Monday Musing: Cocktail Party Conversation Permit

It is a frequently observed phenomenon that the less educated and intelligent people are, the more they tend to have decisive and strong opinions on the most complex political, philosophical, economic, and other pressing issues. You know the kind of person I am talking about, the one who is eager to quickly diagnose and solve a world problem or two with a single profound proclamation at every cocktail party. Like the two urbane and seemingly well-educated and well-dressed slightly older gentlemen I once overheard at a dinner party in Karachi (and there are plenty here in America, or anywhere for that matter) saying with great conviction (and with extremely thoughtful expressions on their faces, and in ponderous cadences, as if they were straining under the burden of a massive feat of cognitive strength and skill):

1st Guy: "Pakistan's only problem has always been that our leaders lack sincerity."
2nd Guy: "No, no, no. Our only problem has always been that our leaders lack committment."

The first guy then actually carefully considered this pearl of wisdom from political philosopher and all-round theorist #2 and finally, having reevaluated his own sophisticated worldview in the light of this new gem, dumped it unceremoniously, humbly but gravely declaring defeat: "Yes... I see... you are right... it is a matter of committment." In the throes of the cringing frustration one feels when faced with this sort of cretinism, I have sometimes felt that people should have to be licensed to spew profundities at cocktail parties, otherwise they should only be allowed to speak about either the weather or quantum theory. And the license would be received after demonstrating the ability to think about really, really, simple problems by passing a test. The idea, of course, being that if you can't think lucidly, logically, creatively and successfully about very simple problems where all the information required to solve them is present in their statement, and which have very clear and demonstrable solutions, what the &[email protected]# makes you think you should be engaging hard and incredibly complicated and intricate issues?

Okay, okay, for the last nine days or so I was out of town and very busy and that is my excuse for not writing a substantive column today. (Perhaps some of you noticed that I wasn't posting all of last week?) Instead, now that I have given you some motivation to try and think about simple problems, I present a challenge to you: solve some logical and mathematical puzzles that my friend Alex Freuman sent me. Alex teaches high school physics and math at La Guardia High School here in Manhattan. (It was the model for the high school in the movie Fame.) I had seen some of the puzzles before but not others, and it took me a while to solve some of those. The first person to email me (click "About Us" at the top left of this page for my email) a full list of correct solutions, wins the privilege of writing one of our Monday columns for November 20th. Okay, so it's not a huge prize, but hey, if you've got something to say, here's your chance. And, of course, you will have earned the cocktail party conversational permit as far as I am concerned.

Don't look up the solutions, and please don't post solutions in the comments. Try to do all of them yourself. Believe me, even if you have to think for some days about a problem before you get it, there is a huge satisfaction and mental reward in doing so yourself. And you will feel more confident of yourself too. I shall, of course, trust you not to cheat. Here they are:

1. You are given two ropes and a lighter. This is the only equipment you can use. You are told that each of the two ropes has the following property: if you light one end of the rope, it will take exactly one hour to burn all the way to the other end. But it doesn't have to burn at a uniform rate. In other words, half the rope may burn in the first five minutes, and then the other half would take 55 minutes. The rate at which the two ropes burn is not necessarily the same, so the second rope will also take an hour to burn from one end to the other, but may do it at some varying rate, which is not necessarily the same as the one for the first rope. Now you are asked to measure a period of 45 minutes. How will you do it?
2. You have 50 quarters on the table in front of you. You are blindfolded and cannot discern whether a coin is heads up or tails up by feeling it. You are told that x coins are heads up, where 0 < x < 50. You are asked to separate the coins into two piles in such a way that the number of heads up coins in both piles is the same at the end. You may flip any coin over as many times as you like. How will you do it?
3. A farmer is returning from town with a dog, a chicken and some corn. He arrives at a river that he must cross, but all that is available to him is a small raft large enough to hold him and one of his three possessions. He may not leave the dog alone with the chicken, for the dog will eat it. Furthermore, he may not leave the chicken alone with the corn, for the chicken will eat it. How can he bring everything across the river safely?
4. You have four chains. Each chain has three links in it. Although it is difficult to cut the links, you wish to make a loop with all 12 links. What is the fewest number of cuts you must make to accomplish this task?
5. Walking down the street one day, I met a woman strolling with her daughter. “What a lovely child,” I remarked. “In fact, I have two children,” she replied. What is the probability that both of her children are girls? Be warned: this question is not as trivial as it may look.
6. Before you lie three closed boxes. They are labeled “Blue Jellybeans”, “Red Jellybeans” and “Blue & Red Jellybeans.” In fact, all the boxes are filled with jellybeans. One with just blue, one with just red and one with both blue and red. However, all the boxes are incorrectly labeled. You may reach into one box and pull out only one jellybean. Which box should you select from to correctly label the boxes?
7. A glass of water with a single ice cube sits on a table. When the ice has completely melted, will the level of the water have increased, decreased or remain unchanged?
8. You are given eight coins and told that one of them is counterfeit. The counterfeit one is slightly heavier than the other seven. Otherwise, the coins look identical. Using a simple balance scale, can you determine which coin is counterfeit using the scale only twice?
9. There are two gallon containers. One is filled with water and the other is filled with wine. Three ounces of the wine are poured into the water container. Then, three ounces from the water container are poured into the wine. Now that each container has a gallon of liquid, which is greater: the amount of water in the wine container or the amount of wine in the water container?
10. Late one evening, four hikers find themselves at a rope bridge spanning a wide river. The bridge is not very secure and can hold only two people at a time. Since it is quite dark, a flashlight is needed to cross the bridge and only one hiker had brought his. One of the hikers can cross the bridge in one minute, another in two minutes, another in five minutes and the fourth in ten minutes. When two people cross, they can only walk as fast as the slower of the two hikers. How can they all cross the bridge in 17 minutes? No, they cannot throw the flashlight across the river.
11. Other than the North Pole, where on this planet is it possible to walk one mile due south, one mile due east and one mile due north and end up exactly where you began?
12. I was visiting a friend one evening and remembered that he had three daughters. I asked him how old they were. “The product of their ages is 72,” he answered. Quizzically, I asked, “Is there anything else you can tell me?” “Yes,” he replied, “the sum of their ages is equal to the number of my house.” I stepped outside to see what the house number was. Upon returning inside, I said to my host, “I’m sorry, but I still can’t figure out their ages.” He responded apologetically, ‘I’m sorry. I forgot to mention that my oldest daughter likes strawberry shortcake.” With this information, I was able to determine all of their ages. How old is each daughter? I assure you that there is enough information to solve the puzzle.
13. The surface of a distant planet is covered with water except for one small island on the planet’s equator. On this island is an airport with a fleet of identical planes. One pilot has a mission to fly around the planet along its equator and return to the island. The problem is that each plane only has enough fuel to fly a plane half way around the planet. Fortunately, each plane can be refueled by any other plane midair. Assuming that refuelings can happen instantaneously and all the planes fly at the same speed, what is the fewest number of planes needed for this mission?
14. You find yourself in a room with three light switches. In a room upstairs stands a single lamp with a single light bulb on a table. One of the switches controls that lamp, whereas the other two switches do nothing at all. It is your task to determine which of the three switches controls the light upstairs. The catch: once you go upstairs to the room with the lamp, you may not return to the room with the switches. There is no way to see if the lamp is lit without entering the room upstairs. How do you do it?
15. There are two gallon containers. One is filled with water and the other is filled with wine. Three ounces of the wine are poured into the water container. Then, three ounces from the water container are poured into the wine. Now that each container has a gallon of liquid, which is greater: the amount of water in the wine container or the amount of wine in the water container?

In case no one gets all the answers right, the highest score wins. In the case of a tie, whoever gets me the next correct answer first wins. And keep in mind that by no means am I suggesting that everyone should get the solutions of all the problems. Some of them are hard, and if you can't figure them out, don't worry about it. But keep trying! Thanks for sending the problems, Alex, and sorry but you are disqualified.

Ready, set, go!

UPDATE: We have a winner!

UPDATE 2: Answers here.

My other Monday Musings can be seen here.

Comments

[S C Agrawal]

Quick comments: Problems 9 and 15 are the same! Problem 7 is neither maths nor logic but simple physics.

[Abbas Raza]

Yes, you are right on both counts. One less problem for you, thanks to my sloppy cutting and pasting. Now send in the solutions...

[Slocum]

Of course, I have run into people who would be able to solve problems like those and would still make pronouncements like the two men at the cocktail party on matters outside their expertise. In fact their very ability to solve hard problems in technical domains may be responsible for a high degree of overconfidence in proposing solutions to, say, political problems.

And as Tetlock showed, even experts in their own domains are problematic -- in particular, their predictive abilities are lousy:

http://www.newyorker.com/critics/books/articles/051205crbo_books1

The critical factors seem to be overconfidence, a tendency to demonstrate expertise by making subtle, non-intuitive pronouncements, and copious knowledge available to justify these subtle (but unlikely) predictions.

[aditya]

i just know there's a punch line coming up that has nothing to do with these reader's digest 'teasers'!

don't disappoint me, raza...

[Abbas Raza]

Hey, DO NOT POST SOLUTIONS TO THE PROBLEMS AS COMMENTS.

Email them to me at s.abbas.raza [at] att.net

Slocum, my proposal wasn't meant seriously, man! But while passing this test certainly is no sufficient condition for profound insights into complex problems, I do think there might be a better chance of at least having a more interesting cocktail party conversation with someone who is at least logical enough to think clearly about little things... No? Maybe?

Aditya, you elitist sub-incontinental theorist, you! Just email me the solutions, and don't disappoint me... You cannot cow me with your word power as I live my life in these United States, trying to write some light humor in uniform prose, continuing to believe that laughter is the best medicine when dealing with any serious drama in real life.

And that is a quotable quote for you!

[Jesse M.]

For #13, can some of the planes be on "suicide missions" (giving up all their fuel to other planes in midair) or does every plane involved have to get home to the island? I assume it's probably the latter, because it makes it harder...

Also, can you post a comment when someone gets 'em all? I think I have almost all of them, but I want someone else to win the big prize before I send them in since I don't actually have any good ideas for a column. Oh, and speaking of the inexhaustible supply of people who make bold pronouncements about things they don't really know anything about, there's a psychological explanation for that! See Unskilled and Unaware of it: How Difficulties in Recognizing One's Own Incompetence Lead to Inflated Self-Assessments

[Abbas Raza]

Hi Jesse,

Yes, your interpretation of the plane problem is correct. No suicides.

And yes, I'll post the winner as soon as I get one. So far only one person claimed to get them all, and he got one wrong. Another person claims to have solved 13 of them, but didn't send me his answers. But he did admit to being stumped by #14, which is the only one which has a little trick.

I will probably not post the answers until at least next week, so people have a chance to think about them.

Thanks.

[aditya]

abbas, i am humbled. and silenced. you the man.

[Abbas Raza]

Dude, Aditya, I hope you caught the joke in my message to you:

Word Power
Life in these United States
Laughter the Best Medicine
Humor in Uniform
Drama in Real Life, and
Quotable Quotes

are all regular columns in Reader's Digest, which you mentioned contemptuously. I was joking that I am a regular enough reader of RD to know all that.

Don't get all offended!

[aditya]

dude, i'm satisfied with my punchline, thank you, and didn't need the answers this time around.

life's like that -- and it can be a real life adventure... like i said, you the man!

[Stephen Frug]

I really think that any invocation of problems such as these has to refer to this page:
http://www.michaelkelly.fsnet.co.uk/lateral.htm

[Craig L.]

My answers are in. I should admit that I've seen #1, 8, 10, 11, and 14 before. But the rest were new to me, and I'm glad that a warning was included with #5.

[George Dickeson]

Likewise. my answers are in, and I had seen a few of these before. In particular, #12 took me a few hours the first time I came across it.

A friend of mine just pointed me to this well presented collection of riddles. Anything to beat away the monday doldrums.

[Jesse M.]

I finally came up with an answer to #13, so now I think I have answers to all of them...but like I said, I'll wait until someone else wins the guest column to send my answers.

Here's a trickier variant of #8:

Suppose you have 12 identical-looking coins, and you know that one has a different weight than the other 11, but you don't know if it's heavier or lighter. Using a balance scale, can you find the odd coin using the scale only 3 times?

[Jesse M.]

Ah, I see there's a winner, so I'll send my answers in now.

[Ben]

For frustrated people out there, I've heard #14, before, and I find the 'solution' extremely unsatisfying. It's more or less a trick, which may or may not be valid.

The other ones which I've encountered are all fairly good puzzles.

[Abbas Raza]

Ben, I agree with you, and in retrospect probably shouldn't have posted #14. Incidentally, it was the only problem I did not get on my own from this list and had to ask someone eventually.

[George Dickeson]

Agreed. #14 is a "lateral thinking" problem, which to me is akin to an excercise in creative writing.

All of the others are logic puzzles.

[Adam]

I disagree with the objections to 14. I think it's perfectly logical, and consistent with the other problems.

#3 was on the original version of the TV series of The Office, though it had a fox instead of a dog. One of the characters responded, "Why has the farmer got a fox? A fox is a farmer's natural enemy! .... Drown the fox in the river!"

[Dave M]

I also disagree with the objections to 14. Of course this is because I eventually figured it out. But that's just it - I eventually *figured it out*. It's true that there is a step which requires "lateral thinking" in a way which the other puzzles don't. But once you ask yourself the right question, that step is fairly straightforward; and then you need more logical reasoning to get the solution. It's not a "trick" like some "lateral thinking" puzzles are.

[Brian]

Late to the party, but I'm curious:

in #14, do you have to assume the light is off to begin with?

[Alain Azzam]

I'd say #14 is pure logic because I was asked this question at a Xmas party when I was 14 years old and the answer occured to me in a flash. I was of course accused of knowing the answer before that day, which was not true. So to me, yes, this is perfectly logical. I "saw" the solution immediately, I saw myself perform the tasks needed and walk to the room.

There is no trick in particular. If you were put in a room and threatened that your whole family would be killed if you didn't find the solution fast, you'd use your logic, not "tricks" :)

p.s.: why are you asking for a valid email here? Those will be collected by spammers...

[David]

@Brian: Concerning #14, you could always turn off all 3 switches, wait 2 minutes and then start your testing.

Concerning other comments on #14, I in no way find the solution unsatisfying. I hadn't heard that problem before right now, but as I was reading through the post, the answer occurred to me almost immediately.

@Alain Good call on the email. The blog should link your name to your website, and have the email address available to the blog administrator only.

[jack]

I recently found a very interesting website:
http://alreadylinked.com/
There you can purchase ad space for your Blog etc.

[Alex Reid]

Don't suppose we could have a version of question 9/15 using SI (metric) units? Those units make my head hurt...

[James]

What a fascinating post. This boy girl connundrum is hilarious. Perhaps I can offer some pointers to make this a little clearer for those still confused.

To begin with there are the possiblities BB, GG, BG and GB. The 1/3 advocates have made the mistake in thinking that the knowledge of the existence of the girl reduces these to GG, BG and GB.

BUT IT DOESN'T. It reduces it to GG and GB. The BG option is not available, BG and GB are representative of variables in a static position, so if the static position of the girl is already established (position one is G) then the variables can not be interchanged.

The other problem is this statistical misuse: that a girl has been taken out from the pool of girls therefore a boy is more likely because overall there are now less girls in the probablity pool. This might be a relevant point if the girl was one in a pool of 10 girls and 10 boys, but she isn't, she is one in 3 billion girls and 3 billion boys. The statistical influence of one in 3 billion is negligble to say the least.

The chance of the other child being a girl, real world, if you're being picky is 2999999999/6000000000 or 49.9999999833%

But, since this is a logic question, this statistical fly in the ointment is irrelevant.

The logical answer is 50%

[James]

What a fascinating thread. This boy girl connundrum is hilarious. Perhaps I can offer some pointers to make this a little clearer for those still confused.

To begin with there are the possiblities BB, GG, BG and GB. The 1/3 advocates have made the mistake in thinking that the knowledge of the existence of the girl reduces these to GG, BG and GB.

BUT IT DOESN'T. It reduces it to GG and GB. The BG option is not available, BG and GB are representative of variables in a static position, so if the static position of the girl is already established (position one is G) then the variables can not be interchanged.

The other problem is this statistical misuse: that a girl has been taken out from the pool of girls therefore a boy is more likely because overall there are now less girls in the probablity pool. This might be a relevant point if the girl was one in a pool of 10 girls and 10 boys, but she isn't, she is one in 3 billion girls and 3 billion boys. The statistical influence of one in 3 billion is negligble to say the least.

The chance of the other child being a girl, real world, if you're being picky is 2999999999/6000000000 or 49.9999999833%

But, since this is a logic question, this statistical fly in the ointment is irrelevant.

The logical answer is 50%

PS. Sorry I posted this accidentally in the other thread marked "no answers please" I meant to post it here.

[Sam Iamb]

Here's a completely different kind of logic, IMHO the kind most useful in the above cases:

Q. There are two men in a boat with three cigarrettes and no matches. How do they manage to smoke?

Give up? A. They throw one cigarrette overboard and make the boat a cigarrette lighter. Da-ching.

Seriously, Western medicine might have temporarily obscured the truth of it, but what's needed here is not more intellect but many lighter spirits. If you don't understand what I mean then please stick around; there will be a huge chance that you will understand by then, in the near future, by simply watching these excessively piled-up political shenanigans along with twelve million plus American minors on antipsychotic drugs which were originally developed for adults experiencing problems perceiving reality not children experiencing problems paying attention. If I asked 5,000 people, "Who would you rather be, yourself or Forrest Gump?" I doubt I'd hear even one choose Gump. But that's the problem IMHO. H like Heep, Uriah Heep that is. Everyone is trying to be God and King, and that's probably because so many of us stay at work all day trying to convince our fellow neighbors that's what they want. Not that we need more jesters, no. More levity, however, yes. How is that achieved? Not pompously or guardedly, I'll tell you that. Not by logic either. There's irrational and then there's superrational. Annoyed confidences aside, how many of us are equipped to discern the difference in any given case?

[GA]

Mmm . Nice post .

Julius Sumner-Miller relates the 'apocryphal' tale of a student who gave an incorrect answer to an ambitious physics puzzle, about measuring the height of a clock tower using a barometer. The student answered that she would measure the length of the barometer, then by repetition the height of the tower. Being chastised for this ‘incorrect’ answer, the student proffered another. Drop the barometer from the tower, measure time of fall, calculate height. With increasing ‘definition’ the student of course gave countless 'subversive' answers, Miller’s delicious punch line being to sell the damn thing and bribe the janitor.

I wonder if in the same spirit we might not examine these puzzles further.

For example,

Problem 1 is less ambiguous (and the offered solution 'more' unique) if you use matches rather than a lighter.

Thoughts in this vein?

[Vinay Singh]

For #7: Ice has a lighter density than water, thus the level should slightly drop.

[gudipudi]

Math game for kids at educationtrak.com will dramatically improve comprehension and test scores.

cheers
gudipudi
---------------------------
www.educationtrak.com

[Bobby]

I'm afraid the answer provided for number 9 is flawed.

If you have two gallon containers, one with water, one with wine. You pour 3 ounces of pure wine into the water container, you then pour 3 ounces of the water container (which now includes some wine) back into the wine container, the water container has more wine than the wine container has water. When pouring the water container into the wine it is also pouring some of the wine that was previously poured back into the wine container, therefore it cannot be an even amount of water as the original pure wine sample.

[Me]

Alex Freuman is my physics teacher at Lag! =] I came across this accidentally and saw his name...

[praveen]

Six actors – Bob, Carol, Dave. Ed, Frank, and Grace – are auditioning for a part in an off-Broadway play. The auditions for a part in an off-Broadway play. The auditions will take place over four consecutive days, starting on a Thursday. Each actor will have one audition. The days on which the different actors will audition must conform to the following conditions :
At least one audition will take place on any day.
No more than two auditions will take place on any day
No more than 3 auditions will take place on any two consecutive days
Bob’s audition must take place on Saturday
Carol’s audition must take place on the same day as another audition
Frank’s audition must take place on a day before grace’s audition
Dave’s audition must take place on a day after Ed’s audition
1. if only one audition takes place on Thursday, which actor could have that audition
a. Bob
b. Carol
c. Dave
d. Frank
e. Grace
2. If Bob’s and frank’s auditions are on the same day, which of the following must be true
a. Dave’s audition will take place on Thursday
b. Dave’s audition will take place on Friday
c. Grace’s audition will take place on Thursday
d. Carol’s audition will take place on Sunday
e. Ed’s audition will take place on Sunday

3. If the director decides to two hold the auditions on Thursday and two on Sunday, how many actors would be eligible to audition on Friday
a. 1
b. 2
c. 3
d. 4
e. 5
4. If Ed and Grace have their auditions on the same day, which of the following must be true?
a. Ed’s audition will take place on Thursday
b. Frank’s audition will take place on Thursday
c. Carol’s audition will take place on Saturday
d. Grace’s audition will take place on Saturday
e. Carol’s audition will take place on Sunday
5. If Ed’s audition is on Saturday, which of the following actors cannot audition on the same day as any other actor?
a. Bob
b. Carol
c. Ed
d. Frank
e. Grace

[James]

Twitter morphs into a conversational medium, a big cocktail party where everybody is constantly eavesdropping on everybody else’s impromptu conversations.

[Sun Valley hotels]

Sun Valley hotels