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
Which of these roads will satisfy a Munchkin builder?
This Sudoku problem consists of a pair of linked standard Suduko puzzles each with some starting digits
This problem involves mathematical reasoning concerning elements of chemistry. For an introduction to mass spectrometry read our article Inspect Your Gadgets.
A diatomic gas of an element with a single stable isotope is analysed in a mass spectrometer. How many peaks will there be? How many peaks will there be if the element forming a diatomic gas has $2$ or $3$ stable isotopes?
When water is analysed in a mass spectrometer there are peaks at relative atomic mass $17$ and $18$. What chemicals do these peaks correspond to? Why are there no peaks at $1$ and $16$?
A compound is analysed and has peaks at $35, 37, 70, 72$ and $74$. What is this compound?
Another compound has peaks at $12, 13, 14, 15, 16$. What might this be? What is it definitely not?
Another compound has peaks at $14, 15, 16, 17$. What might this be? What is it definitely not?
A mixture of two chemicals is analysed and has peaks at $35, 36, 37, 38$ and $40$. What might this be? What is it definitely not?
Extension: A final compound has peaks at (from tallest to smallest) $31, 45, 29, 27, 46, 43, 26, 30, 15, 42, 28, 19, 25, 14, 13, 41, 47, 44, 17, 24, 18, 33, 12$. Can you suggest a likely candidate for the compound? What could the various peaks correspond to?
Other mathematical chemistry problems can be found on the chemNRICH pages.