Brain Teasers
Frogger's Pond
Frogger the magic frog can jump 10 feet using his magical magic jump, but his magic loses its power by a half each time, so his next jump only goes as far as 5 feet. The next jump will take him 2.5 feet, and so on. How many jumps does it take to make it all the way across a 100 foot long pond?
Answer
He can't make it to the other side. No matter how much he jumps, he will only travel about 20 feet at the most.Hide Answer Show Answer
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he'd still be able to jump, only it would take him a REALLY, REALLY, REALLY long time. because every time he would still go somewhere from where he was standing. the distance of each jump would never quite reach zero.
The distance would aproach zero and in effect would be just like being zero at some point, but it would never reach zero. This is covered in Calculus. The answer to this question is correct, unless of course the frog could recharge his powers after a few hours of rest.
I remember this question from calculus class. Good teaser though.
Teasers that involve infinite coverging series can be quite confusing, especially if the word time is mentioned. But Xenos paradox can be quite easily explained if time is in fact introduced. Froggers friend Goldie the goldfish doesn't jump but swims smoothly at a constant speed. Presumably, if Froggers jumps half the distance of the last jump, then it only takes him half the time of the last jump. Thus, if he takes 1 second to make the first 10 foot jump, then it only takes him 1/2 a second to make the next jump and 1/4 second to make the next jump etc. Now Goldie who is swimming alongside remember, swims 10 feet in the first second. That's a speed of 10 feet per second. She then swims 5 feet in 1/2 a second, thats 10 feet per second still. The question now becomes how long does it take Goldie to swim 20 feet swimming at 10 feet per second, and the answer is 2 seconds exactly. During these 2 seconds, Frogger has completed an infinite number of jumps! That is the hard bit to comprehend, but it is absolutely true because the time taken for each jump gets smaller and smaller. But yes he does get to the 20 metre mark!
Of course if you say that each of Froggers jumps takes 1 second, then he needs an infinite number of seconds. But if you drop a table-tennis ball and listen to it bounce, do all of the bounces take the same amount of time? NO.
Of course if you say that each of Froggers jumps takes 1 second, then he needs an infinite number of seconds. But if you drop a table-tennis ball and listen to it bounce, do all of the bounces take the same amount of time? NO.
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