Henry Ernest Dudeney/Modern Puzzles/47 - The Runner's Refreshment/Solution
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Modern Puzzles by Henry Ernest Dudeney: $47$
- The Runner's Refreshment
- A man runs $n$ times round a circular track whose radius is $t$ miles.
- He drinks $s$ quarts of beer for every mile that he runs.
- Prove that he will only need one quart!
Proof
A lame variant of the Second Pizza Theorem that the author of this page did not believe was worth adding to the jokes page.
From Perimeter of Circle, the distance run is $n \times 2 \pi t$.
During that run, he drinks $n \times 2 \pi t \times s$ quarts of beer.
That is, rearranging the variables:
- $2 \, \text {pi} n t s$
The result follows from the definition of a quart.
Ba-dum tsh.
$\blacksquare$
Sources
- 1926: Henry Ernest Dudeney: Modern Puzzles ... (previous) ... (next): Solutions: $47$. -- The Runner's Refreshment
- 1968: Henry Ernest Dudeney: 536 Puzzles & Curious Problems ... (previous) ... (next): Answers: $75$. The Runner's Refreshment