Are you a cognitive miser?
December 30, 2014 2:42 PM   Subscribe

A bat and a ball cost $1.10 in total. The bat costs $1 more than the ball. How much does the ball cost? Many people give the first response that comes to mind—10 cents. But if they thought a little harder, they would realize that this cannot be right. Keith E. Stanovich writes in Scientific American about “dysrationalia” and how having a high IQ doesn't guarantee that your brain won't take shortcuts when it can.
posted by jzed (165 comments total) 36 users marked this as a favorite
 
The ball costs $0.05, by the way.
posted by NoxAeternum at 2:50 PM on December 30, 2014 [29 favorites]


I kept RTA, waiting for the moment when I'd find out how much the ball cost. That moment never came.
posted by cheeken at 2:51 PM on December 30, 2014 [17 favorites]


You have 15 cents in change, made up of two coins. One of the coins is not a nickel. What coins do you have?

See also: System 1 and System 2 thinking
posted by the man of twists and turns at 2:52 PM on December 30, 2014 [15 favorites]


I don't really care how stupid I sound, the example in the post doesn't make sense to me whatsoever. The breakdown in the article is equally unenlightening.
posted by Dark Messiah at 2:52 PM on December 30, 2014 [1 favorite]


How does it not make sense? x + y = 1.1, x - y = 1.
posted by kmz at 2:53 PM on December 30, 2014 [4 favorites]


No doubt you know several folks with perfectly respectable IQs who repeatedly make poor decisions.

Nice to see Scientific American so honestly addressing their core readership.
posted by 7segment at 2:54 PM on December 30, 2014 [39 favorites]


It's the wording. I didn't even figure it out; I just back-tracked from NoxAeternum's answer after assuming it was right.

I knew 10¢ was wrong because that would be pointless.
posted by Dark Messiah at 2:54 PM on December 30, 2014 [3 favorites]


the man of twists and turns

...but the other one is! That's more of a wordplay question, though.
posted by leotrotsky at 2:55 PM on December 30, 2014 [5 favorites]


I can't answer this question without a BTC chart for the day in which these sports products were procured.
posted by b1tr0t at 2:56 PM on December 30, 2014 [2 favorites]


If you're interested in this subject (Nobel Prize winner) Kahneman's Thinking, Fast and Slow is right on point. We may actually see some empirical psychology in the near future.
posted by Invisible Green Time-Lapse Peloton at 2:56 PM on December 30, 2014 [5 favorites]


@the man of twists and turns: It's still a dime and a nickel. Only *one* coin isn't a nickel, so the other one can be. :)
posted by aurynn at 2:56 PM on December 30, 2014 [2 favorites]


Something about the phrasing just turned my brain off: I kept reading it as "the bat is a dollar" even though that was stupidly wrong and clearly not what was written.
posted by Dark Messiah at 2:56 PM on December 30, 2014 [2 favorites]


No doubt you know several folks with perfectly respectable IQs who repeatedly make poor decisions.

One of them is still buying Scientific American.
posted by chavenet at 2:57 PM on December 30, 2014 [10 favorites]


Something about the phrasing just turned my brain off

Well, it turned on a heuristic.
posted by anotherpanacea at 2:58 PM on December 30, 2014 [8 favorites]


A better example is the pond that doubles in lily pads every day. If it's completely full of lily pads on the 30th day, when is it half full?
posted by leotrotsky at 2:59 PM on December 30, 2014 [5 favorites]


The 29th day, of course.
posted by Pope Guilty at 3:00 PM on December 30, 2014 [2 favorites]


(Also I kind of want a website that will just give me a problem like these when asked.)
posted by Pope Guilty at 3:00 PM on December 30, 2014 [23 favorites]


It's the wording. I didn't even figure it out; I just back-tracked from NoxAeternum's answer after assuming it was right.

I knew 10¢ was wrong because that would be pointless.


And that's the point - we look for guideposts in the phrasing, not looking to make sure that they're not off. The focus on the $1 draws you, and throws you off.

The logic, for those curious:

Let x = ball price, y = bat price.
x + y = 1.1
y = 1 + x
x + 1 + x = 1.1
1 + 2x = 1.1
2x = .1
x = .05
posted by NoxAeternum at 3:00 PM on December 30, 2014 [18 favorites]


The 29th?
posted by Segundus at 3:01 PM on December 30, 2014


A better example is the pond that doubles in lily pads every day. If it's completely full of lily pads on the 30th day, when is it half full?

The 29th day obviously, but holy fuck that's either an enormous pond or those are super tiny lily pads.
posted by kmz at 3:03 PM on December 30, 2014 [23 favorites]


The focus on the $1 draws you, and throws you off.

Nice to know I still fall for the same tricks, 14 years removed from high school math.
posted by Dark Messiah at 3:03 PM on December 30, 2014 [2 favorites]


How does it not make sense?

If the ball cost 10c, and the bat cost a dollar more than the ball, the bat would have to cost $1.10, making the total cost $1.20.

The right system of equations is Ball +100 = Bat, and Ball + Bat = 110
posted by internet fraud detective squad, station number 9 at 3:03 PM on December 30, 2014 [1 favorite]


The 29th?

Except February doesn't have 29 days!
posted by chavenet at 3:03 PM on December 30, 2014 [20 favorites]


Eh, this used to be trick questions. Now it's dysrationalia. Your kid will soon be able to get therapy for it.
posted by Segundus at 3:04 PM on December 30, 2014 [44 favorites]


Mainly I would assume the bundle is discounted.
posted by Artw at 3:05 PM on December 30, 2014 [21 favorites]


The cost of the bat took me a minute too. The article didn't explain it well, but it makes sense -

The price of the bat is $1 more than the price of the ball.

So: the price of the ball is A.
The price of the bat is A + 1.

And A + (A + 1) = 1.10.

Now if you assume that A = .10, then it doesn't work because:

0.10+ (0.10 + 1) = 1.20.

So you instead need to solve for A, and that makes it an algebra problem instead of something you can just fudge. Or:

Something about the phrasing just turned my brain off: I kept reading it as "the bat is a dollar" even though that was stupidly wrong and clearly not what was written.

That's exactly the point the article is trying to make - that we assume that that's what's there even though it's not what's written. We read it as:

a + b = 1.10

instead of

a + (a+1) = 1.10.
posted by EmpressCallipygos at 3:05 PM on December 30, 2014


The right system of equations

My system of equations was perfectly fine.
posted by kmz at 3:06 PM on December 30, 2014


The right system of equations is Ball +100 = Bat, and Ball + Bat = 110

To solve this:

Ball + (Ball + 100) = 110

2Ball + 100 = 110

2Ball = 10

Ball = 5
posted by internet fraud detective squad, station number 9 at 3:06 PM on December 30, 2014 [5 favorites]


And that's why I have 2 general math credits. :P
posted by Dark Messiah at 3:06 PM on December 30, 2014 [3 favorites]


My system of equations was perfectly fine.

Ah, I thought you were saying the article didn't make sense! I should have read more closely. You are correct; apologies for being a pedant!
posted by internet fraud detective squad, station number 9 at 3:07 PM on December 30, 2014 [1 favorite]


Ah, yeah, sorry, I was replying to the comment directly above mine. I should learn to quote more often...
posted by kmz at 3:09 PM on December 30, 2014


There's no way we'd bother to fix this as a society. If we cured dysrationalia, American capitalism as we know it would be absolutely fucked.
posted by starbreaker at 3:09 PM on December 30, 2014 [33 favorites]


Pope Guilty: A rope-ladder is hanging over the side of a ship. The ladder is 12 feet long, and the rungs are one foot apart. The lowest rung is resting on the top of the ocean. The tide rises at the rate of four inches per hour. How long will it take before the first four rungs of the ladder are under water?
posted by leotrotsky at 3:09 PM on December 30, 2014 [19 favorites]


Eh, this used to be trick questions. Now it's dysrationalia. Your kid will soon be able to get therapy for it.

Diseases used to be demons or the will of God. Now that we know more about them, we call them other things and have ways of treating them.
posted by Steely-eyed Missile Man at 3:10 PM on December 30, 2014 [3 favorites]


A rope-ladder is hanging over the side of a ship. The ladder is 12 feet long, and the rungs are one foot apart. The lowest rung is resting on the top of the ocean. The tide rises at the rate of four inches per hour. How long will it take before the first four rungs of the ladder are under water?

Depends. Got a drill handy?
posted by NoxAeternum at 3:12 PM on December 30, 2014 [14 favorites]


It's a trick question. The ship is actually the rope ladder's mother.
posted by Atom Eyes at 3:13 PM on December 30, 2014 [87 favorites]


Never because the boat rises with the tide, what kind of lubbers do you think we are.
posted by poffin boffin at 3:14 PM on December 30, 2014 [26 favorites]


The part that still frosts my balls is people using this as an indicator of intelligence. Like, doesn't matter that you can't make an argument for/against artificial turf or discuss things like guns or abortion, who's buried in Grant's Tomb? You're in a pitch black room with a lantern, a stove, and a Molotov cocktail, which do you light first? OMFG IT'S THE MATCH I THOUGHT YOU WERE SO SMART HA HA.

AND. People who use these in a job interview deserve to be stabbed in the face. Nah, let's not actually talk about the job requirements, go ahead and ask me the one about the surgeon who's not the kid's dad (spoiler alert: it's 2014, can we maybe talk to each other like people do?).
posted by disconnect at 3:15 PM on December 30, 2014 [43 favorites]


A bat and a ball cost $1.10 in total. The bat costs $1 more than the ball. How much does the ball cost?

I like this. It shows how long this question has stood the test of time. Although honestly, it was probably done with "A spear and an axe cost 110 shells. The spear costs 100 shells more than the spear. How much does the spear cost?"

And I bet people made all sorts of excuses like "oh, my neanderthal cranial capacity doesn't allow me to think that way".
posted by hal_c_on at 3:16 PM on December 30, 2014 [6 favorites]


A train leaves Chicago and heads west at 50 MPH. On the train is a cow. Another train leaves Los Angeles and heads east at 70 MPH. On this train is a chicken.

In Billings, Montana, there is a saloon by the train tracks. The saloon keeper is a mime.

When will the fish fall out of the sky? Show your work.
posted by potsmokinghippieoverlord at 3:18 PM on December 30, 2014 [31 favorites]


Pope Guilty: There are these woods in the shape of a regular polygon with n sides. A bear of unknown color runs at his maximum rate of speed directly into the woods. How far can the bear run into the woods?
posted by sammyo at 3:20 PM on December 30, 2014 [3 favorites]


In a large western city, 80% of the phone numbers are listed, 20% of the phone numbers are businesses, and 20% of the phone numbers start with the numeral "2". If you were to take a random sample of 1000 phone numbers from the city's phone book, how many numbers would you expect to be unlisted, non-business phone numbers that start with a numeral other than "2"?
posted by leotrotsky at 3:20 PM on December 30, 2014 [7 favorites]


One of my personal favorites is the Hundred Locker Problem (I'm a fan of the presentation on The Daily WTF). It's not really a trick question, but a test of pattern recognition based on limited information.
posted by NoxAeternum at 3:20 PM on December 30, 2014 [3 favorites]


Sammyo: halfway, of course!
posted by leotrotsky at 3:22 PM on December 30, 2014 [2 favorites]


I'm going to create a book of unsolvable puzzles for smartasses, the gimmick being that the first and most obvious answer is always the right one.
posted by Artw at 3:22 PM on December 30, 2014 [18 favorites]


from the city's phone book, how many numbers would you expect to be unlisted

None.
posted by the man of twists and turns at 3:22 PM on December 30, 2014 [11 favorites]


When will the fish fall out of the sky? Show your work.

the answer is bees
posted by poffin boffin at 3:22 PM on December 30, 2014 [6 favorites]


Disconnect: sure, but they're only marginally worse than the ping pong balls in the 747 type questions, and usually asking those type of questions is a good indicator of the bullshitty nature of the profession. Why do you think they're so popular with management consultants?
posted by leotrotsky at 3:25 PM on December 30, 2014 [4 favorites]


Just to complete the Cognitive reasoning test (CRT) (which I just learned about from How to think like Sherlock Holmes):

(2) If it takes 5 machines 5 minutes to make 5 widgets, how long would it take 100 machines to make 100 widgets?
posted by pjenks at 3:26 PM on December 30, 2014 [3 favorites]


Five minutes
posted by leotrotsky at 3:27 PM on December 30, 2014 [1 favorite]


There are these woods in the shape of a regular polygon with n sides. A bear of unknown color runs at his maximum rate of speed directly into the woods. How far can the bear run into the woods?

Let's consider a spherical bear in a vacuum...
posted by Greg_Ace at 3:30 PM on December 30, 2014 [14 favorites]


(2) If it takes 5 machines 5 minutes to make 5 widgets, how long would it take 100 machines to make 100 widgets?

5 minutes?

The bat is one dollar more than the ball, not $1--it's right there in the problem. Once you think it over a bit, you see the right way to frame the problem, but the brain automatically tries to simplify and prefers the simple but wrong solution because it feels so clever and pat. We really should try to train ourselves to be vigilant against these kinds of errors, because they're all too easy to make and can lead to really bad compounding effects when introduced in more complex chains of reasoning.
posted by saulgoodman at 3:30 PM on December 30, 2014 [1 favorite]


If it takes 5 machines 5 minutes to make 5 widgets, how long would it take 100 machines to make 100 widgets?

Five minutes


Trick question! The machines are French, so they go on strike after making only 20 widgets.
posted by Greg_Ace at 3:32 PM on December 30, 2014 [16 favorites]


My dad had one that he used to ask us when we were kids: "If a hen and a half lays an egg and a half in a day and a half, how many eggs will it lay in a week?"

My sister and I both puzzled over that one for most of our childhoods, but I don't think either of us came very close to solving it, particularly since he'd completely misstated the flipping puzzle. The correct version of the puzzle is here.
posted by pipeski at 3:32 PM on December 30, 2014 [5 favorites]


I didn't read the article, but I sure want everyone to know that I'm smart enough to figure these trick questions out.
posted by MoonOrb at 3:33 PM on December 30, 2014 [8 favorites]


If your dad is sawing laying hens in half you should probably contact your local ASPCA.
posted by poffin boffin at 3:35 PM on December 30, 2014 [8 favorites]


I just passed the one about the widgets on to my son, and he's still puzzling over it. Supposedly his IQ is 180 or so, so don't feel bad if they trick you.
posted by saulgoodman at 3:35 PM on December 30, 2014 [2 favorites]


> Trick question! The machines are French, so they go on strike after making only 20 widgets.

The Dave Barry thread is two posts down.
posted by The Card Cheat at 3:38 PM on December 30, 2014 [26 favorites]


Says saulgoodman to MoonOrb
posted by leotrotsky at 3:40 PM on December 30, 2014


Oops, the CRT is the "cognitive reflection test". I guess with the point being that you can answer these questions correctly if you stop to reflect, but likely won't if you don't.
posted by pjenks at 3:40 PM on December 30, 2014


clearly the coins in question are a quarter and an undime, which is an antimatter coin equal to a debt of ten cents
posted by NoraReed at 3:40 PM on December 30, 2014 [61 favorites]


I'm fine with these, but often it was because I had encountered a similar problem before and had learned the more appropriate heuristic for it.

#4 and #5 thanks to statistics courses. The bat and ball thanks to algebra. #1 and #5 because I had encountered them before as "trick" questions. And #3 could reveal a bias based on nationality, but it's more of an opinion question than one with a clear-cut correct answer.

Of course, I'm a sample of one, but my own experience leads me to question how analogous this is to dyslexia rather than to being illiterate. Is it something you innately have difficulty with or is it something you haven't learned?
posted by RobotHero at 3:42 PM on December 30, 2014 [3 favorites]


I didn't mean to say that to MoonOrb necessarily. I read the article. Just came here to find everyone else having fun woth silly puzzles and thought I'd join in. Didn't mean to put on high-toned airs or nothing.
posted by saulgoodman at 3:44 PM on December 30, 2014 [1 favorite]


The only reason I can even keep a thought in my head for more than two seconds os because I had to learn how to for my work as a programmer, honestly. I never even qualified for gifted in my own school days.
posted by saulgoodman at 3:45 PM on December 30, 2014


Once you think it over a bit, you see the right way to frame the problem, but the brain automatically tries to simplify and prefers the simple but wrong solution because it feels so clever and pat.

The "right way" only if you want the answer. The point of these is to make you think in new and different ways.

Or to be a smart ass. I can imagine the author getting beat up a lot in grade school.
posted by IndigoJones at 3:46 PM on December 30, 2014


Robothero: Is it something you innately have difficulty with or is it something you haven't learned?

I think those CRT questions (bat/ball, lily-pad, widget machine) questions are meant to be solvable without advanced skills, and therefore test whether you stop to think (check your answer) or not. The rest of the questions in the TFA seem to lean on "mindware" (i.e., learning stuff).
posted by pjenks at 3:47 PM on December 30, 2014


The one with the airplane on a treadmill was better.
posted by ryanrs at 3:47 PM on December 30, 2014


I ain't a cognitive miser, but I might be cognitively lazy.

This social scientist appears to be using that old saw about various types of intelligence and then promoting his own work and coining a neologism.

I do note that most of the examples are LSAT logic problems...phew, I hated those (but crushed the SAT/GRE/MENSA tests).

Fortunately, the only folks who seem to give credence to IQ tests are university admissions departments--where it is usually just a weighted factor--and other social scientists, eh?

Love the various thought problems though; good exercise.
posted by CrowGoat at 3:50 PM on December 30, 2014


You are all wrong. The bat cost a dollar. The ball is free with the bat. 10 cents is tax. Come on, people! Live in the world!
posted by It's Raining Florence Henderson at 3:55 PM on December 30, 2014 [37 favorites]



The one with the airplane on a treadmill was better.


Yes, that's where mefi is a viking.
posted by poffin boffin at 3:57 PM on December 30, 2014 [13 favorites]


Only *one* coin isn't a nickel, so the other one can be.

No, the other one isn't a dime. Pay attention moar!
posted by It's Raining Florence Henderson at 4:00 PM on December 30, 2014 [3 favorites]


the pond that doubles in lily pads every day. If it's completely full of lily pads on the 30th day, when is it half full?

I prefer to think of it as half empty.
posted by It's Raining Florence Henderson at 4:02 PM on December 30, 2014 [3 favorites]


Obviously, the statement that one coin isn't a nickel is equivalent to the statement that one coin is an un-nickel. Which obviously means that the other coin is worth 20 cents, your dirty quarter imperialists.
posted by halifix at 4:02 PM on December 30, 2014 [1 favorite]


Actually, the bat costs $100.00, and you use it to beat the smart-ass questioner into a pulp. Rifling their pockets, you find a ball and $99.

Then you get on a train to Chicago going 100 KPH.
posted by Celsius1414 at 4:09 PM on December 30, 2014 [2 favorites]


With the $1.10, I'd much rather buy a bowtie and a henway.
posted by tallmiddleagedgeek at 4:10 PM on December 30, 2014 [1 favorite]


Please define "henway."
posted by ROU_Xenophobe at 4:11 PM on December 30, 2014 [30 favorites]


For what it is worth, Google no longer asks job candidates to solve brainteasers. Because science! Maybe I can work there some day after all!
posted by Bella Donna at 4:11 PM on December 30, 2014 [3 favorites]


The right system of equations is Ball +100 = Bat, and Ball + Bat = 110

To solve this:

Ball + (Ball + 100) = 110

2Ball + 100 = 110

2Ball = 10

Ball = 5


Aren't you going to buy a glove?
posted by Brandon Blatcher at 4:11 PM on December 30, 2014 [1 favorite]


from the city's phone book, how many numbers would you expect to be unlisted

None.


Exactly. Cities don't have phone books, phone books are printed by businesses in support of phone companies, to whatever extent actual physical phone books even exist as anything more than cheap booster seats these days.
posted by It's Raining Florence Henderson at 4:12 PM on December 30, 2014 [3 favorites]


Please define "henway."

It's also known as "Prince Albert in a can".
posted by tallmiddleagedgeek at 4:14 PM on December 30, 2014


But what answer would a wise person give?
posted by McMillan's Other Wife at 4:14 PM on December 30, 2014


Is your refrigerator running? Yes? Better shut it off, you're killing the planet.
posted by It's Raining Florence Henderson at 4:15 PM on December 30, 2014 [3 favorites]


THEN WHO WAS PHONEME?
posted by Celsius1414 at 4:17 PM on December 30, 2014 [1 favorite]


...dysrationalia. Your kid will soon be able to get therapy for it.

I blame Obama.
posted by It's Raining Florence Henderson at 4:18 PM on December 30, 2014


I like how when MeFites have nothing to say about the post we teach the train to fly and do humorous pirouettes in the air.

Calculate the number of pirouettes the train is doing.
posted by halifix at 4:30 PM on December 30, 2014


Don't we need to know the tax rates for balls and bats to solve this problem?
posted by GenjiandProust at 4:31 PM on December 30, 2014


But what answer would a wise person give?

No, it's "what would the other guardian tell me?"
posted by the man of twists and turns at 4:31 PM on December 30, 2014 [1 favorite]


Is this one of those questions you can only get right by giving your answer, not the answer you think the questioner wants you to give?
posted by Mitrovarr at 4:37 PM on December 30, 2014


With the $1.10, I'd much rather buy a bowtie and a henway.

Heck, with that kind of cheese, you could get a Dikfer!
posted by leotrotsky at 4:39 PM on December 30, 2014 [1 favorite]


The thing that gets me about "Here are tricky questions that show that it's not enough to be good at tests" is that one reason I'm good at tests is that I've seen all these tricky questions before.
posted by dfan at 4:40 PM on December 30, 2014 [13 favorites]


A more interesting example of the 6th question is the 'guess my rule' game. Try it on your friends! Most people, even smart ones (unless they've come across that game before) will approach it the wrong way for a good long time. It's not a trick question, it's just that most people really don't think things through unless they're specifically expecting a trick question. Hell, I do it too, all the time.

Call it gut feeling, common sense, the obvious answer, whatever, but virtually everybody leaps at quick and simple answers to problems all the time by default, and it's why people peddling quick, simple solutions to what are in fact complex problems a) easily fool people who theoretically should know better and b) are so dangerous.
posted by ArkhanJG at 4:51 PM on December 30, 2014 [14 favorites]


I would need to know whether the correct amount of depreciation was applied to either the bat or the ball, both, or neither, before proceeding.

/fuckingtaxes
posted by disclaimer at 4:51 PM on December 30, 2014 [2 favorites]


But these kinds of tricky questions are a staple of "reasoning" tests, no? It's been a long, long time since I took an actual IQ test, and I understand they include a variety of kinds of questions but certainly the SAT and of course LSAT do stuff like this. I don't care to get into the debate about what intelligence is and what tests measure right now, but certainly a lot of tests we use *do* attempt to gauge the taker's ability to catch things like this (in a situation where they know they are required to be careful).
posted by atoxyl at 5:03 PM on December 30, 2014


A mother is 21 years older than her son. Six years from now, she will be five times his age. Where’s the father?

(puzzle stolen from here)
posted by xbonesgt at 5:07 PM on December 30, 2014 [12 favorites]


I like how when MeFites have nothing to say about the post we teach the train to fly and do humorous pirouettes in the air.

Calculate the number of pirouettes the train is doing.


Flying requires several overhead movement patterns, involving continuous humeral circumduction in clockwise and counterclockwise directions. An engine with 69-inch drivers makes 292.2 revolutions in running a mile over track. 26-inch strokes force the pistons to travel 1,266 feet at 60 miles per hour over land. A flying train, therefore, usually exceeds 4000 pirouette strokes for one shoulder in a single mile, making this sport a common source of shoulder pathology in trains...

Oh. You said humorous. Never mind.
posted by It's Raining Florence Henderson at 5:09 PM on December 30, 2014


Where’s the father?

He's in the rectory.
posted by It's Raining Florence Henderson at 5:11 PM on December 30, 2014 [2 favorites]


People are approaching this problem from the wrong direction entirely: was it ever possible to buy a bat and ball for $1.10?

A bat and ball cost about $76 today. According to a handy inflation calculator, you have to go back before 1800 to find a time when today's $76 would have been equivalent to their $1.10. And baseball didn't exist before the 19th century. So this is a trick question, and there is no correct answer.

Am I hired?
posted by tallmiddleagedgeek at 5:12 PM on December 30, 2014 [13 favorites]


Not at the Dollar store, you aren't.

#WhiffleWhileYouDontWork
posted by It's Raining Florence Henderson at 5:15 PM on December 30, 2014 [5 favorites]


The bat and ball thing isn't a trick question though, it just effectively triggers heuristic thinking.
posted by jomato at 5:18 PM on December 30, 2014 [1 favorite]


xbonesgt's word problem is pretty clever (and not really such a trick question at all, or at least not the sort of absurdist teaser it appears to be at first glance).
posted by nobody at 5:36 PM on December 30, 2014


ArkhanJG: "A more interesting example of the 6th question is the 'guess my rule' game."


It helps that he has a very permissive rule in mind and then primes them with an example that would fit a much more restrictive rule. He calls them out for trying to get Yes as an answer, but I got the sense that after the first couple Yeses, they did start to try to get No, the problem was they were still expecting a more restrictive rule.
posted by RobotHero at 5:45 PM on December 30, 2014


I was told there'd be no math.
That said- I'd stick around, but Lincoln runs by my house, so I have to ...
posted by NorthernLite at 5:49 PM on December 30, 2014


The right system of equations is Ball +100 = Bat, and Ball + Bat = 110

To solve this:

Ball + (Ball + 100) = 110

2Ball + 100 = 110

2Ball = 10

Ball = 5

Aren't you going to buy a glove?


Why, sure! With the extra five cents!
posted by salishsea at 6:07 PM on December 30, 2014 [2 favorites]


from the city's phone book, how many numbers would you expect to be unlisted

None.

Exactly. Cities don't have phone books, phone books are printed by businesses in support of phone companies, to whatever extent actual physical phone books even exist as anything more than cheap booster seats these days.


I dunno, seems to me "city's phone book" just means the phone book that covers the city. Not necessarily the phone book generated by the city's printing office. E.g. the Philadelphia phone book is the phone book for the city of Philadelphia, not some imaginary phone book printed by the Philadelphia government. Although some cities do print phone books that are just for official contacts; that could also be the city's phone book, I suppose.

Anyway, in case it's not super obvious, the real reason the answer is "zero" is because if it's listed in the phone book, by definition it's not "unlisted."

Why, sure! With the extra five cents!

Salishsea, I think I love you?
posted by xigxag at 6:21 PM on December 30, 2014 [2 favorites]


leotrotsky, I actually don't mind Fermi problems, as long as one is demonstrated first (so maybe show how many rubber molecules are worn off a car tire per revolution, then say "now do ping pong balls in 747"). Expecting someone to be able to make that series of leaps cold is Mensa-level douchebaggery.
posted by disconnect at 6:28 PM on December 30, 2014


How does it not make sense? x + y = 1.1, x - y = 1.

And the sad and sorry thing is that this made sense to me until it was explained as being wrong.

I've passed math classes with As and Bs. Doesn't mean I knew which way was up. I took an innumeracy class in collage designed to make one unafraid of basic math. I never was afraid of math, I just DON'T get it.

Yes, I am nearly math illiterate.
*hangs head*
posted by BlueHorse at 6:36 PM on December 30, 2014 [1 favorite]


How much does the ball cost?

$20, SAIT.
posted by Greg_Ace at 6:38 PM on December 30, 2014 [11 favorites]


Many of these are tests to see if you will confidently spout out the obvious, but wrong, answer or if you will take a second to sanity check it first. I think that's valuable information in an interview setting, if not overdone. You can cut it off as soon as the person says, no that can't be right; you don't actually have to wait for them to get the right answer.

I like the OKCupid question that takes this a step further by making the common sense check support the wrong answer:

Some doctors are men, and some men are tall. Does it follow that some doctors are tall? I might be misremembering the wording, but when you leap to the "yes" answer, you can then imagine a plausible tall doctor, and may even know some.
posted by ctmf at 6:46 PM on December 30, 2014 [1 favorite]


>We may actually see some empirical psychology in the near future.

Hey Invisible Green Time-Lapse Peloton, snark aside, you would probably like Gerd Gigerenzer's school of psychology - they are focused on "simple heuristics that make us smart", with a focus on experiments in naturalistic settings (e.g. asking US and German students to pick the largest of two US cities) followed up with computational decision making models (e.g. "take the first"). It's good stuff and if i weren't on my phone I'd link some.
posted by anthill at 6:54 PM on December 30, 2014


Wait, couldn't the ball cost anywhere between $0.01 and $0.09, and the bat makes up the remaining amount? Or do I not understand the problem?
posted by zardoz at 7:00 PM on December 30, 2014


A strict reading of the problem is that the bat costs exactly $1 more than the ball, so cost of ball + $1 = cost of bat.

If the ball costs $0.01, then the bat will cost $1.01, for a total of $1.02; not the $1.10 answer it's expecting.

Similarly, a $0.09 ball makes the bat $1.09, for a total of $1.18.
posted by fragmede at 7:04 PM on December 30, 2014


Why I always come away broke from garage sales.
posted by Oyéah at 7:22 PM on December 30, 2014 [5 favorites]


They were both poisoned. I spent the last few years building up an immunity to iocane powder.
posted by blue_beetle at 7:37 PM on December 30, 2014 [8 favorites]


... large numbers of highly select university students ...

Organically grown, no steroids

Yuck.
posted by sylvanshine at 8:02 PM on December 30, 2014


Trick question! The machines are French, so they go on strike after making only 20 widgets.

Yes, but when they go on strike, they go to their homes which are paid off, their cars that are maintained and running, and to their bank accounts which aren't empty.

France-1; US-0
posted by hal_c_on at 8:05 PM on December 30, 2014 [5 favorites]


I like this. It shows how long this question has stood the test of time.

I remember my mum asking me this question when I must have been 9 or 10 - although I think it was something like "a bottle and its cap cost $1.10 together....". We were sitting in the car, in a carpark. We sat there for 45 minutes while I tried to understand it and get the answer right.
posted by Jimbob at 8:47 PM on December 30, 2014


It's a language problem, not a math problem.
posted by Brandon Blatcher at 9:13 PM on December 30, 2014 [1 favorite]


A more interesting example of the 6th question is the 'guess my rule' game.

I'm agreeing with RobotHero's comment, and upon some reflection I think that the video's host could have parsed the exposition a little differently. It's a good point that people could have been happy concluding that "double the previous number" was the rule if he hadn't revealed that it wasn't. However, after that, they really were trying as hard as they could to find the boundaries of the rule. What it really illustrated was that even when you feel like you're trying really hard, you may still have big blind spots regarding what tests you may think to devise.
posted by polecat at 10:03 PM on December 30, 2014


Ugh. If you're going to compel me to do arithmetic, explain the problem clearly and unambiguously. If you want to discuss cognitive biases, assumptions, and impulse control, don't pretend that the problem here is that I can't add.
posted by desuetude at 10:28 PM on December 30, 2014 [4 favorites]


How many letters are in the answer to this question?
posted by Combat Wombat at 10:50 PM on December 30, 2014


0
posted by flabdablet at 10:57 PM on December 30, 2014 [2 favorites]


The problem here is not that people don't immediately get the right answer. I think it was a decent shortcut to take: the 10c answer is obviously pretty close to correct, and once you figure out exactly how far off you are, it's pretty easy to adjust your answer. It's an iterative method that can sometimes get you to the truth in situations where it would be impossible to use an algebraic equation. (The one here is pretty simple, but still a little bit time-consuming to figure out, and requires its own round of double-checking to make sure you formulated the right equation: x+x+1 = 1.10)

The real problem is that people don't circle back and test their answer against the information provided in the question to make sure it works out as expected.

I notice this all the time at work. People (myself included on occasion) submit software components that either don't function at all, or fail to function as expected/required. There's no reason the submitter couldn't have figured this out prior to submitting; they just didn't take the time to double back and test their work (or, for longer tasks, double back and check their assumptions before diving into implementation).

I've always thought that stopping at 90% (before testing) has less to do with avoiding that final 10% of work, and more to do with fear of having to start over from scratch if their solution gets disproven.
posted by mantecol at 10:59 PM on December 30, 2014 [3 favorites]


Suck it, Trebek.
posted by Invisible Green Time-Lapse Peloton at 10:59 PM on December 30, 2014 [3 favorites]


One thing's for damn sure: that bat ain't never gonna take off from the treadmill.
posted by five fresh fish at 11:10 PM on December 30, 2014 [2 favorites]


A bat and ball cost about $76 today.

I bought a Louisville Slugger ash bat for half that over the summer. Baseballs can get kind of hilarious, but if you're just hitting it back and forth in the back yard like me, the fake leather balls go for about $3 / ball and deliver a more satisfying crack when you hit them (not as good for throwing, though -- too slippery).
posted by dirigibleman at 11:20 PM on December 30, 2014


How many letters are in the answer to this question?

Four
posted by the man of twists and turns at 11:36 PM on December 30, 2014 [6 favorites]


The point of these is to make you think in new and different ways.

But they never do. Either you've memorised the correct answer from the previous asshole who asked them, they're blindingly obvious if stated correctly, or they're tiresome gotcha questions.

Whenever I see questions like this I don't feel cognitive misery, just this sense of enormous ennui and disinterest in solving them.
posted by MartinWisse at 2:12 AM on December 31, 2014 [1 favorite]


Metafilter: My system of equations was perfectly fine.
posted by SPrintF at 3:02 AM on December 31, 2014 [1 favorite]


I am not careful and have almost no attention to detail. These puzzles are hell for me. Bat and ball took me quite a while to understand why it would be five cents.
posted by josher71 at 3:03 AM on December 31, 2014


I like the boat/tide/ladder one more if it's not a boat, but the required distance is longer. You get to see if someone will disregard the first rung (which is just the zero mark, not a portion of the distance to be covered. )

Then you get to see if they common-sense check that expecting a tide to rise for say, 18 hours is not realistic.

As is, it's just a trick question, although I guess you could see it as a test of visualizing the overall system in your mind before starting. That's a stretch, though.
posted by ctmf at 4:01 AM on December 31, 2014


Okay, a man and his son are in a horrible train wreck. There are no survivors. The son is immediately taken to surgery on a boat which has 12 rungs on its ladder, one of which is not a dime. The surgeon appears and says, I can not operate on that child, I have only a ball and a bat and a dollar and five cents. Besides that child is my son. So, how many toes does the surgeon have?
posted by dances_with_sneetches at 5:46 AM on December 31, 2014 [9 favorites]


How many letters are in the answer to this question?

Exactly twenty-four letters.
posted by flabdablet at 5:50 AM on December 31, 2014 [3 favorites]


We get one, good, rollicking dance on this muddy lump of rock.
Give me a dance partner with a high EQ. You can keep your high IQ.

Real intelligence is about party planning.
posted by Baby_Balrog at 6:14 AM on December 31, 2014 [1 favorite]


Which store is this? I'm going to load up on $1.05 bats and then show them all.
posted by Legomancer at 6:17 AM on December 31, 2014 [1 favorite]


I got this right off the bat (heh) because I used to teach algebra. Once you start doing a lot of system-of-equations word problems, it becomes easy to recognize them - especially ones with phrases like "more than" or "less than". I liken solving problems like this to how a pilot flies a plane - sometimes you have to trust your instruments instead of going with intuition.
posted by jenh526 at 6:32 AM on December 31, 2014 [1 favorite]


How many letters are in the answer to this question?

Exactly twenty-four letters.


Or seven.
posted by StephenB at 7:06 AM on December 31, 2014 [1 favorite]


Okay, a man and his son are in a horrible train wreck. There are no survivors. The son is immediately taken to surgery on a boat which has 12 rungs on its ladder, one of which is not a dime. The surgeon appears and says, I can not operate on that child, I have only a ball and a bat and a dollar and five cents. Besides that child is my son. So, how many toes does the surgeon have?

Four: a bear of unspecified color ate the others when the surgeon walked halfway into the woods .
posted by MikeMc at 7:10 AM on December 31, 2014 [2 favorites]


Actually it's sixty-four, along with several spaces and assorted punctuation.
posted by flabdablet at 7:12 AM on December 31, 2014 [1 favorite]


That is incorrect, MikeMc; the bear was green.
posted by flabdablet at 7:13 AM on December 31, 2014


That is incorrect, MikeMc; the bear was green.

Damn! I never was any good with this type of question, I just don't take the time needed for proper analysis.
posted by MikeMc at 7:21 AM on December 31, 2014 [1 favorite]


Don't feel too bad. I got that one wrong too, and it cost me a job at Microsoft.
posted by flabdablet at 7:28 AM on December 31, 2014 [1 favorite]


If you're a fan of this sort of thing, check out the Game Show Network's Idiotest.
posted by DrAstroZoom at 7:28 AM on December 31, 2014 [1 favorite]


Trick question! The machines are French, so they go on strike after making only 20 widgets.

Hah! The correct answer is 0. One of the factory workers is a police informant and all are arrested by Fouchés agents before the Machine infernale can be put into operation.
posted by MikeMc at 7:30 AM on December 31, 2014


A mother is 21 years older than her son. Six years from now, she will be five times his age. Where’s the father?
Probably within a month's travel time from the mother, assuming medical intervention isn't involved. If we also assume the question is being asked today, in late December 2014, and that the mother is on Earth, that leaves open every place that humans are known to live except for the four men currently on the International Space Station. (They had a crew change 51 days ago, and the next scheduled one is months away.) If the question were asked in a few months, we could rule out some Antarctic bases as well.

If, instead, we assume the mother is on board the ISS, then we can rule out the rest of the planet. And we can infer that NASA administrators will soon be fretting about a serious PR event.

If we allow that the mother may or may not be an astronaut, and assume both parents are human, then we can say nothing at all about the father's current whereabouts based on the age information given.

(I suggest we avoid discussing the politically charged use of the word "son" to describe a zygote, and assume good intentions on the part of the puzzle writer.)
If a hen and a half lays an egg and a half in a day and a half, how many eggs will it lay in a week?
That's a really weird question. First of all, why would anyone bother with the half hen and half egg? Surely "if a hen lays an egg in a day and a half" is the natural way to discuss egg production.

Second, the answer requires significant outside knowledge about egg laying. Does a hen lay exactly one egg at an interval of 36 hours, or is egg laying random with a mean period of 36 hours? If the former, then the answer is depends on when the week begins and the alignment of chicken cycles. (Assuming the half chicken laying half an egg is related to the division of egg rights among chicken co-owners, not vivisection.)

My vague memories of tending chickens as a kid suggest the latter is closer to being correct. However, the process can't really be described as a series of independent events. The likelihood of a chicken laying 5 eggs in an hour is surely lower than Poisson statistics would suggest. (Laying 100 eggs an hour would seem to violate conservation laws, given how quickly chicken eat and for reasonable definitions of "egg.") Without a detailed description of the statistics of egg laying, the question isn't really answerable. The best we can do is to say, "describing the number of eggs as drawn from a Poisson distribution with an average value of 10.5 is probably not a terrible approximation. Thus, there are likely to be between 7 and 14 eggs after a week."

The take home message from this thread seems to be: people who write math puzzles have very strange notions about animal reproduction.

Is there an equivalent of IQ that specifically relates to bean plating? BPQ?
posted by eotvos at 8:12 AM on December 31, 2014 [10 favorites]


I... I just looked up the definition of beanplating...

'Derived from the expression "HI I'M ON METAFILTER AND I COULD OVERTHINK A PLATE OF BEANS."' [1]

Maybe we can start a certification program.
posted by I-Write-Essays at 8:59 AM on December 31, 2014


> It's a language problem, not a math problem.

> Ugh. If you're going to compel me to do arithmetic, explain the problem clearly and unambiguously.

I don't get these responses at all (assuming we're talking about the bat + ball problem). That problem could not be stated more clearly or unambiguously.
posted by Turd Ferguson at 9:47 AM on December 31, 2014 [2 favorites]


an average value of 10.5
Except, of course, for my inability to correctly multiply numbers by 1. Say, why does everything taste like my foot?
posted by eotvos at 9:53 AM on December 31, 2014




How many toes did the surgeon have?
Ten or twelve, depending, and then possibly less...depending. Sturgeon have no toes at all, in case of a typo.
posted by Oyéah at 12:11 PM on December 31, 2014


I've bean certified.
posted by Oyéah at 12:14 PM on December 31, 2014


I was at a training recently on mental status exams, and the psychiatrist leading the training used a number of these puzzles/tricks/questions as a way of illustrating why none of the clinicians in the room should get too comfortable in assuming our own thought processes and cognitive abilities are objectively right while those of our patients (many of whom have schizophrenia) are objectively wrong. I thought it was definitley useful in that context.
posted by jaguar at 2:57 PM on December 31, 2014 [2 favorites]


MetaFilter: just this sense of enormous ennui and disinterest
posted by Johnny Wallflower at 3:10 PM on December 31, 2014 [2 favorites]


Cognitively lazy while diagnosing crazy...but I have two sets of three wine glasses I bought at a yard sale, or was it three sets of two wine glasses, if three of them are half full, but two have lipstick marks, how can Willy get the reluctant sheep over the stile?
posted by Oyéah at 8:00 PM on December 31, 2014 [1 favorite]


Heh. xbonesgt's puzzle is totally worth the effort to solve.
posted by Johnny Wallflower at 12:25 AM on January 1, 2015 [1 favorite]


For the misers:
A snail is climbing out of a well.
The well is 20 feet deep.
Every day the snail climbs up 3 feet and every night he slips back two feet.
How many days will it take the snail to get out of the well?
posted by Obscure Reference at 5:19 AM on January 1, 2015


He gets within three inches of the lip of the well before he's snatched up and eaten by a thrush.
posted by Grangousier at 5:33 AM on January 1, 2015 [3 favorites]


African or European?
posted by flabdablet at 7:36 AM on January 1, 2015 [1 favorite]


Wait, wait! Hold on! We need to start over; I have a coupon.
posted by dances with hamsters at 9:14 AM on January 1, 2015


How many times can you fold it in half?
posted by flabdablet at 10:25 AM on January 1, 2015


Real world example of why such questions are relevant: Australia has a 10% "Goods and Services Tax" (GST) that is added to most things you buy. The ticketed price always includes the GST. Something is priced at $1.00 including GST. How much GST is included in the price?
posted by Autumn Leaf at 2:19 PM on January 1, 2015


9 cents?
posted by Justinian at 2:29 PM on January 1, 2015


gst_free_price x 11/10 = 1 dollar

so gst_free_price = 10/11 dollars, and so

GST = 1-(10/11) = 1/11 dollars

(( = 9.0909... cents. I hope...))
posted by pjm at 5:58 PM on January 1, 2015


Now calculate for Canada, remembering that we don't do penny change any more.
posted by five fresh fish at 7:31 PM on January 1, 2015


Sorry, but that was a trick question from fff, as you paid by debit or credit card and the numbers do not round. Don't forget to solve for all provinces and territories.
posted by jeather at 10:10 AM on January 2, 2015


I did badly on all of these. I can't help but wonder if it made a difference that they were all very math-oriented, as I have a learning disability and it affects my math skills. My brain just tends to fritz out on math.
posted by eternalstranger at 7:15 AM on January 16, 2015


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