### 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.

# Square Ratio

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

1:3

Let the length of a short side of a rectangle be $x$ and the length of a long side be $y$. Then the whole square has side of length $(y+x)$, whilst the small square has side of length $y-x$. As the area of the whole square is four times the area of the small square, the length of the side of the whole square is twice the length of the side of the small square. Therefore $y+x=2(y-x)$, i.e., $y=3x$ so $x:y=$1:3.

This problem is taken from the UKMT Mathematical Challenges.

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