Modular arithmetic

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?

Choose any whole number n, cube it, add 11n, and divide by 6. What do you notice?

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?

What day of the week were you born on? Do you know? Here's a way to find out.

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?