# Who drinks beer while running anyway?

A variant (I don't have the book in front of me, so this is a paraphrase) of this puzzle was in the book Brainteasers and Mindbenders, by Robert Hamilton. It has stuck in my mind since I read it in junior high or whenever.

A runner is running around a circular track with a radius of $t$ miles. The runner runs around the track a total of $n$ times. Every time the runner completes one mile of his run, he takes a chug of beer, drinking a total of $s$ quarts for every mile he runs. So, given this information...

Prove that the runner only drinks a single quart of beer over the course of his run!

• Would lateral thinking be appropiate? (I assume so, because for example t,n,s=50000,5,5 obviously disproves this claim) – Quintec Feb 19 '18 at 1:05
• I was thinking, but the tag specifies logic to be used, and it's not exactly logic that is used in the correct answer. – Exal Feb 19 '18 at 1:10
• added it after seeing the solution - the last step is definitely lateral thinking. – Quintec Feb 19 '18 at 1:26
• Meanwhile the rest of us that were cursed with the metric system are out of luck on this one. – Amit Naidu Feb 19 '18 at 2:39
• relevant: en.wikipedia.org/wiki/Beer_mile – dpel Feb 19 '18 at 14:31

Turns out that he drinks exactly

2 pints = 1 quart

because

Circ = 2 * pi * t
Miles = Circ * n
Beer = Miles * s
Beer = 2 * pi * n * t * s = 2 pints

Just to answer the title "Who drinks beer while running anyway?". How about legend Paul Armstrong. He drinks pints while running, even if the reason he's running is he's in the middle of a terror attack.

When people said we aren't going to let terrorists affect our way of life, Paul took that very seriously.

To answer the posed question, Paul can drink at most 1 quart of beer while running because he only has two hands and a pint in each is a quart of beer. Going back for more is probably not an option.

http://metro.co.uk/2017/06/05/revealed-the-man-who-refused-to-let-terrorists-ruin-his-pint-6685736/

I'd also like to give an answer to the title question by mentioning Andy Holden:

https://en.wikipedia.org/wiki/Andy_Holden_(athlete)

He was a famous amateur long-distance runner, who could also drink copious amounts of alcohol - he once was rumoured to have run 100 miles and drunk 100 pints (50 quarts) in one week. About a half-marathon and 14 beers a day!