The number my5teries
Marcus du Sautoy, Professor of Mathematics at Oxford University, has devised a set of five Christmas puzzles especially for Spectator readers. Go on — test yourself!
The Royal Institution Christmas Lectures this year are dedicated to a grand tour of the great mysteries of the universe that mathematics has helped to solve. But at the heart of each of the five lectures is an enigma mathematicians have failed to crack and there is a million-dollar prize waiting for the person who can
PUZZLE 1: the curious incident of the never-ending numbers ‘On the first day of Christmas my true love gave to me a partridge in a pear tree’. But how many presents did ‘my true love’ send on the twelfth day of Christmas?
PUZZLE 2: the story of the elusive shapes Many a stocking will be bulging with the latest computer game but you can’t beat the classic 1979 game Asteroids. In this finite universe, when your rocket shoots off the bottom of the screen it reappears at the top. And if you shoot off the left hand side you reappear on the right. But what is the true shape of the two dimensional astronaut’s universe?
PUZZLE 3: the secret of the winning streak Santa can’t decide which elf to take with him on his big Christmas Eve trip. Since he’s got to get round all the chimneys of the world in one night, he decides to take the elf who can find the shortest path round a test route he’s laid out at the North Pole. What’s the shortest path you can find which visits each of the ten penguins once and once only and returns to the starting point?
You must travel along the paths between the penguins. The numbers denote the distances in metres between penguins. unravel any one of these knotty problems. So as a warm-up to winning your million, here are five seasonal puzzles to get those neurons firing.
Find out more about the million-dollar enigmas that have stumped even the greatest minds (as well as the solutions to our rather more solvable, seasonal puzzles) on page 120.
PUZZLE 5: the quest to predict the future Santa’s reindeer double in population each season but there’s not enough food for all to survive. If last season there were N reindeer, then next season (N/10)x2N of the 2N reindeer will not survive. So if Santa starts with two reindeer, then next season there will be four but 2/10x4=8/10≈ 1 doesn’t survive. So only three survive.
(i) What happens to the population of reindeer over the years?
(ii) Starting with 2 reindeer, what happens if each year the reindeers triple?
(iii) What happens if each year the reindeer quadruple?
What if you start with a different number of reindeer in each model? (Fractions get rounded up or down to the nearest whole number with the convention that 1/2 gets rounded down.)
Solutions on page 120.
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