### Isosceles Meld

Weekly Problem 9 - 2012
What is the angle QPT in this diagram?

Weekly Problem 10 - 2012
If you know how long Meg's shadow is, can you work out how long the shadow is when she stands on her brother's shoulders?

### Heptagon Has

Weekly Problem 15 - 2012
How many of the five properties can a heptagon have?

# Ice Cream Pie

##### Age 11 to 14 Short Challenge Level:

$90$ chocolate ice creams were sold.

The angle occupied by the 'chocolate' sector is $1/2(360^{\circ} - 90^{\circ}) = 135^{\circ}$.

This is $1.5$ times bigger than the 'strawberry' sector, so the number of chocolate ice creams sold is $1.5 \times 60 = 90$.

This problem is taken from the UKMT Mathematical Challenges.
You can find more short problems, arranged by curriculum topic, in our short problems collection.