Exploring and noticing

problem
Favourite

Three by One

Age

16 to 18

Challenge level

1 out of 3

There are many different methods to solve this geometrical problem - how many can you find?
problem
Favourite

Equation Attack

Age

16 to 18

Challenge level

1 out of 3

The equation a^x + b^x = 1 can be solved algebraically in special cases but in general it can only be solved by numerical methods.
problem
Favourite

Root Hunter

Age

16 to 18

Challenge level

1 out of 3

In this short problem, try to find the location of the roots of some unusual functions by finding where they change sign.
problem
Favourite

Climbing Powers

Age

16 to 18

Challenge level

2 out of 3

Does it make any difference how we write powers of powers?
problem
Favourite

Spinners

Age

16 to 18

Challenge level

2 out of 3

How do scores on dice and factors of polynomials relate to each other?
problem
Favourite

It's Only a Minus Sign

Age

16 to 18

Challenge level

2 out of 3

Solve these differential equations to see how a minus sign can change the answer
problem
Favourite

Into the Normal Distribution

Age

16 to 18

Challenge level

2 out of 3

Investigate the normal distribution
problem
Favourite

Folium of Descartes

Age

16 to 18

Challenge level

3 out of 3

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

Counting on Letters

Age

11 to 14

Challenge level

1 out of 3

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

1 out of 3

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.