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Peter’s just finished building a new staircase up to the attic. It just fits along the four-metre-long wall of his lounge room, and it’s three metres tall. It has exactly 15 steps. Peter wants to have a carpet running along the staircase. How long does it need to be?

Time to celebrate! For only the second time ever, an Australian has won the most famous prize in mathematics – the Fields Medal. Let’s take a moment to celebrate the achievements of the winner, Akshay Venkatesh.

Can you work out the next letter in this sequence? H, T, Q, F, S, S, E, N, … Hint: There are numbers lurking behind those letters. And as it grows, this sequence is shrinking!

Imagine your calculator is broken. Although it will still display numbers, only the 4 key, + key, = key and clear key work. Starting at 0, can you get the calculator to display 1000? What’s the fastest way, with the fewest button presses?

Twenty years ago, my mum was twice my age. I’m 42 years old. How old is my mum?

Tomas is putting a number on a letterbox. He puts on one digit. Then he adds another digit. Tomas looks at it and notices that it makes a number exactly five times the first digit.

Kelly has a pet store. She recently got in a whole litter of puppies and tried to sell them all. On the first day, she sold half of the puppies, plus half a puppy.

I caught a bus the other day with a very interesting number. Can you work out the number on the bus?

I want to find a number that is divisible by three. I also want all of its digits to be 8s. Does my number exist?

Here’s a traditional card game that’s bound to get your brain pumping. Being able to add up will help, but there’s plenty more to puzzle over!