Modular arithmetic

problem
Take three from five

Age

11 to 16

Challenge level

Caroline and James pick sets of five numbers. Charlie tries to find three that add together to make a multiple of three. Can they stop him?
problem
Grid lockout

Age

14 to 16

Challenge level

What remainders do you get when square numbers are divided by 4?
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
Filling the gaps

Age

14 to 16

Challenge level

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