Prove that k.k! = (k+1)! - k! and sum the series 1.1! + 2.2! + 3.3! +...+n.n!

Find the smallest value for which a particular sequence is greater than a googol.

What is the sum of: 6 + 66 + 666 + 6666 ............+ 666666666...6 where there are n sixes in the last term?

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

The problem is how did Archimedes calculate the lengths of the sides of the polygons which needed him to be able to calculate square roots?

A weekly challenge concerning prime numbers.

Can you invert this confusing sentence from Lewis Carrol?

Can you solve this problem involving powers and quadratics?

A weekly challenge concerning the interpretation of an algorithm to determine the day on which you were born.

This problem explores the biology behind Rudolph's glowing red nose.

A weekly challenge: these are shorter problems aimed at Post-16 students or enthusiastic younger students.

A weekly challenge: these are shorter problems aimed at Post-16 students or enthusiastic younger students.

A weekly challenge: these are shorter problems aimed at Post-16 students or enthusiastic younger students.

Consider these weird universes and ways in which the stick man can shoot the robot in the back.

An arithmetic progression is shifted and shortened, but its sum remains the same...

Can you massage the parameters of these curves to make them match as closely as possible?

Can you rotate a curve to make a volume of 1?

What can you deduce about the gradients of curves linking (0,0), (8,8) and (4,6)?

A weekly challenge concerning combinatorical probability.

Trigonometry, circles and triangles combine in this short challenge.

Can you make all of these statements about averages true at the same time?

Find the location of the point of inflection of this cubic.

A weekly challenge: these are shorter problems aimed at Post-16 students or enthusiastic younger students. What has happened with my online integrator?