Modular arithmetic

problem

Knapsack

Age

14 to 16

Challenge level

You have worked out a secret code with a friend. Every letter in the alphabet can be represented by a binary value.
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
Favourite

Filling the Gaps

Age

14 to 16

Challenge level

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

Guesswork

Age

14 to 16

Challenge level

Ask a friend to choose a number between 1 and 63. By identifying which of the six cards contains the number they are thinking of it is easy to tell them what the number is.
article
The Chinese Remainder Theorem

In this article we shall consider how to solve problems such as "Find all integers that leave a remainder of 1 when divided by 2, 3, and 5."
problem

Obviously?

Age

14 to 18

Challenge level

Find the values of n for which 1^n + 8^n - 3^n - 6^n is divisible by 6.
problem
Favourite

Prime AP

Age

16 to 18

Challenge level

What can you say about the common difference of an AP where every term is prime?
problem

Dirisibly Yours

Age

16 to 18

Challenge level

Find and explain a short and neat proof that 5^(2n+1) + 11^(2n+1) + 17^(2n+1) is divisible by 33 for every non negative integer n.
$Happy \birthDay$

problem

Happy BirthDay

Age

16 to 18

Challenge level

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

Rational Round

Age

16 to 18

Challenge level

Show that there are infinitely many rational points on the unit circle and no rational points on the circle x^2+y^2=3.