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What exactly is a number machine?

This is a question I asked myself when I returned to tutoring Maths a few years ago. Number machines often turn up in questions of Foundation papers. They provide a useful introduction to quite a few things

  • Algebra
  • Functions
  • Computer Programming – Which is what I was doing before I turned to Tutoring.


Here is an example Number Machine. The idea is we ‘feed in’ a number on the left, and see what comes out on the right.

A simple starter question would be : If a 4 in entered into this number machine, what would the result be. Number machines work left to right, just like reading. In this case, if the input is 4, we follow the boxes left to right and get  4 x 4 = 12 then + 2 = 14 .

A more advanced question would be – If the output is 8, what is the input.  This asks us to move right to left but also do the operations if reverse. Remember reverse of adding is taking away. The opposite of multiplying is dividing.

8 – reverse of + 2 is -2   so the number between the boxes is 6.  6 Divide by 3 is 2.  So the in number must be 2.

Try putting 2 into the machine and see how this is a reverse of what we did above.

The more complicated questions miss out the instructions. For example.

If we put 6 into this number machine we get 6 out. What is missing in the second box?

Clue – Its an subtraction sum.

I’ll show how to answer that in my next post.


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