Combinatorics

problem
Plum tree

Age

14 to 18

Challenge level

Label this plum tree graph to make it totally magic!
problem
Magic caterpillars

Age

14 to 18

Challenge level

Label the joints and legs of these graph theory caterpillars so that the vertex sums are all equal.
problem
Euler's officers

Age

14 to 16

Challenge level

How many different ways can you arrange the officers in a square?
problem
Snooker frames

Age

16 to 18

Challenge level

It is believed that weaker snooker players have a better chance of winning matches over eleven frames (i.e. first to win 6 frames) than they do over fifteen frames. Is this true?
problem
N000ughty thoughts

Age

14 to 16

Challenge level

How many noughts are at the end of these giant numbers?
problem
Snooker

Age

16 to 18

Challenge level

A player has probability 0.4 of winning a single game. What is his probability of winning a 'best of 15 games' tournament?
problem
Russian cubes

Age

14 to 16

Challenge level

I want some cubes painted with three blue faces and three red faces. How many different cubes can be painted like that?
problem
Doodles

Age

14 to 16

Challenge level

Draw a 'doodle' - a closed intersecting curve drawn without taking pencil from paper. What can you prove about the intersections?
article
An introduction to computer programming and mathematics

This article explains the concepts involved in scientific mathematical computing. It will be very useful and interesting to anyone interested in computer programming or mathematics.
article
Symmetric tangles

The tangles created by the twists and turns of the Conway rope trick are surprisingly symmetrical. Here's why!