### Days and Dates

Investigate how you can work out what day of the week your birthday will be on next year, and the year after...

### Plum Tree

Label this plum tree graph to make it totally magic!

### Magic W

Find all the ways of placing the numbers 1 to 9 on a W shape, with 3 numbers on each leg, so that each set of 3 numbers has the same total.

# Relative Powers

##### Stage: 3 and 4 Short Challenge Level:

-3.

Let the number be $x$. Then $x^3 = 9x$, so either $x=0$ or $x^2 = 9$, giving $x = 3$ or $x = -3$. Of these three values of $x$, only $-3$ is also a solution of the equation $x^2 = x + 12$.

This problem is taken from the UKMT Mathematical Challenges.
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