Combinatorics

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?

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?

Third challenge cipher

Fourth challenge cipher

Fifth challenge cipher

Seventh challenge cipher

Second challenge cipher