### Approximating Pi

By inscribing a circle in a square and then a square in a circle find an approximation to pi. By using a hexagon, can you improve on the approximation?

Which of these roads will satisfy a Munchkin builder?

### Twin Equivalent Sudoku

This Sudoku problem consists of a pair of linked standard Suduko puzzles each with some starting digits

# Spectrometry Detective

##### Stage: 5 Challenge Level:
A diatomic gas with a single stable isotope will give two peaks in the mass spectrometer. One of these peaks will be the molecular ion. The other peak will be seen at half the m/z of the molecular ion, and will be due to a fragment of the diatomic gas. For example, Nitrogen gas would give a molecular ion peak due to $N_2^+$ and a fragment peak due to $N^+$.

Look for key facts about the data: smallest numbers, largest numbers, conspicuous gaps in the sequence. What elements in individual form would give rise to some of these? From this you can probably rule out the existence of certain elements, which will allow you to make a start.

There will be an iteration of attempts as you rule out various possibilities.

Be sure to double-check that your final answer gives a convincing explanation for the whole spectrum.