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Difficulty: Tricky Clare and Jeremy just finished a job overseas, on Dough Island. They received the following as payment, in the island’s currency: A $3 coin A $4 coin A $6 note An $8 note and A $9 note. Clare and Jeremy want to share the money so they both get the same number of…

Picture this: you’ve just bought a nice little cake, just for you. Then your friends show up, wanting a piece. Lucky for you, mathematicians have developed some pretty cool ways of sharing.

Imagine this game: you and a stranger are sitting in front of a machine. The machine has two piles of lollies. There’s one pile for you and one for your partner. You have two handles. Pull the green handle and you both get lollies. Pull the red one and no one gets anything.