## Brain Teasers! (No really, this is homework.)

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Sun Sep 13, 2009 10:26 pm
LowKey says...

20. It turns out there is a final exam for this course. I give you 8 marbles that are exactly alike except that one of them is slightly heavier than the others. I then give you a balance scale and ask you to determine the heavier marble in 3 weighings. Will you pass your final exam?

21. Okay, you got through that one, but now it turns out that you don’t obtain math certification unless you can determine the heavier marble in only 2 weighings. Will you get your certification?

22. Why does time seem to pass more quickly as we get older? (I’m not just making small-talk here; there’s an actual mathematical reason for this. And I’m not suggesting that any of us are getting old—although you may feel that you’ve aged just because of these quantitative reasoning exercises.)

24. You and a friend stand side by side and begin walking so that your right feet hit the ground at the same time. You take exactly 3 steps for each 2 steps of your friend. How many steps go by before you and your friend’s left feet simultaneously hit the ground?

26. Enough fairy tales; let’s do something down-to-earth. Suppose the earth is a smooth, perfectly round sphere. Imagine a rope pulled snug around the earth’s equator. If we add 10 feet of length to this rope and then prop it up evenly all the way around the planet, how far above the earth’s surface would it be? And since this exercise may feel a little more like math than the rest, here are 4 answers to choose from:

a) less than one millimeter
b) between one millimeter and one inch
c) between one inch and one foot
d) greater than one foot

I've done the others already. These are just what I need help on still.
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Once was Dreamer, is now LowKey_Lyesmith.

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Sun Sep 13, 2009 10:46 pm
Karsten says...

Dreamer wrote:20. It turns out there is a final exam for this course. I give you 8 marbles that are exactly alike except that one of them is slightly heavier than the others. I then give you a balance scale and ask you to determine the heavier marble in 3 weighings. Will you pass your final exam?

First weighing: Weigh four marbles against the other four.
Take the heavier four, and split them into two sets of two.
Second weighing: Weigh two marbles against the other two.
Take the heavier two, and split them.
Third weighing: Weigh one marble against the other.

By now we should have a winner.

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Sun Sep 13, 2009 10:49 pm
Karsten says...

(These are all really famous, by the way - if you're already cheating by asking us to do them for you, you could just google them.)

Dreamer wrote:24. You and a friend stand side by side and begin walking so that your right feet hit the ground at the same time. You take exactly 3 steps for each 2 steps of your friend. How many steps go by before you and your friend’s left feet simultaneously hit the ground?

Um ... four steps for your friend, and six steps for you? I think? I feel like there should be some underlying algebra here, but it's quick enough to just count off the steps.

Friend takes two steps: one right, one left.
In that time you take three steps: one right, one left, one right.

Friend takes two steps: one right, one left.
In that time you take three steps: one left, one right, one left.

Both finish on the left foot.

edit: Aha, there is a simple rule. Every time the friend takes two steps, they will finish up on the left foot. During that same time, you will take three steps, except you end up on alternate feet. So you need to take three steps twice.

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Sun Sep 13, 2009 11:06 pm
Karsten says...

Dreamer wrote:21. Okay, you got through that one, but now it turns out that you don’t obtain math certification unless you can determine the heavier marble in only 2 weighings. Will you get your certification?

First weighing: Weigh three marbles against another three.

If both sets are equal, the heavier marble is one of the two that you didn't weigh. In that case, your second weighing is to weigh them against each other. The heavier one is the winner.

If one set is heavier than another, take the heavier set.

Second weighing: Weigh one marble against another.

If both marbles are equal, the heavier marble is the one you didn't weigh. That's the winner.

If one marble is heavier than another, that's the winner.

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Thu Sep 17, 2009 9:15 am
asxz says...

I got the first two easy. The third one,
22. Why does time seem to pass more quickly as we get older?

That's easy too. If you're thinking mathematically about it, then every second that passes makes every second that has already passed a smaller percentage or our life. If you are five years old, then your fifth year will seem like a fifth of your life. If you are eighty years old, then every year will only seem like an eighty-ith and therefore, because you have already lived so long, such a small percentage of your life will seem insignificant.
Of coarse... I could be wrong, but that's what came to my mind when I saw the problem.

The 24th one... shouldn't that just be six? TI think it's been answered already though.

26... less than a millimeter? It seems like ten meters will be a significantly small amount compared to the diameter of the earth.
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