When Thomas Povey prepared a new volume of brainteasers, he ended up with more than would fit between its covers. Here are three more. Please note that the competition is now closed. 

The S factor

In a recent Oxford Today article, Thomas Povey, Professor of Engineering Science, and Tacchi Fellow at University College, spoke about the need to inspire school pupils with an interest in science. Now we hope he can inspire you too.

These three questions are selected from several hundred which didn’t quite manage to beat off the competition to squeeze between the pages of his new book Professor Povey’s Perplexing Problems. His science puzzles have appeared in the Guardian and been featured on BBC Radio 4. A delightful and idiosyncratic romp through pre-university maths and physics, the book is designed to engage students at the school–university boundary — a manifesto that science should be playful, and that we should celebrate the curious.

The puzzles here give a flavour of the book, which has over a hundred questions ranging in difficulty from ★ to ★★★★. If you answer them correctly, you have the chance to win one of five signed copies. Correct answers will be put in a hat from which the five winners will be drawn. Remember that even the ★ puzzles require a little thought. Good luck!

The winners were Jonathan Waldron, John Hart, John Ward, Carol Webster and Robert Payne.

How it works

The deadline for the competition on this page is 31 July 2015. Please send your entries by post or email to Janet Avison, University Offices, Wellington Square, Oxford OX1 2JD.

Email: janet.avison@admin.ox.ac.uk

Please include your full name, alumni number if known, college and matriculation year, and postal address and phone number.

1) Boating party

‘What a lovely morning for a boating party,’ said Professor Sinker, as the party of twelve made their way down to the mooring, ‘the light is Caravaggesque.’ The light was indeed spectacular, the dark clouds of a gathering storm contrasting splendidly with morning light, and with steep waves on the lake adding a little drama to the scene. They walked on for a moment, then Professor Downer, who was clearly troubled by the Caravaggio reference, turned to Sinker and said ‘I think you mean Géricault. It’s the spitting image of The Raft of the Medusa.’ They continued towards the lake.

‘I believe I saw that in the Louvre,’ said Colonel Cadaver. ‘Is it the one where they ate each other?’

‘The very same,’ said Downer. ‘Clearly the subtlety of the work wasn’t lost on you.’

At that moment they arrived at the mooring to find four boats, each of which could take three people. ‘Only four of us including myself know how to row,’ said Sinker, ‘and I always take this boat.’ He pointed to the only boat in a sound state of repair. ‘No need to worry though,’ he continued, ‘once we bail out these other three boats they will be perfectly serviceable. We just need to work out who is going in which boat.’

Professor Povey's perplexing prize quiz

How many ways are there of arranging a boating party of 12 people into four different boats containing three people each if only four of the party are oarsmen, each boat must contain an oarsman, and if one of the oarsmen must be in a particular boat?

Answer: a) 479, 001, 600; b) 39, 916, 800; c) 79, 833, 600; d) 19, 958, 400; e) 40, 320; f) 30, 240; g) 15, 120.


2) A pemmican puzzle ★★

When I was about seventeen, my brother became interested in nutrition. He had a theory that a diet consisting of only brown rice and butter had sufficient nutritional content to keep a person well nourished for months. A devotee of the the scientific method, he stuck to this diet for an entire summer. So far as we could tell he suffered no ill effects.

The real experts on the most calorific and nutritionally sound foods were the early polar explorers. During the Arctic and Antarctic expeditions of the early 1900s, the staple of explorers was pemmican, a pounded mixture of dried meat, fat, and berries, that is extremely rich in both protein and energy. They even fed it to their sled dogs, which in turn became a mobile food store that was similarly rationed. Rear Admiral Robert Peary, a pioneering American explorer who is thought by some to have been the first person to reach the North Pole,  wrote in his 1917 book Secrets of Polar Travel:

‘Too much cannot be said of the importance of pemmican to a polar expedition. . . . Without it a sledge-party cannot compact its supplies within a limit of weight to make a serious polar journey successful. . . . With pemmican, the most serious sledge-journey can be undertaken and carried to a successful issue in the absence of all other foods. Of all foods that I am acquainted with, pemmican is the only one that, under appropriate conditions, a man can eat twice a day for three hundred and sixty-five days in a year and have the last mouthful taste as good as the first.’

As an avid reader of accounts of polar exploration myself, I think it is probably true that Peary was almost alone in finding pemmican delicious. Most people seem to be revolted by its flavour. Peary was so enthusiastic about this magical foodstuff that he even imposed it on his sled dogs. On his last expedition he packed 30,000 pounds of tinned pemmican. I’m glad I wasn’t travelling with his party.

Professor Povey's perplexing prize quiz

A party of explorers has two remaining unopened cans of pemmican. The cans are exactly the same shape, and are manufactured from the same sheet of tin. One can stands three times taller than the other. The smaller unopened can has a mass of 1lb, and the larger unopened can a mass of 25lb. What is the total mass of pemmican in the cans?

Answer: a) 25  8 ⁄ 9  lb; b) 26  lb; c) 25  lb; d) 25  7 ⁄ 8  lb; e) 24  8 ⁄ 9  lb; f) 22  4 ⁄ 5  lb; g) 23  1 ⁄ 9  lb.

NB. Peary’s claim to have reached the North Pole overland by sled on April 6, 1909, went unchallenged for many years, but was later disputed when inconsistencies in his navigational records were found. Amazingly, the first undisputed attainment of the pole by land was not until 19 April 1968, when the American Ralph Plaisted and fellow explorers reached it by snowmobile, an expedition supported by air-drops of fuel and food. Plaisted’s accomplishment only serves to underline how pioneering Peary’s expeditions really were.

3) Elastic bands ★★

I have always enjoyed playing with mechanical equipment. As a child I was endlessly fascinated by combination locks on safes, pulley systems, epicyclic gearboxes and the like. Even the humble elastic band can provide hours of entertainment in the right pair of hands. I remember spending days making a huge  super-ball, the size of a large grapefruit, that was responsible for many high-energy collisions at home; a fly-swatter that could stun flies with pinpoint accuracy from a distance of about half a metre;  and a number of puzzle-boxes with internal guillotine-like mechanisms that would delight guests once the pain caused by almost amputating their fingers had subsided. Elastic bands are also a rich source of amenable puzzles.

Professor Povey's perplexing prize quiz

Two identical elastic bands are each of natural length L (here we refer to half the circumference of the band). One is looped so that it is doubled, creating a band of natural length L ⁄ 2. The other is tripled, so that its natural length is L ⁄ 3. The bands are knotted together at one end, creating a band of overall length L ⁄ 2 + L ⁄ 3 = 5L ⁄ 6. The combined band is stretched over two nails of separation L, with the doubled band looped over the left nail and the tripled band looped over the right nail. Assuming linear behaviour — spring force proportional to extension — what position does the knot take?

Answer: From the left-hand nail: a) (1 ⁄ 2)L; b) (3 ⁄ 4)L; c) (4 ⁄ 5)L; d) (5 ⁄ 6)L; e)(8 ⁄ 13)L; f) (7 ⁄ 12)L; g) (5 ⁄ 12)L.

NB. The fly-swatter design is incredibly simple, and much more accurate and hygienic than any commercial one I have seen. Join elastic bands with simple knots to form a length of about 30cm. When extended to about 75cm and fired at a fly, the free end has a range of about 50cm and arrives sufficiently fast and with low enough energy that the fly never sees it coming, and is normally incapacitated rather than squashed, allowing the offending creature to be safely removed in tissue paper. With a little practice the success rate is about 90 per cent.

Book jacket © Oneworld Publications. Quiz images © Thomas Povey. Listing image, ‘When we begin life, we are given a puzzle’, by Eli Santana via Flickr under Creative Commons licence.