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  • Qu117 - A pemmican puzzle
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Posted March 31, 2015 by in Bonus Scaling Questions 2485

Qu117 - 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 foods were the early polar explorers. During the Acrtic and Antarctic expeditions of the early 1900s, the staple of explorers was pemmican, a pounded mixture of dried meat, fat, 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 though 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 enthustiastic about this magical foodstuff that he even imposed it on his sled dogs, writing

Pemmican is the only food for dogs on a serious polar sledge journey.

On his last expedition he packed 30,000 pounds of tinned pemmican. I’m glad I wasn’t travelling with his party.

A party of explorers has two remaining tins of pemmican. One stands three inches high and has a mass of 1  lb. The second stands 9 inches high, and has a mass of 25  lb. The tins are exactly the same shape, and are manufactured from the same sheet of tin. What is the total mass of pemmican in the tins?

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  1. Profile photo of Carol
    Carol April 12, 2015
    Reply

    Proposed solution:
    Mass of tin scales as dimension^2 because it scales by surface area.
    Mass of pemmican scales as dimension^3 because it scales by volume.
    The large tin is 3 times as tall as the small tin.
    Therefore, the mass of the large empty tin is 9 times the mass of the small empty tin.
    The mass of the large wodge of pemmican is 27 times the mass of the small wodge of pemmican.
    Writing simultaneous equations for the combined mass of pemmican and tin for both tins, we can solve for the mass of each wodge of pemmican (and also the mass of each empty tin).
    I obtain the following result: total mass of pemmican contained within both tins: 24 8/9 lb.
    More specifically, mass of pemmican in large tin = 24 lb, mass of pemmican in small tin = 8/9 lb, mass of large empty tin = 1 lb, mass of small empty tin = 1/9 lb.

  2. Profile photo of Carol
    Carol April 12, 2015
    Reply

    How many stars for that one?? Other questions that spring to mind are: 1. How does pemmican compare with brown rice and butter in terms of calorie density? 2. Was pemmican transported in cylindrical tins? Surely rectangular would pack more compactly. Perhaps cylindrical was less prone to leakage/botulism? 3. What do they eat now, and is it any nicer?

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