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The Guardian - UK
The Guardian - UK
Lifestyle
Alex Bellos

Running puzzle: marathon mathematics

OK, it’s not quite tortoise and hare, but ...
OK, it’s not quite tortoise and hare, but ... Photograph: GK Hart/Vikki Hart/Getty Images

The running styles

Constance and Daphne are running a marathon, which we take as being a race of exactly 26.2 miles. Constance runs the entire marathon at a constant speed of 8 minutes a mile. Daphne runs at different speeds, with fast spurts and slower sections, such that she covers every mile in 8 min 1 sec. In other words, whichever mile you take – the first mile of the course, the last mile or, say, the interval between 13.6 miles and 14.6 miles – Constance will run it in 8 minutes and Daphne will be a second slower.

Is it possible that Daphne will win the race?

• Can You Solve My Problems? A Casebook of Ingenious, Perplexing and Totally Satisfying Puzzles by Alex Bellos, £10.99 at bookshop.theguardian.com

• Find the solution here

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