Modular arithmetic

problem
What numbers can we make now?

Age

11 to 14

Challenge level

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

problem
Happy birthDay

Age

16 to 18

Challenge level

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

Age

14 to 16

Challenge level

Which numbers can we write as a sum of square numbers?
problem
What numbers can we make?

Age

11 to 14

Challenge level

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

Age

16 to 18

Challenge level

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

Age

11 to 14

Challenge level

Mathematicians are always looking for efficient methods for solving problems. How efficient can you be?
problem
How much can we spend?

Age

11 to 14

Challenge level

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?
problem
Elevenses

Age

11 to 14

Challenge level

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

Age

14 to 16

Challenge level

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

Age

11 to 14

Challenge level

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?