At the end of her rope? The Wknd Puzzle by Dilip D’Souza

Sharvari the ant is asking the age-old question: Are we there yet? The rope she’s walking across keeps stretching out in front of her. Can she get to the other side?

An old chestnut of a puzzle that we used to puzzle over as schoolkids involves an elastic rope and an intrepid ant, let’s call her Sharvari.

The rope is stretched taut between two posts that are exactly 10 ft apart. Sharvari climbs up one post and onto one end of the rope. She starts crawling towards the other end at a steady speed of 1 ft per minute. Naturally, you expect that she will reach the other end in 10 minutes.

Only, at the end of the first minute, the rope is stretched uniformly — let’s say the posts are pulled apart — so that it becomes 1 ft longer, 11 ft. At the end of the second minute, it’s stretched again, to 12 ft. Third minute, 13 ft. In fact, this happens with every minute that passes. As for Sharvari, she plods steadily along, unmindful that the pole in front of her seemingly recedes with every minute.

Assume the rope is infinitely stretchable.

Question: Will Sharvari ever reach the other pole?

Scroll down for the answer.

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Answer:

Yes!

If the rope keeps expanding by exactly the distance Sharvari has covered, how will she ever reach the end?

Think about this: The length of rope behind her also expands. So pay attention not to the actual distance Sharvari travels, but to the fraction of the rope’s length she has traversed.

At the start, that fraction is zero. After a minute, she has plodded 1 ft, but there’s 1.5 ft behind her, 9.5 in front. She has travelled 1.5 / 11, or about 12% of the rope.

After two minutes, there’s 3 ft of rope behind her, 9 in front. She has travelled 3/12, or 25% of the rope.

Keep this up and you realise that Sharvari is making progress all the time. She will, in fact, reach the other end in 20 minutes.