Combinatorics

How many tours visit each vertex of a cube once and only once? How many return to the starting point?

Can you find squares within a number grid whose entries add up to an even total?

Investigate the molecular masses in this sequence of molecules and deduce which molecule has been analysed in the mass spectrometer.

Label the joints and legs of these graph theory caterpillars so that the vertex sums are all equal.

Imagine you have six different colours of paint. You paint a cube using a different colour for each of the six faces. How many different cubes can be painted using the same set of six colours?

To win on a scratch card you have to uncover three numbers that add up to more than fifteen. What is the probability of winning a prize?

Find integer solutions to: $\sqrt{a+b\sqrt{x}} + \sqrt{c+d.\sqrt{x}}=1$

I was in my car when I noticed a line of four cars on the lane next to me with number plates starting and ending with J, K, L and M. What order were they in?

Is it possible to use all 28 dominoes arranging them in squares of four? What patterns can you see in the solution(s)?

Third challenge cipher