Wrapping one helicopter is easy. More than one and you run into trouble (Image: Roger Bamber/Rex)

Try to solve two of Professor Stewart’s puzzles here

WHEN I was 14 years old, I started a notebook of every interesting thing I could find out about mathematics that wasn’t taught at school. My notebook grew to a set of six, which I still have, and then spilled into a filing cabinet. Its contents are a miscellany of mathematical games, puzzles, stories and factoids. I recently compiled this miscellany into the book Professor Stewart’s Cabinet of Mathematical Curiosities.

It was fun to go through all those old oddities, not least because it reminded me about, what in my view, is the strangest conjecture in the whole of mathematics – the sausage conjecture.

A conjecture is a statement that mathematicians think could be true, but which no one has yet proved or disproved. It is a problem waiting to be solved, where we have reason to think we know what answer to expect.

The sausage conjecture appears to deal with a simple problem, yet a proof has proved elusive. It asks how efficiently circles or spheres can be wrapped. If you arrange a number of identical circles in the same plane and tie a length of string tightly around them, which arrangement minimises the area inside the string? Santa and his elves would encounter exactly this problem if they were looking to free up some space on the sleigh.

Mathematicians could offer them some help because they have thought long and hard about how to pack things into the smallest possible space.

Not that …