The Breakroom > The Water Cooler

Bit of a maths puzzle

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raynerd:
I was talking to some students a few weeks ago and they showed me this puzzle, I know the answer and have been amazed with it for the last few days. I thought with you guys being use to dimensions and sizes you might like it.

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Imagine a perfect sphere, about the size of the Earth and tie a string around it, pull it tight...really tight, so tight that you can`t even slide a razor blade under it at any position. Now you cut the string and add a meter. So now if you like, you have the original length that fit perfectly around the Earth plus this meter slack. Now if you got millions of people/robots to line up around the string and pull upwards perfectly evenly to move the string off the Earth, would that meter now give you enough slack to now slide a razor blade under it all the way around?

No tricks...just maths.
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 :smart:
Chris

z3t4:
Yep.

Circumference of sphere, of radius r, = 2πr.
Increase circumference by 1, so new circumference = C+1 = 2πr + 1 =2π(r+1/2π).

The string is then 1/2π metres (about 6") above the surface of the sphere.

Very counterintuitive.

HTH

John

cidrontmg:
It is indeed. Itīs the same amount (15.9 cm) no matter what the original sphere diameter. If the "sphere" is a point, it is the radius of a circle with a circumference of one meter.
Another counter-intuitive fact: Most people have more legs than the average.   :scratch:   Huh???    :doh:
Most people have 2 legs. But not all. Even if thereīs just one one-legged man, the average is below 2. I.e. most people have more than the average number of legs.  :smart:
 :wave:

andyf:
And another: if 23 people are in a room, there is more than 50% probability that two of them will share the same birthday (day and month, not the year of birth). With 50 people, the probability rises to 97%.

Andy

mklotz:
Suppose you're on a game show and you're given the choice of three doors [and will win what is behind the chosen door]. Behind one door is a car; behind the others, goats [unwanted booby prizes]. The car and the goats were placed randomly behind the doors before the show. The rules of the game show are as follows: After you have chosen a door, the door remains closed for the time being. The game show host, Monty Hall, who knows what is behind the doors, now has to open one of the two remaining doors, and the door he opens must have a goat behind it. If both remaining doors have goats behind them, he chooses one [uniformly] at random. After Monty Hall opens a door with a goat, he will ask you to decide whether you want to stay with your first choice or to switch to the last remaining door. Imagine that you chose Door 1 and the host opens Door 3, which has a goat. He then asks you "Do you want to switch to Door Number 2?" Is it to your advantage to change your choice?

I'll publish the answer after you've had a chance to confuse yourselves.

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