A function pyramid is built up layer by layer — enter the values for the bottom layer, and each value higher up the pyramid is determined by applying some function to the two values immediately below it.

This activity challenges you to experiment with various values and try and determine the particular function being applied.



Function Pyramids
Can you crack the code and find the function?
Select a function using the buttons at the bottom, and try and work out the function by entering various values in the bottom cells. (The higher numbers are harder.) Use the … button to enter your own function and challenge a friend!
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About the activity

Some things to try:

  • Choose function 1 and look for patterns in the numbers at the top. Can you explain any patterns you find?
  • Still with function 1, can you get all the numbers from 0 to 20?
  • When exploring other functions, limit your options by only allowing distinct numbers in the bottom row.
  • Once you've found out the function, choose a particular target number, and see if you can get it at the top of the pyramid.
  • Don't forget to try negative numbers and decimals.
  • Can you get an integer at the top but decimals in the middle with function 9 selected?

The rightmost button, labelled …, allows you to enter your own functions using a and b as variables for the values of the left and right cells below, basic expressions using the operators +, −, * and /, and functions from the javascript Math object. For example, to simply add the two inputs you would enter:

a + b
whereas
Math.abs(a - b)
would calculate the absolute difference between the inputs. Allowed functions are described here.