📖Definition
A Number Machine (or Function Machine) is basically a set of instructions that are performed on a number.
For example, a Machine divides a number by 2 and adds 3.
Normally, in the 11+ exam, you're told what the Machine does and then given a result and asked to work out what number was put into the machine.
Method
The way to solve this type of question is to start from the end, work backwards and reverse everything.
Sometimes you're not explicitly told it's a Number or Function Machine and you'll get a question like the one in the second example below.
Just follow the same method.
Follow the worked examples to get an idea of how to solve this type of question.
✏️Example
A number machine multiplies a number by 4 and adds 3.
Diagram
✅Solution
What number was put into the machine?
Follow the method start from the end, work backwards and reverse everything
So, at the end, we know the answer 27.
Working backwards we have +3
Reverse this so it becomes -3
27 - 3 = 24
Step backwards again to x 4
Reverse it to ÷ 4
24 ÷ 4 = 6
Now we're at the start so 6 is our answer.
Check by putting it into the machine:
( 6 x 4 ) + 3 = 24 + 3 = 27. So that's right.
✏️Example
3 is added to a number and the result is then squared. The result is 25. What was the original number?
✅Solution
Follow the method start from the end, work backwards and reverse everything
At the end we know the answer 25.
Working backwards, the number was squared so to reverse that, we take the square root of 25.
√25 = 5
Stepping backwards again, 3 was added to the number.
Reverse and subtract 3: 5 - 3 = 2.
2 is our answer.
Check by putting it back into the question.