Magazine article The Spectator

# The Num8er My5teries Solutions

Magazine article The Spectator

# The Num8er My5teries Solutions

## Article excerpt

Puzzle 1: the curious incident of the never-ending numbers There are 78 presents in total. Mathematicians are lazy at heart so we like quick ways to calculate things. So here is a way to make a formula for the presents using a bit of geometry. Stack the presents in a triangle, as below. At the top is one pear tree (P). The second layer contains two turtle doves (T). The third lay contains three French hens (F). The last layer of the triangle (not pictured) would contain 12 drummers drumming along the bottom. Now take an another copy of this triangle, turn it upside down and place it on top of the first triangle.

There are 12 x 13 boxes in total in this rectangle of presents you've built. But this rectangle has twice as many presents as we are trying to calculate. So divide this number by 2 to get 12x13/2=78 presents.

The geometric trick explained with the presents received on the third day of Christmas:

The million dollar question: The Riemann Hypothesis. This prize is associated with another sequence of numbers which doesn't seem to have any formula to help us explain them: the primes. A prime number is a number only divisible by itself and 1, like 17 and 23. The sequence starts with 2, 3, 5, 7, 11, 13, 17, 19, 23, 29. . . The Ancient Greeks proved that the primes continue for ever.

Can you spot the pattern in the primes?

Puzzle 2: the story of the elusive shapes The astronaut lives on a doughnut or bagel or what mathematicians call a torus. Since the astronaut flies off the bottom and comes on at the top, we can join these two bits of the universe up to make a cylinder. But when he flies off the left he rejoins the world on the right hand side of the screen. So the two ends of the cylinder need to be joined to make a bagel shape. The letters and numbers (A, B, 1, 2) show how that universe needs to be joined up.

The million dollar question: The Poincaré Conjecture. What are the possible mathematical shapes that our three-dimensional universe could be? Is it a hyperbagel or can it be something more exotic? It may be that this million will soon be claimed. A Russian mathematician, Grigori Perelman, grabbed the headlines this summer with the news that he might have cracked the search for the elusive shapes.

Puzzle 3: the secret of the winning streak 238 metres is the shortest path round the penguins. But don't despair if you couldn't find a clever way to the solution. Mathematicians can only solve this by trial and error.

The million dollar question: P versus NP.

This is an example of NP-complete problem or "a needle in a haystack" problem. Called the Travelling Salesman Problem, the only way to guarantee finding the shortest path seems to be by trying them all out. …

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