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[Other] Word problems for fun!

esidebill

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I have a huge amount of word problems I figured that I might as well post to see how people reason them out! Ahem. Without further delay, the first of however many you guys feel like posting! Cheating is highly discouraged. I'm sure some may be documented on the web.

***************************************

Before the printing press, books could be purchased
only in expensive manuscript copies. The printing
press produced books that were significantly less
expensive than the manuscript editions. The public’s
demand for printed books in the first years after the
invention of the printing press was many times greater
than demand had been for manuscript copies. This
increase demonstrates that there was a dramatic jump
in the number of people who learned how to read in
the years after publishers first started producing books
on the printing press.

Which one of the following statements, if true, casts
doubt on the argument?

(A) During the first years after the invention of the
printing press, letter writing by people who
wrote without the assistance of scribes or clerks
exhibited a dramatic increase.

(B) Books produced on the printing press are often
found with written comments in the margins in
the handwriting of the people who owned the
books.

(C) In the first years after the printing press was
invented, printed books were purchased primarily
by people who had always bought and read
expensive manuscripts but could afford a
greater number of printed books for the same
money.
(D) Books that were printed on the printing press in
the first years after its invention often circulated
among friends in informal reading clubs or
libraries.

(E) The first printed books published after the
invention of the printing press would have been
useless to illiterate people, since the books had
virtually no illustrations.
 

Coriolis

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C. The marked increase in book purchases could be due to any of a number of reasons. It is likely that more people did learn to read once books became cheaper and more readily available, but I would expect some lag between the initial increase in availability, and the increase in literacy. Thus the second is more likely an effect of the first rather than a cause.

Now for another, really more of a riddle:

The beginning of eternity,
The end of time and space;
The beginning of every end,
The end of every place.

What is it?
 

esidebill

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C. The marked increase in book purchases could be due to any of a number of reasons. It is likely that more people did learn to read once books became cheaper and more readily available, but I would expect some lag between the initial increase in availability, and the increase in literacy. Thus the second is more likely an effect of the first rather than a cause.

Now for another, really more of a riddle:

The beginning of eternity,
The end of time and space;
The beginning of every end,
The end of every place.

What is it?

This was a sneaky one! Hah. I was trying to think of like an actual thing... but then I figured well... the beginning of eternity or the beginning of an end. Then I noticed the letter e was at the beginning LITERALLY and at the end... bahah. Some people would go mad looking into that with some type of scientific answer.
 

esidebill

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Here's another.

If you climb mountains, you will not live to a ripe old
age. But you will be bored unless you climb mountains.
Therefore, if you live to a ripe old age, you will have
been bored.
Which one of the following most closely parallels the
reasoning in the argument above?

(A) If you do not try to swim, you will not learn how
to swim. But you will not be safe in boats if you
do not learn how to swim. Therefore, you must
try to swim.

(B) If you do not play golf, you will not enjoy the
weekend. But you will be tired next week unless
you relax during the weekend. Therefore, to
enjoy the weekend, you will have to relax by
playing golf.

(C) If you work for your candidate, you will not improve
your guitar playing. But you will neglect
your civic duty unless you work for your candidate.
Therefore, if you improve your guitar
playing, you will have neglected your civic duty.

(D) If you do not train, you will not be a good
athlete. But you will become exhausted easily
unless you train. Therefore, if you train, you will
not have become exhausted easily.

(E) If you spend all of your money, you will not
become wealthy. But you will become hungry
unless you spend all of your money. Therefore,
if you become wealthy, you will not become
hungry.
 

Xyk

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That one's C also. Pretty clearly.
 

esidebill

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That one's C also. Pretty clearly.

Very good :p

I might have a few questions based on this one... so heads up.

***************************************

An official is assigning five runners—Larry, Ned,
Olivia, Patricia, and Sonja—to parallel lanes numbered
consecutively 1 through 5. The official will also assign
each runner to represent a different charity—F, G, H, J,
and K—not necessarily in order of the runner’s names
as given. The following ordering restrictions apply:
The runner representing K is assigned to lane 4.
Patricia is assigned to the only lane between the
lanes of the runners representing F and G.
There are exactly two lanes between Olivia’s lane
and the lane of the runner representing G.
Sonja is assigned to a higher-numbered lane than
the lane to which Ned is assigned.

Which one of the following is a possible assignment
of runners to lanes by the charity they
represent?

___1 2 3 4 5
(A) F G H K J
(B) G H J K F
(C) G K F J H
(D) H J G K F
(E) J H F K G
 

Red Herring

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The answer to the runners' puzzle is the same as to Coriolis' puzzle! I first thought way too complicated, but it is far easier than it looks.

Come on guys, I have work to do and need a reason to procrastinate...bring on a real challenge! So far those were all too easily solvable. Please keep me away from that boring translation I have to get done by totommrow!!!
 

Red Herring

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Okay, I shouldn't just complain. Here is a funny problem:

There are three switches downstairs. Each corresponds to one of the three light bulbs in the attic. You can turn the switches on and off and leave them in any position.
How would you identify which switch corresponds to which light bulb, if you are only allowed one trip upstairs?
 

Hive

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You leave on switch on, one off and the third you turn on and then off. Then you go upstairs, and touch both lamps that are off to see wich is warm?
 

Hive

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Hooray for feelers solving riddles!
 

Red Herring

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Three Masters of Logic wanted to find out who was the wisest amongst them. So they turned to their Grand Master, asking to resolve their dispute. “Easy,” the old sage said. "I will blindfold you and paint either red, or blue dot on each man’s forehead. When I take your blindfolds off, if you see at least one red dot, raise your hand. The one, who guesses the color of the dot on his forehead first, wins." And so it was said, and so it was done. The Grand Master blindfolded the three contestants and painted red dots on every one. When he took their blindfolds off, all three men raised their hands as the rules required, and sat in silence pondering. Finally, one of them said: "I have a red dot on my forehead."
How did he guess?
 

Jonny

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Let us name the men A, B, and C respectively; furthermore, let us assume that A is the man who guessed correctly.

A observes that both B and C have raised their hands, indicating both have seen a red dot. However, let us assume that A is observed to have a blue dot on his head. Then, when B saw C raising his hand, he must conclude that he, B, has a red dot, since C could only see a red dot on his forehead. Therefore, he would have immediately guessed that his dot was red. Therefore, since A having blue would immediately lead to a correct guess by either B or C, he must have a red dot.

This solution assumes that the man who guessed correctly believes the other men to be smart enough to guess rather quickly should he have had a blue dot. This, of course, isn't a certainty. I would imagine if the other two had down syndrome, or some other mental defect, he would have had a more difficult time.

Edit: The essential part of this problem rests in the fact that if at least one blue dot is present, then guesses will come within a given time X. A person must be certain of the fact that the others haven't been able to reach a conclusion before he himself can make one. Without this, it cannot be known with certainty.
 

Red Herring

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Let us name the men A, B, and C respectively; furthermore, let us assume that A is the man who guessed correctly.

A observes that both B and C have raised their hands, indicating both have seen a red dot. However, let us assume that A is observed to have a blue dot on his head. Then, when B saw C raising his hand, he must conclude that he, B, has a red dot, since C could only see a red dot on his forehead. Therefore, he would have immediately guessed that his dot was red. Therefore, since A having blue would immediately lead to a correct guess by either B or C, he must have a red dot.

This solution assumes that the man who guessed correctly believes the other men to be smart enough to guess rather quickly should he have had a blue dot. This, of course, isn't a certainty. I would imagine if the other two had down syndrome, or some other mental defect, he would have had a more difficult time.

Edit: The essential part of this problem rests in the fact that if at least one blue dot is present, then guesses will come within a given time X. A person must be certain of the fact that the others haven't been able to reach a conclusion before he himself can make one. Without this, it cannot be known with certainty.

That is an interesting angle, psychologically speaking. Your analysis is of course correct, but my personal approach was: if A had a blue dot, this would give the other two men an unfair advantage over him because for him his dot could technically be either color (provided nobody lied) while the other two would have been able to almost immediately see that theirs had to be red.

Be it because we assume the others aren't stupid or because we assume the chances of winning the challenge have to be even, we path there is the same. So we agree. :)
 

Jonny

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Suppose there exist 1000 gold coins which are to be split up among five pirates: 1,2,3,4, and 5 in order of rank. We assume that the coins must remain wholly intact and that the pirates have the following characteristics: a pirate is infinitely knowledgeable; a pirate values his own life above wealth and above his need to kill, and will thus always vote for his own proposal; a pirate will always choose a greater amount of wealth over killing another pirate; caeteris paribus, a pirate will kill another pirate if given the chance; a pirate is risk neutral.

Starting with the highest numbered pirate, he can make a proposal as to how the coins will be split up. This proposal can either be accepted or the pirate making the proposal is killed. A proposal is accepted if and only if a majority of the pirates accept it. If a proposal is accepted the coins are split up in accordance with the proposal. If a proposal is rejected and the pirate making the proposal is killed, the next ranking pirate makes a proposal, so on and so forth.

What proposal should pirate 5 make?
 

Jonny

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A man has a lighter and two lengths of robe with varying densities. The only thing the man knows about each length of rope is that if he lights an end of a rope, it will burn for exactly one hour; however, it may be that 90% of a rope burns up in 1 minute, and it takes 59 minutes for the remaining section of rope to burn (this is a product of the varying densities).

How can this man accurately measure 45 minutes?
 

Jonny

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I see a thing. Of this thing I know these three:
1) The man who makes this will sell it.
2) The man who buys this will not use it.
3) The man who uses this will not know it.

What do I see?
 
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