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Subject: Friday puzzle- running a marathon rss

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¡dn ʇǝƃ ʇ,uɐɔ ı puɐ uǝllɐɟ ǝʌ,ı
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Chestermere
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There are 10 kinds of people who understand binary: Those who do, and those who don't.
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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 even, say, the interval between 13.6 miles and 14.6 miles – Constance will run it in 8 minutes, and Daphne will be one second slower.

Come up with a "running style" strategy that makes it possible for Daphne to win the race.
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¡dn ʇǝƃ ʇ,uɐɔ ı puɐ uǝllɐɟ ǝʌ,ı
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Chestermere
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There are 10 kinds of people who understand binary: Those who do, and those who don't.
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This puzzle was in The Guardian (last week, I think) so a solution has been posted there for it. I can reproduce the solution if no one here gets it, but I believe in the math minds of Chit Chat so I don't think that I'll have to.
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Christopher Dearlove
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Yes, I did the instant "that's not possible" followed fairly quickly by "aha".

Spoiler (click to reveal)
Run 0.2 mile very, very fast, then 0.8 mile in 8 minutes 1 second (minus how long the 0.2 mile took) each part at constant speed, finishing with a fast spurt.

In the limiting case where you run the 0.2 second in zero time, you lose 26 seconds but gain 0.2x8 minutes or 96 seconds, a net gain of 70 seconds.

To break even the 0.2 mile stretches have to be run in 70 seconds, to win, faster than that. Which is within human limits.
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Geeky McGeekface
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Spoiler (click to reveal)
The key has to be that final 0.2 of a mile. So here's one approach (other methods may be possible). Daphne is actually an android capable of unbelievable speeds, but one that must shut it down often for maintenance. So for every mile of the race, she turns on the afterburners for the first 0.2 of a mile and covers that distance in only 1 second ("We have the technology!"). For the last 0.8 of a mile, she goes into maintenance mode, so that it takes her 8 minutes to run it. Despite this feast or famine style of running, Daphne covers every one mile segment of the race in exactly 8 minutes and 1 second.

Constance's time: 8 x 26.2 = 209 minutes, 36 seconds.
Daphne's time: (26 x 8 minutes) + 27 x 1 second = 208 minutes, 27 seconds.

Daphne wins! Daphne wins! Daphne wins! Fly the D!
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Billy McBoatface
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If I got it right, then it's pretty easy...
Spoiler (click to reveal)
If Daphne teleports 1 mile, then sits still for 8m1s, she will finish in 26tpt×481s/1tpt = 12506s = 208m26s (note that you only count 26 teleports, the last will happen right at the end of the time period and will cross the 26.2 boundary).

Constance will take 26.2mi×480s/1mi = 12576s = 209m16s.

Daphne wins by over a minute!

If teleportation is illegal, then just make Dapne cover the mile in, say, 1s, then wait for 8 minutes. It will only make her take 1s longer, she will still win.
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¡dn ʇǝƃ ʇ,uɐɔ ı puɐ uǝllɐɟ ǝʌ,ı
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Chestermere
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There are 10 kinds of people who understand binary: Those who do, and those who don't.
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The "running teleport" is so much more difficult to pull off than the "standing teleport". laugh
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