Imagine we have four bags containing numbers from a sequence. What numbers can we make now?

Can you interpret this algorithm to determine the day on which you were born?

Which numbers can we write as a sum of square numbers?

Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?

Mathematicians are always looking for efficient methods for solving problems. How efficient can you be?

A country has decided to have just two different coins, 3z and 5z coins. Which totals can be made? Is there a largest total that cannot be made? How do you know?

How many pairs of numbers can you find that add up to a multiple of 11? Do you notice anything interesting about your results?

Where will the point stop after it has turned through 30 000 degrees? I took out my calculator and typed 30 000 ÷ 360. How did this help?