number pyramid, where the bottom layer can go up by numbers other than one, which can be used to test out your conjectures.
You might now like to have a go at Top-heavy Pyramids

Age 11 to 14 

This problem follows on from Number Pyramids.

Algebra & Pre-Algebra, Linear Equations, Quadratic Equations
Middle School, High School, Educator

What are you looking for?


NRICH (University of Cambridge)

Website URL

Type of Resource

Online Interactive Activity

Assigned Categories