Copyright © University of Cambridge. All rights reserved.

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

This problem explores structures
like those found in Number Pyramids
and More Number
Pyramids.
A function pyramid is a structure where each entry in the pyramid
is determined by the two entries below it, together with some
function:

The function used in the problems

Number Pyramids
and

More Number
Pyramids could be expressed as:

$$f(a,b) = a+b$$

Here is a function pyramid for you to explore. Type some numbers
into the three spaces on the bottom layer.

Can you figure out how
the rest of the pyramid is generated?
Here are some questions you might like to consider:
Can you choose numbers for the bottom layer so that the number 1
appears in the top cell?

Can you choose numbers for the bottom layer so that the number 5
appears in the top cell?

Can you identify the function used to determine the next layer,
given the bottom layer?

Can you choose numbers for the bottom layer so that the number in
the top cell is negative?

Why not make up some function pyramids of your own, and ask
yourself some similar questions?