Exploring and noticing

problem
Favourite

Folium of Descartes

Age

16 to 18

Challenge level

Investigate the family of graphs given by the equation x^3+y^3=3axy for different values of the constant a.
problem

Approaching Midnight: First or Second?

Age

7 to 14

Jennie tried the Approaching Midnight game and wondered if it matters whether you go first or second.
problem

Approaching Midnight: Start Time

Age

7 to 14

Bernard played Approaching Midnight and wondered whether the start time affects who wins.
problem

Approaching Midnight: Changing Smallest Step

Age

7 to 14

Liz played Approaching Midnight and wondered how changing the smallest step size affects the game.
problem

Counting on Letters

Age

11 to 14

Challenge level

The letters of the word ABACUS have been arranged in the shape of a triangle. How many different ways can you find to read the word ABACUS from this triangular pattern?
problem

Alphabet Soup

Age

11 to 14

Challenge level

This challenge is to make up YOUR OWN alphanumeric. Each letter represents a digit and where the same letter appears more than once it must represent the same digit each time.
problem

Only Connect

Age

11 to 14

Challenge level

The graph represents a salesman’s area of activity with the shops that the salesman must visit each day. What route around the shops has the minimum total distance?
problem

Royal Arm Wrestling

Age

11 to 14

Challenge level

How many arm-wrestles will there be in the royal arm wrestling championship?
problem

Mobile Numbers

Age

5 to 11

Challenge level

In this investigation, you are challenged to make mobile phone numbers which are easy to remember. What happens if you make a sequence adding 2 each time?
problem

Suit Sequence

Age

11 to 14

Challenge level

A pattern repeats every six symbols. What are the 100th and 101st symbols?