Try to solve this very difficult problem and then study our two suggested solutions. How would you use your knowledge to try to solve variants on the original problem?
A weekly challenge: these are shorter problems aimed at Post-16 students or enthusiastic younger students.
The active Stage 5 problems. Why not submit a solution or chat about things on the blogs?
Advent Calendar 2011 - a mathematical activity for each day during the run-up to Christmas.

Hi, I'm Steve. I look after all aspects of the Stage 5 parts of NRICH. I like inventing maths problems and activities on anything to do with maths. You can email me on post16.nrich@maths.org if you'd like to see something specific. I'm keen that all students are given the opportunity to enjoy maths irrespective of their particular interests or ways that they think and learn.