Copyright © University of Cambridge. All rights reserved.
'No Matter' printed from https://nrich.maths.org/
Answer: a multiple of $7$.
Using letters
Let the number thought of be $x$
Double it, then add 3: $2x+3$
Multiply your answer by 4: $4(2x+3)=8x+12$
And then take away 5: $(8x+12)-5=8x+7$
Now take away the number you first thought of: $(8x+7)-x=7x+7 = 7(x+1)$ multiple of $7$.
Using a diagram
Think of a whole number
double it, then add 3
Multiply your answer by 4 and then take away 5
Now take away the number you first thought of
Your answer will always be a multiple of which number?
7