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While working on an old weaving machine, Aisha spied a dial that needed repairing. The dial had numbers counting upwards, evenly spaced around the outside. Although she couldn’t see the whole dial, she could see that the number 6 was directly opposite 17. Can you work out how many numbers there are on the dial?

Fred is a biologist doing an experiment with pademelons. They have a square paddock and four feeding bowls. They also have two laser detectors that each shoot a straight beam all the way across the paddock.

Terri was doing sums for her signwriting business. She worked out that one-third of six and two-thirds of eleven together made seven. Her maths might seem wonky, but she was completely correct. Can you work out what she was trying to do?

There are three types of fruit in the fruit bowl: All pieces of fruit are bananas, except for three of them. All pieces of fruit are apples, except for four of them. All pieces of fruit are oranges, except for five of them.

Alice, Bernice and Claire are all speedy bike riders. They decided to race against each other to find out who is fastest cyclist. They ran three races together. In two races, Alice beat Bernice. In two races, Bernice beat Claire.

On Dr Vine’s desk there is some money. There are six pieces of Australian money. The money adds up to $63.

I have four playing cards: two of them are black and two are red. I turn them face down so you can’t see the colours, and shuffle them so you don’t know which is which.

This shape has a little secret. It’s known as a chamfered cube, and it’s not as perfect as it first seems…

Gerri has two identical square tarpaulins. Unfortunately, these tarps aren’t quite big enough to cover the brand new spa bath. So Gerri’s decided to cut the tarps and tape them together to make a bigger tarp. They want their final tarp to be a square, and they want it to be as big as possible.

There’s a lot we don’t know about the tooth fairy. We don’t know what they look like, or how they get around, or even what they do with all the teeth they gather. But researchers around the world have been keeping tabs on the finances of this elusive tooth collector.