#### You may also like

List any 3 numbers. It is always possible to find a subset of adjacent numbers that add up to a multiple of 3. Can you explain why and prove it?

### Magic Sums and Products

How to build your own magic squares.

### No Matter

Weekly Problem 2 - 2013
After performing some operations, what number is your answer always a multiple of?

# Multiple Magic

##### Stage: 3 Short Challenge Level:
3.

Call your first number $x$. Doubling and adding five gives $2x+5$. Doubling and adding two gives $2(2x+5)+2=4x+12$. Subtracting $x$ then leaves $3x+12=3(x+4)$ which is always a multiple of 3.

This problem is taken from the UKMT Mathematical Challenges.
View the archive of all weekly problems grouped by curriculum topic

View the previous week's solution
View the current weekly problem