Wednesday, September 23, 2009

Counter-intuitive puzzles

I've always found that some of my favorite puzzles are those which upon first glance seem to have obvious solutions, but upon deeper analysis end up having answers which defy "gut logic" (an oxymoron if ever there was one). A great example is the classic MontyHall question (Google it if you aren't familiar) and there are others which even when explained they just do not feel right. With that preface answer the following:

Select from the following choices for each of the following questions:

A) giraffe
B) man
C) cat
D) mouse
E) ant

1. The circumference of the earth is about 25,000 miles.
If an elevated road is built around the world that is 50 feet longer than the circumference then what is the largest object which could pass under it?

2. Now imagine a sphere with a diameter of 1/3 of a mile, which gives it a circumference of about a mile.
If an elevated road is built around this sphere that is 50 feet longer than sphere’s
circumference then what is the largest object which could pass under it?

3. Finally, if you could take a basketball and somehow build an elevated road on it that was 50 feet longer than its circumference what could fit under it?


Answers posted in a few days...


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1 comment:

  1. SteveOctober 2, 2009 at 2:35 PM

    ANSWER BELOW








    The answer for all three is B) man.
    If you run through the math it ends up that the length of the radius cancels out of the equation. The critical variable is the increase in the size of the circumference.

    The height of the elevated road is determined by the increased size of the circumference (in this case 50 feet) divided by 2*pi. So the elevated road is 7.96' high in each scenario.

    It doesn't seem like that would be the case by just adding 50 feet to the 25000 MILE circumference of the world, but it is!

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