### Snooker

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

### Snooker Frames

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?

### Modular Knights

Try to move the knight to visit each square once and return to the starting point on this unusual chessboard.

# Jluuis or Even Asutguus?

##### Stage: 5 Challenge Level:

Have you managed to solve the entire Stage 5 Cipher Challenge? Solutions are now closed, but perhaps you want to take up the full challenge.

Successful solvers of this part were

Patrick from Woodbridge School, England
An Anonymous Solver from Somewhere in the US
Joseph from Hong Kong

The solution is:

This was a Caesar shift of seventeen followed by a transposition of rows and columns. This of course retains the letter frequencies of English, which probably helped you decipher this. In this case, the two methods of encryption commute, however this isn't always the case. Apart from some special cases, if we use a vigenere cipher and then a transposition, we will get a different result depending on which order we do them in. Can you find any cases for which these will commute?