Combinatorics

Chris and Jo put two red and four blue ribbons in a box. They each pick a ribbon from the box without looking. Jo wins if the two ribbons are the same colour. Is the game fair?

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?

Second challenge cipher

Sixth challenge cipher

Can you crack these very difficult challenge ciphers? How might you systematise the cracking of unknown ciphers?

Seventh challenge cipher

Fifth challenge cipher

Fourth challenge cipher

Third challenge cipher

Label this plum tree graph to make it totally magic!