Reasoning, convincing and proving

problem
Would you like a jelly baby?

Age

11 to 14

Challenge level

What is the smallest number of jelly babies Tom must take, to be certain that he gets at least one of each flavour?
problem
Would you rather?

Age

7 to 11

Challenge level

Would you rather: Have 10% of £5 or 75% of 80p? Be given 60% of 2 pizzas or 26% of 5 pizzas?
problem
Strange bank account

Age

11 to 14

Challenge level

Imagine a very strange bank account where you are only allowed to do two things...
problem
Magical products

Age

11 to 14

Challenge level

Can you place the nine cards onto a 3x3 grid such that every row, column and diagonal has a product of 1?
problem
Perimeter possibilities

Age

11 to 14

Challenge level

I'm thinking of a rectangle with an area of 24. What could its perimeter be?
article
Binomial coefficients

An introduction to the binomial coefficient, and exploration of some of the formulae it satisfies.
problem
Odds and evens made fair

Age

14 to 16

Challenge level

In this follow-up to the problem Odds and Evens, we invite you to analyse a probability situation in order to find the general solution for a fair game.
problem
To run or not to run?

Age

11 to 14

Challenge level

If an athlete takes 10 minutes longer to walk, run and cycle three miles than he does to cycle all three miles, how long does it take him?
problem
Summing geometric progressions

Age

14 to 18

Challenge level

Watch the video to see how to sum the sequence. Can you adapt the method to sum other sequences?
problem
Kite in a square

Age

14 to 18

Challenge level

Can you make sense of the three methods to work out what fraction of the total area is shaded?