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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