[kenberg]

Some friends visited over the weekend and the guy told this story about his school experience in Manhattan. The kids read some poem and the teacher asked, without any apparent intended humorous intent, if any of the kids in the class had ever been on an island.

Another story I heard. In a probability class of about 30 students, the prof asked the class to estimate the probability that at least two members of the class share a common birthday. A nice problem, except for the fact of identical twins sitting in the front row.

I would not want a record kept of all the really stupid things that I have said or done.

I don't really know how to eliminate these errors, but having a healthy respect for our own limitations is probably a good start. Many years back, working on my Ph.D. thesis, I proved this really nice result quite simply. Then I saw that the same technique would prove another really nice result. And then maybe another. And then I decided it would be a good idea to go back and find the flaw in my reasoning. Yep, there it was.

As to the bat and ball, one possibility is that the person answering the question doesn't much care what the answer is, and so does not give it serious and careful thought.

[Fluffy]

 ArtK78, on 2012-June-25, 13:56, said:

The "other" answer, which was the common answer, was 24 days.

humans only see arithemtic progressions on their world, and our mind is trained for them, need to study to understand geometric ones.

[barmar]

 gwnn, on 2012-June-25, 16:24, said:

But the whole idea that it doubles every day is preposterous.

I think that's the point. In many math word problems, the stated conditions don't mirror real world situations. Common sense and intuition evolved to address problems that actually occur efficiently, not hypotheticals.

TV shows and movies often milk this for comedic effect. Someone is tutoring a "dumb" person in math, and gives them a word problem with a condition like "Two trains leave the station 15 minutes apart." The student then starts asking irrelevant questions, because his mind works intuitively by imagining the whole situation, he doesn't boil it down to just the mathematical aspects.

[ArtK78]

 gwnn, on 2012-June-25, 16:24, said:

BTW another one for people here: you want to organise a knock-out tournament, no group stage/second chances. You have 79 teams. How many matches will you need?

The answer is a minimum of 78 matches, as every team but the ultimate winner must lose a match. But it could be more if a team may lose a match and continue in the event (such as in a three-way match with 2 survivors). You stated no second chances - I do not know if a three-way match with two survivors counts as a second chance. The only way to run a single-elimination event with 79 teams without multiple-way matches is to give byes - this could be accomplished easily by giving byes to 49 teams and having 15 head-to-head matches in the first round, leaving 64 teams for the second round. In that case, you would have 78 head-to-head matches before determining a winner.

The question sounds a lot like a story related by Jerry Machlin in his memoir. He was telling of an exchange between his uncle, Al Sobel, the famous tournament director of the early days of the ACBL, and Ozzie Jacoby. Jacoby was the youngest person to pass the actuary exam when he was 18.

Sobel asked Jacoby how many matches it would take to determine the winner of a single-elimination knock-out teams event if the original entry was 64 teams. Ozzie responded "32 and 16 and 8 and 4 and 2 and 1 - 63." Sobel said, "You are right, Ozzie, but it took you too long. You should realize that since every team but one must lose a match, it would take 63 matches to determine a winner." To which Ozzie replied, "Yes, but if you were running the event, it could take anywhere from 45 to 110 matches!"

[gwnn]

A three-way match is a group stage.

[TimG]

 ArtK78, on 2012-June-26, 12:13, said:

The answer is a minimum of 78 matches, as every team but the ultimate winner must lose a match. But it could be more if a team may lose a match and continue in the event (such as in a three-way match with 2 survivors). You stated no second chances - I do not know if a three-way match with two survivors counts as a second chance.

If the three-way is considered a single match and there is one team eliminated in this match, it won't change the answer. Still 78 matches required.

[mgoetze]

So intelligence is measured by SAT scores nowadays? Also,

Quote

In a lake, there is a patch of lily pads. Every day, the patch doubles in size. If it takes 48 days for the patch to cover the entire lake, how long would it take for the patch to cover half of the lake?

Surely the only way you can get this wrong is by forgetting the second sentence by the time you've finished the third? 24, seriously?

[Zelandakh]

 gwnn, on 2012-June-26, 13:01, said:

A three-way match is a group stage.

Depends on the sport, no? If we put 79 extreme figting teams into one big ring and whichever team walks out at the end of it is the winner, that to me would be a single multe-way match and not a group stage.

[gwnn]

 Zelandakh, on 2012-June-27, 08:53, said:

Depends on the sport, no? If we put 79 extreme figting teams into one big ring and whichever team walks out at the end of it is the winner, that to me would be a single multe-way match and not a group stage.

That would not really be a sport, no? Anyway, my definitions are based on Humpty-Dumptism.

[dustinst22]

 ArtK78, on 2012-June-25, 10:04, said:

Funny, I got this right almost immediately. Maybe it is because I went to Princeton.

Apparently that's not much of a help:

Shane Frederick first noted many years ago, more than fifty per cent of students at Harvard, Princeton, and M.I.T. gave the incorrect answer to the bat-and-ball question.

[TimG]

 dustinst22, on 2012-June-29, 12:36, said:

Shane Frederick first noted many years ago, more than fifty per cent of students at Harvard, Princeton, and M.I.T. gave the incorrect answer to the bat-and-ball question.

I bet if the question was in an SAT type setting, a significantly higher percentage of those students would give the correct answer.

[Mbodell]

 dustinst22, on 2012-June-29, 12:36, said:

Apparently that's not much of a help:

Shane Frederick first noted many years ago, more than fifty per cent of students at Harvard, Princeton, and M.I.T. gave the incorrect answer to the bat-and-ball question.

Not quite the same thing, but in a small sample of graduating Harvard students more than half gave an incorrect answer (in a Jay walking interview setting at graduation) as to what is the primary causes of the seasons (winter/summer) - including an astronomy major. That got a little bit more in to how people learn and what is taught about the Earth and the solar system.

I find all of the logic puzzle / math questions in this thread pretty straightforward, but I've been doing those sorts of puzzles for as long as I remember, so they seem second nature. There are harder puzzles that I find, well, hard, but they aren't generally in the form of asking a simple question but in a way that many people leap to the wrong answer unthinkingly.

Another other classic question like this is:

Quote

A father and young son are seriously injured and unconscious in a car accident who are then rushed to the hospital and taken in to adjacent operating rooms. The surgeon comes in to operate on the child and says "I can't operate on him, he's my son!". How is this possible?

I was surprised that the last time I told this question (at my gym) the 3 folks who had never heard it couldn't solve it in 10+ minutes.

[Vampyr]

 Mbodell, on 2012-June-30, 01:04, said:

I was surprised that the last time I told this question (at my gym) the 3 folks who had never heard it couldn't solve it in 10+ minutes.

That's what you get for asking muscleheads -- you should first have asked them whether they've ever had a conversation with a woman!

[Mbodell]

 Vampyr, on 2012-June-30, 23:29, said:

That's what you get for asking muscleheads -- you should first have asked them whether they've ever had a conversation with a woman!

2 of the 3 people were women.

[Winstonm]

 kenberg, on 2012-June-25, 17:46, said:

As to the bat and ball, one possibility is that the person answering the question doesn't much care what the answer is, and so does not give it serious and careful thought.

Another problem is people like me, probably a little too literal, who look at a bat and ball for $1.10 and immediately (mentally) lose interest because nothing but a cholesterol burger from the dollar menu costs $1.10, and a bat and ball combo (even plastic kid types) would have put grandmother into a home if quoted today's price.

Mathematics is a model that may match reality, but it is not reality. This question would have been better to me if it were simply about abstracts of X and Y.

[barmar]

I'll bet there wouldn't be much difference for the bat-and-ball problem if it were X and Y. In fact, I suspect that form would cause more anxiety in people who think they don't understand algebra -- they tend to be scared by the abstract letters.

[daveharty]

 kenberg, on 2012-June-25, 17:46, said:

Another story I heard. In a probability class of about 30 students, the prof asked the class to estimate the probability that at least two members of the class share a common birthday. A nice problem, except for the fact of identical twins sitting in the front row.

It probably does skew the probabilities to have identical twins in the class, but not as absolutely as it might seem. I once met a pair of identical twins that not only had different birthdays, but were born in different months.

[psyck]

The matches required for a knockout is always one less than the total number of players, so it is 78 for 79 players (or 79 if you include the 1st round bye as a match as there are odd number of contestants)

[psyck]

Duh, i just saw the 1st page of this post while posting that reply...

[psyck]

 daveharty, on 2012-July-02, 09:51, said:

It probably does skew the probabilities to have identical twins in the class, but not as absolutely as it might seem. I once met a pair of identical twins that not only had different birthdays, but were born in different months.

Yeah, & the older twin celebrated the b'day a couple of days after the younger