WHY SMART PEOPLE ARE STUPID

[TimG]

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,

 

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]

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]

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]

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]

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]

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:

 

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]

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]

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]

 

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]

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]

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 :)

[barmar]

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.

 

They were twins, but not of each other.

 

[ArtK78]

Funny thing about the birthday problem.

 

In one of the first days of my college course in statistics and probability, we were asked to solve the birthday problem. The question is: How large a group of people (selected at random) do you have to have before there is a 50% or more probability that two or more of them will have the same birthday? The answer is 23.

[daveharty]

They were twins, but not of each other.

:D

Actually it was pretty straightforward, twin #1 was born at 11:15 p.m. on May 31, his reluctant brother made his first appearance 90 minutes later. Their family chose to preserve the distinction.

[kenberg]

Preserving the distinction of course makes sense. For one thing, as a legal matter they have different birthdays and there is no reason to confuse matters by acting otherwise.

 

But of course I submitted the story as an example of how a mindset (wanting to present a mathematics problem) can blind a person to obvious conditions making the problem as stated, taken literally, quite different.

 

 

There was an interesting, and tragic, story on NPR sometime back about a psychological experiment and a possible application. The experiment documented how people, when assigned a task, can be very oblivious to things going on around them. The subjects were to run behind someone, always keeping at the same pace (or some such assignment). Fights were staged not far off the path, in full view. Many of the subjects were totally unaware of the fights.

The real life application: Cops were trying to apprehend a suspect in a large park (maybe Central Park). He was described as African-American. One cop thought he saw him and was chasing him. Unfortunately some other cops spotted another suspect, call him suspect 2.. The real criminal had shot a cop and suspect 2 was beaten by the police. In fact, suspect 2 was an off-duty cop who had joined in trying to help. Now the first cop admitted to being on the very path where, off to the side, the guy was being beaten. He said that yes, he was on that path but had not noticed the beating. He was not believed he lost his job, I think he went to jail, and in general his life was ruined.

 

Other cops, some quite possibly in sight of the beating, said they were never in the vicinity. No way to prove otherwise, so they got off. The guy who acknowledged being on the path but not noticing because he was in pursuit of a different possible suspect had his life ruined.

 

 

Of course we don't know what actually happened, but reasoning that a guy who planned on lying would lie and say he was not there rather than say he was there but didn't see anything strikes me as pretty plausible. It may seem impossible, apparently many thought so, that he did not notice the beating. The psychology experiment suggests we rethink what is possible.

[barmar]

Inattentional blindness has been documented numerous times. One of the best examples is the "invisible gorilla test", described on the wikipedia page (the fight test as also described there).

[gwnn]

In unrelated news, Y U NO COUNT TO 13?

[Vampyr]

Inattentional blindness has been documented numerous times. One of the best examples is the "invisible gorilla test",

 

I did this one once, but is it really possible that people fail to see the gorilla? I have doubts.

[RMB1]

I did this one once, but is it really possible that people fail to see the gorilla? I have doubts.

Yes

 

I saw several videos of such experiments while touring London psychology departments last autumn.

[Mbodell]

I did this one once, but is it really possible that people fail to see the gorilla? I have doubts.

 

It was shown without explanation to my psych class in University. Only about 20% of the class noticed the Gorilla (I was in the minority that noticed it). Note that you are asked to count the number of times the team in white passes the ball, so it isn't just some video, but one where you have a task.

 

And there are lots of example videos where people switch on people when they are doing something like looking at a map, or getting directions, or signing in at a desk. As in the stranger who started with them becomes a different person. Sometimes even changing height, hair color, and gender. Many, many people don't notice.

[Vampyr]

Note that you are asked to count the number of times the team in white passes the ball, so it isn't just some video, but one where you have a task.

 

Yes, and the gorilla gets in the way and makes it harder to follow the motion of the ball and of course obscures some of the players, so while I guess I accept that some people miss it I just don't undrestand.