Reasoning, convincing and proving
problem
The London Eye
Age
14 to 16
Challenge level
The 80 spokes of The London Eye are made from 4 miles of cable. What is the approximate circumference of the wheel?
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
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?
article
Binomial Coefficients
An introduction to the binomial coefficient, and exploration of some of the formulae it satisfies.
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?
problem
Interpolating polynomials
Age
16 to 18
Challenge level
Given a set of points (x,y) with distinct x values, find a polynomial that goes through all of them, then prove some results about the existence and uniqueness of these polynomials.