Help me understand a little logic problem.
September 5, 2012 4:39 AM Subscribe
Help me understand this. Math/logic puzzle follows...
posted by TheHollowSeasThatRoar to grab bag (6 answers total) 3 users marked this as a favorite
Here are the puzzle and answer, as given by Futility Closet
A worm crawls along an elastic band that’s 1 meter long. It starts at one end and covers 1 centimeter per minute. Unfortunately, at the end of each minute the band is instantly and uniformly stretched by an additional meter. Heroically, the worm keeps its grip and continues crawling. Will it ever reach the far end?
Surprisingly, yes. At the end of the first minute the worm has crawled 1/100 of the way to the far end. At the end of the second minute, it’s crawled (1/100 + 1/200) of the way. So it will reach the far end in t minutes when 1/100 (1/1 + 1/2 + 1/3 + … + 1/t) equals or exceeds 1. The expression in parentheses is the harmonic series, which can be made as large as one desires, but it’ll take a while: In this example the worm will reach its goal in t = 1.509269 × 1043 minutes, or about 286,961,000,000,000,000,000,000,000,000,000,000 centuries.
This makes zero sense to me. Won't the worm always be 1/100 of the way along? First minute: 1 cm of 1 metre. Second minute: 2 cm of 2 metres. Third minute: 3cm of 3 metres. And so on forever.
Am I mistaken somehow?