Spaceship

A spaceship is carrying Bings and Bongs, creatures from the planet Sapphire.

On the spaceship, there are:

* 20 Bings

* 15 green creatures

* 3 Bongs who are not green

* 11 Bings who are green How many creatures are on the spaceship?

Matchbox

The length of a main diagonal through the centre of a large matchbox is 6cm.

The sum of the areas of all the faces is 64cm2.

What is the sum of all the edges of the matchbox?

SOLUTIONS Spaceship (age 6-10) There are 27 creatures on the spaceship.

SOLUTIONS Matchbox (age 14-16) 40cm. The sum of all the edges is 4(a+b+c).

We are given that 2(ab+ac+bc64. Using Pythagoras, a2+b2+c2 = 36.

But (a+b+c)2 = a2+b2+c2+2(ab+ac+bc). So a+b+c = C(36+34)=10. So the sum of all the edges is 40cm.