The tangles created by the twists and turns of the Conway rope
trick are surprisingly symmetrical. Here's why!
How many ways can the terms in an ordered list be combined by
repeating a single binary operation. Show that for 4 terms there
are 5 cases and find the number of cases for 5 terms and 6 terms.
A walk is made up of diagonal steps from left to right, starting at
the origin and ending on the x-axis. How many paths are there for 4
steps, for 6 steps, for 8 steps?
Libby Jared helped to set up NRICH and this is one of her favourite
problems. It's a problem suitable for a wide age range and best
Find the values of n for which 1^n + 8^n - 3^n - 6^n is divisible