Friday Pop Quiz (Determining Your Risk-Tolerance Level Edition)

Former Reason editor Virginia Postrel has an interesting NY Times column up about different people's tolerance for risk. In explaining the latest research on the matter, she pops this quiz, which has been used to predict whether you're willing to take a gamble on a long-odds payout:

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

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

3) 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 the lake?

Answers and a whole lot more--a journey into the hidden recesses of your mind in fact--here.

Comments

[Mith]

I'd love to look at it, but it's behind the firewall, and I refuse to even use bugmenot.com to go look. Why waste my time?

[Pete Rose]

I must be a frickin GENIUS!

[Evan]

Coincidentally, Mith, if you actually read the article, you'd realize that you are not a risk-taker. Maybe that was your subtle point. Dunno.

BTW, what were your answers? All of them had obvious answers to me, but after a few seconds of reflection, I had a "duh" head-slap moment. The silliest one was the last one, where my dumb ass started doing Nth degree calculations for a couple seconds, then I realized what I was doing.

[joe]

Wouldn't the answer to Number 2 depend on whether the machines work sequentially on different tasks required to make the widget, and the details of the process?

[Dave W.]

maybe he should have said five machines working continuously at full capacity.

[Number 6]

Can someone with access post the answers?

[Phil]

One assumes that, for the purposes of the question, each machine is a complete widget-making machine. I often see the same question posed by asking, "If it takes 5 men 5 hours to mow 5 lawns, how many hours will it take 10 men to mow 10 lawns" or something to that effect.

[Qbryzan]

Can someone with access post the answers?

"The correct answers, by the way, are 5 cents, 5 minutes, and 47 days."

[jeffiek]

Wouldn't the answer to Number 2 depend on whether the machines work sequentially on different tasks required to make the widget, and the details of the process?

No

[Phil]

Number 6, the answers are:

1. $1.05 and $0.05
2. Five minutes
3. 47 days

I didn't read the article -- I've seen these same types of puzzles posed often enough. And #3 is a gimme.

[Rodney]

"Wouldn't the answer to Number 2 depend on whether the machines work sequentially on different tasks required to make the widget, and the details of the process?"

Given that "100 machines/widgets" is a multiple of the "5 machines/widgets" scenario, you can treat the 5 machines an abstracted widget-producing group and not have to worry about the internal process.

However, there could still be economies of scale that could allow 100 machines to do the task faster. I think you are only guaranteed that the task has an upper-bound of 5 minutes.

[David]

Wouldn't the answer to Number 2 depend on whether the machines work sequentially on different tasks required to make the widget, and the details of the process?

I think you're just supposed to asuume that one machine makes one widget in five minutes.

[Russ 2000]

Wouldn't the answer to Number 2 depend on whether the machines work sequentially on different tasks required to make the widget, and the details of the process?

Best...post...ever!!

[Number 6]

Looking again, those are all "duh" questions. I think I need more coffee.

[thoreau]

Who does question number 2 work for?

[smalls]

thoreau,
Great post.....especially for a brain-dead Friday.

[cjp]

I don't like the way the article talks about "mathematically equivalent" outcomes, when it's not at all clear what that means.

If I have a 50% chance winning $10, or a sure thing to win $5, then the expectated dollar amount in the two cases is the same. Whether my expected utility is the same is another question entirely. This is because utility doesn't scale linearly with dollar amount. If I have few assets, I get a lot of extra utility from a million dollars. If I'm already a billionaire, a million dollars doesn't add nearly as much utility.

That's why it may be advantageous to take the lower-risk option, even if it yields a lower expected dollar amount. I'd rather have $10000 for sure than a .01% chance for a $billion, even though taking the risk pays off 10 times as much in expectation.

[Dave W.]

Wouldn't the answer to Number 2 depend on whether the machines work sequentially on different tasks required to make the widget, and the details of the process?

I remember explaining this aspect of industrial engineering to some co-workers at IBM one summer. They did not believe me about the effect of continuous thruput on production speed until I showed them that I could make accurate predictions on pilot lines that were run continously (as possible). Because the pilot lines usually weren't run continuously for various reasons, they were very suspicious about claims I made about increased production speed on continous pilot lines.

[Twba]

Maybe, suggested Professor Frederick in the interview, "it's because one study was done at University of Toledo" ? where the mean score on his test was 0.57 out of a possible 3 ? "and one study was done at Princeton," where the mean was 1.63. The test groups may not really be the same.

I can't wait to tell my brother. He went to UT.

[Evan]

#6: I'm working through my 4x-spresso right now, but I don't think that's the issue. They're all "duh" questions, regardless of the amounf of caffeine in your system---but, if you're like me, the first two have immediately obvious (and wrong) answers...while the third lacks the same obvious-but-wrong answers, and instead presents itself as a complex math problem worthy of calculations (well, I suppose, if you were dumb enough, the immediately obvious & wrong answer would be 24). I don't think that's the point, though. The point is whether you go with the obvious answer, or whether you invest time in making sure it's right.

[SR]

I got 1 and 3, but I had the same issue as joe with 2 -- as written it can either refer to 5 machines each separately making widgets, or 5 machines that contribute some part of collectively making widgets.

[cjp]

Another way to phrase question 2 is: "if it takes 9 months for 9 women to produce 9 babies, how long does it take 18 women to produce 18 babies?"

Although I think the "duh" answer for this question happens to be the right one.

[quasibill]

cjp, you're right, but you're only hitting the tip of the iceberg.

Risk assessment, like all value, is nearly totally subjective in nature. You see, even if you were a millionaire, the ten dollars in pocket are worth far, far more if you're starving with no access to your bank. Or if you don't have time to go the bank before going to a client dinner, and know you need to leave a cash tip at dinner in order to impress the client. Or you know that the vendor down the street has a rare Joe DiMaggio (sp?) card for sale for 10 bucks, but doesn't take credit, and you know someone else will recognize it soon. Or any number of other personally relevant, but objectively untestable, factors come into play.

Hence, all these attempts at objectively defining risk assessment are just micturating in the wind...

[cjp]

What's the problem if the machines participate collectively? If you were simply to clone the original 5 machines and put them to the exact same task, independently of the first 5, you'd still end up with 10 widgets in 5 minutes.

[pigwiggle]

?or 5 machines that contribute some part of collectively making widgets.?

If five machines sequentially create the widgets then they make 1 complete widget /min as opposed to 5, 1/5 complete widgets /min. But you will notice that at 1wdg/min, 20 blocks of five machines will turn out 20 complete widgets/min or 100 in 5 min.

It does not matter.

[cjp]

quasibill -- you're talking about a very different thing than I am.

All your examples relate to the different utility that $10 can yield in different (extreme) situations.

But when presented with one of the abstract risk-assessment scenarios, a person has a relatively fixed notion of what utility $10 has to him. And to probably every person, the utility of $million is not nearly 100,000 times as large as the utility of $10.

[thoreau]

In December I caught a few episodes of "Deal or no deal." I would never make it onto that show because they want audition tapes and I'm not the most telegenic person. Nor am I a risk taker. But I figured out my strategy pretty quickly: I have a certain amount of debt. I'd make damn sure that my payout couldn't go below the level of my debt. Once I thought I might go below my level of debt, I'd call it quits and take the cash.

In other words, if they're giving you money for a short TV appearance, don't do anything stupid. Figure out how much money you need to solve some of your problems and once you get it take it. Don't gamble away the chance to solve your finanical ills.

(The rules are somewhat complex, but suffice it to say that my debt is modest enough that in most cases on that show the money offered would exceed my debt. Of course, with a really bad starting hand I'd probably get an offer below my debt, but even then it would be enough to make a big dent in it.)

[Evan]

thoreau,

I wonder: did you figure into your calculations the dire fact that tax withholding on game show winnings is something like 95%? So every time you "thought the payout might go below your level of debt", you'd have to amend that to "will 5% of this payout, which is all I'll take home once unkie sam robs me of his cut, be enough to cover my debt?"

[thoreau]

Evan-

I'm pretty sure 95% is an exaggeration. When I won $850 of Ben Stein's money the tax was...um, much lower (I forget what it was). Then again, I won small change.

Short answer: I assumed a tax rate that was probably way too low.

[joe]

OK, here's the deal on the machines.

If each machine spits out a whole widget in five minutes, 100 machines make 100 widgetsin five minutes.

If each set of five machines (A,B,C,D, and E), each doing a discreet task, spits out a widget every minute (and, thus, five widgets in five minutes), than twenty such sets will produce 100 widgets in five minutes.

If, however, the 100 machines consists of one A, one B, one C, one D, and ninety six Es, it will take some amount of time longer than five minutes to produce 100 widgets, depending on how long the A through D portion takes, and how long Machine E's task takes.

[cjp]

thoreau, you won Ben Stein's money??! That's awesome! I loved that show... such low production value, but very funny and cool. And Ben Stein is one smart dude who asks tough questions.

[Allen T]

Alright, I have obviously not had enough coffee yet today. WRT question 1, how did they arrive at 5 cents?

Bat + Ball = $1.10. (total)
Bat - Ball = $1.00. (difference of $1)

Seems to me Ball has to equal 10 cents.

Er? What am I missing here?

[mike in ftw]

micturating in the wind
bettin I'm losin friend
making the same mistakes I swore I'd never make again, again....

It looks like in the study that the majority of the high CRT group came from MIT and Princeton the majority of the low CRT group came from Toledo and Michigan State. You could make some assumptions about the difference in true opportunity costs of $60 now if that sixty bucks is going to be spent on keeping the power on in your apartment or going to be spent on apple martinis for Muffy.* The author did talk about wage utility in his conclusions but I don't see that he tried to control for it.

*While characterizations of all ivy leaguers as Dan Akroyd's friends in Trading Places may be unfair, I find it amusing.

[cjp]

Or, joe, the machines, being the means of production, might rise up against their masters and overthrow them in revolution, leading to a futuristic hellscape dystopia in which humans become the fuel with which the machines power themselves.

The fact that the question is being asked means it has a straightforward answer.

[Dave W.]

Or if machine E was slower than the other machines, then your 96 Machine E setup might take a lot shorter than 5 minutes.

[cjp]

Allen, if the ball costs 10c then the bat costs 1.10, so the total is 1.20, not 1.10.

When the ball costs 5c, the bat costs 1.05, and the total is 1.10 -- plus tax!! (If we're going to parse the hell out of these questions, I might as well throw that one in.)

[thoreau]

cjp-

The most embarrassing thing is that I missed the math question. If I had gotten that I would have tied him in the final round and gotten an extra $1000. The question was "Two angles that add up to 180 degrees are said to be what?" I can't remember whether the answer is supplementary or complementary, but I gave the opposite answer. The thing is, as a practicing physicist I never use those terms. I just say "The angles add up to 180 degrees" and go on doing my calculation. I don't give it a name.

[cjp]

thoreau -- ha, I saw that episode.

And made fun of the guy who answered complementary.

(But only after I couldn't remember the answer myself 🙂 )

[downstater]

dude, i'm going nuts with this and i think i may need to reevaluate my life because of question #1. for all those who found it to be a no-brainer, please explain it. for some reason i can't see it and until i can, i will never fully appreciate a sunset.

[downstater]

nevermind, cjp explained it.

hey! i never noticed that rainbow over there!

[Gimme Back My Dog]

What I noticed about Deal or No Deal was that the offers started out much lower than the expected value and gradually increased to about ten percent over expected value. So I would amend your strategy to say never take the first three offers as you are virtually guaranteed the offers will increase.

And if you saw the show, you will know that telegenicity is not a big criteria for contestants.

[cjp]

I think question 1 is definitely the "hardest," in that the duh (but wrong) answer is the most obvious.

Here's how to arrive at the answer:

we know bat = ball + 1.00.
and ball + bat = 1.10. So replace "bat" with "ball+1.00" to get:

ball + ball + 1.00 = 1.10

so ball+ball=0.10, and ball=0.05.

[Allan]

Allen T:

Try this...

(1) Bat + Ball = $1.10
(2) Bat - Ball = $1.00

Rearrange (2)
=> Bat = $1.00 + Ball

Substitute into (1)
=> ($1.00 + Ball) + Ball = $1.10
=> 2*Ball = $0.10
=> Ball = $0.05
=> Bat = $1.05

[Allen T]

Thanks cjp. I hate story problems. 😉

Where B is Ball.

Batt = (B + 100)

substituting (B + 100) for Batt we get...

B + (B + 100) = 110
2B + 100 = 110
2B = 10
B = 5

Lord, my math skills have atrophied.

-Allen T

[thoreau]

cjp-

You saw it? Wow.

Did you know that off camera Ben Stein kept raving about how awesome my "Arab League" answer was? He was just stunned by it. The question was "[Insert some Arab name here] was the first Secretary General of this [insert some small number here]-member league founded in 194[insert digit here] to resolve conflicts."

The number of members was too small to be the UN, and given the history I was pretty sure that the first UN Sec. General wouldn't have been from an Arab country. I figured it had to be the Arab league. He was just awed by it, for some reason.

I'm embarrassed by a couple other answers that I gave in the final round as well, but you have to understand that with 6 seconds per question, most of it occupied by Nancy reading, there's simply no time to think.

dude sans dog-

Not all of the contestants are attractive, but they have personalities that make for good drama. I did notice that the offers didn't quite match the expectation values, and that the discrepancy changed. If I were on the show I'd factor that into my calculations (plus the tax code).

But overall I'd make a boring contestant. I'd calculate the expectation value if opening a few more boxes went poorly for me, factor in a correction for their systematic discrepancy, and then compare it with the amount I need to pay my debts (pre-adjusted for taxes). I wouldn't have any drama to offer them. So they'd never put me on there.

[Allen T]

Heh. Thanks everyone.

I need a nap now.

-Allen T

[Mo]

Allan
Or you could do it like this:
Bat + Ball = 1.10
Bat - Ball = 1.00

Then you add the two equations together to get:

Bat + Ball + Bat - Ball = 2.10
or
2(Bat) = 2.10

Divide both sides by 2 and get

Bat = 1.05

[anomdebus]

I think the third question should read:
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 at least half the lake?

The 48th day does not necessarily have to completely double the previous day to fill the whole lake. Not unless the lily patch can grow outside the lake.

[jroh]

I was never any good at baseball.

[Tim Higgins]

thoreau,

For Deal or No Deal, it might be wise to select briefcase 1, and eliminate briefcases from highest (26?) to lowest (2). That way, the number of the highest remaining briefcase would save you from having to count suitcases to determine EVs.

[Warren]

I can't believe how much dissecting is being done over these "trick" questions. They are all straightforward and undue analysis violates the spirit of what is so simply stated. If you guessed wrong, once you've been given the answer you should immediately see that it is correct (and feel foolish for being so easily tricked).

thoreau,
I never use the terms supplementary or complementary either. But I would say, "these angles make a straight line (or right angle)". The special character of right angles and straight lines, being the thing that I wish to point out, is not necessarily expressed with a number.

[Matt]

Obviously the original article needs to have a new category. Those who are a) those who are more risk tolerant, b) those who are less risk tolerant, and a new category, c) those who can't even get to the risk tolerance decision point as they're all caught up in machines working sequentially in an infinte "do" loop...;>

[anon2]

Joe,

Your objection is just as valid as the answers:

"Who knows? The floor may only be able to bear the weight of five machines and adding even a single machine will cause production to cease."

or

"Who knows? Some of the 100 machines may be broken."

or

"Who knows? One of the machines may be super special and able to produce 1,000 widgets a second."

They and your answer are all correct in the real world, but questions like those posed are implicilty asked about a fictional world where extraneous constraints aren't taken into consideration.

BTW, you can also answer #1 with "I don't know, the $1.10 price may be a package deal." or #3 with "It depends. Is the lake itself growing or shrinking?" etc.

[rox_publius]

what a bunch of dorks...

doing algebra repeatedly on an online forum.

sadly, i belong.

[v]

downstater,

>for some reason i can't see it and until i can, i will never fully appreciate a sunset.

i can't decide which would be a more moral choice -- eating you or a chimpanzee.

[brainiac]

If, however, the 100 machines consists of one A, one B, one C, one D, and ninety six Es, it will take some amount of time longer than five minutes to produce 100 widgets, depending on how long the A through D portion takes, and how long Machine E's task takes.

If I can choose the A-B-C-D-E mix of the 95 new machines (since they are apparently free machines), why put in 95 more E's if it's going to slow the throughput down? Put in 19 more A's, 19 more B's, 19 more C's, 19 more D's and 19 more E's!

[happyjuggler0]

You don't really need a formula to answer #1. They cost $1.10 together with the difference being $1. 1.10-1=0.10. Ten cents divided by 2 is 5 cents. The ball is 5 cents and the bat is $1.05. Nuff said.

Buy as many balls and bats as you have money for. Resell them for a massive profit elsewhere.

You have a choice between a sure $200 or a 1/10,000 chance at $2,000,000, tax-free in both cases. I pick the free $200 if I am sure I'll get laid by "that amazing babe" if I take her out to that fancy dinner. If the dinner won't do the trick, but if being worth about $2,000,000 will get me laid by "that amazing babe", then I pick the 1/10,000 chance at $2,000,000. I'm assuming that offering to give her $200 for sex won't work.

[Happy Jack]

This whole exercise is apt at this time of year.
When you are in a Super bowl pool and draw one of the finalist team names, try this:

Let's say the pot is worth $100, and the entry was $5. Offer to "purchase" the other finalists team for $10. Point out that they get a guaranteed doubling of their money. Hope that they improve your payout chances to 100%.

[Ethan]

it takes five machines five minutes to make five widgets

Like some others I saw this as ambiguous. It could mean (1) In a five minute period these machines together make five widgets [25 minutes of total machine-minutes producing 5 widgets, for a rate of one widget every 5 minutes] or (2) Five widgets are made after five total machine-minutes [for a rate of one widget per minute].

[Happy Jack]

Er, that would be $80 if you have 16 teams and each pull a team name.

[Ethan]

Also, it seems that the lily pad one makes a lot of assumptions about the shape of the pad and of the lake and about how the pad is doubling in size. The pad could double in size forever and never cover the lake. Perhaps they should have phrased the question in terms of the areas of the pad and lake.

[Michael A Clem]

I've seen these types of questions before, so I didn't have much trouble answering them (correctly, I might add). But what do they have to do with risk-taking??
I rememeber reading an article about risk-taking (but I've forgotten who wrote it, some anthropologist, I believe), and he concluded that people are less willing to take risks when the factors are beyond one's control (i.e. flying by plane) and more willing to take risks when one can control the factors (like skydiving). That seems like an interesting enough conclusion for a Reasonite to do an article on, doesn't it?

[Morgan]

Ouch,

My head is hurting. The H&R version of question one looks like this:

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

How are people, CJP for example, getting to the conclusion that "we know bat = ball + 1.00?"

-Morgan

[Michael A. Clem]

Morgan, it says right in the question that the bat costs a dollar more than the ball. ball + 1.00 equals bat.

[joe]

Morgan,

Because the question tells us "The bat costs $1.00 more than the ball."

[Morgan]

Got it. Whew.. I was never an algebra guy. I guess I'm the perfect mark for these types of questions.

Thanks!

[downstater]

v,
i can't decide which would be a more moral choice -- eating you or a chimpanzee.

i'm not sure, but if you are so morally inclined to take a bite, then i am happy to oblige - you are more then welcome to eat me. 😉

[Russ 2000]

Postrel, a former reason staffer, mentions Kahneman and Tversky.

Barry Schwartz, ripped a new one in Reason in 2004, sort of swears at the altar of Kahneman and Tversky.

I'm not saying Schwartz didn't deserve it, but isn't Ginny sort of explaining the point Schwartz was observing? Certainly joe's initial post did - assuming it was a 5-step process rather 5 machines all doing the same process is a perfectly valid assumption. But when given the opportunity to add 95 machines, he chose to add machines all of the same type even though his own asumption was that the 5 machines all did different work. When given the opportuninty for choice, a reasonably intelligent person like joe still shit the bed (or at least demonstrated his bureaucratic tendency).

[Jim]

When my kids were younger I posed the question to them this way:

If a man and a half can dig a hole and a half in a day and a half, how long does it take a man to dig a hole?

I like that wording much better. The confusion it engenders makes the (basically very obvious) answer more difficult to see.

[v]

downstater,

>you are more then welcome to eat me. 😉

Zing!

[Larry N. Martin]

Obviously, Jim, it would take 2/3 of a day. After all, a half a man isn't going to be doing much digging--the whole man is probably digging the hole for the half a man.

😉

[ben]

What is half of a hole?

[Stevo Darkly]

what a bunch of dorks...
doing algebra repeatedly on an online forum.
sadly, i belong.

If you can rewrite that second line down to seven syllables, you've got yourself a lovely haiku.

Or a senryu. Whatever.

Maybe:

What a bunch of dorks ...
Doing math online for fun.
Sadly, I belong.

[MIchael A. Clem]

Hey, that's a keeper, Stevo!

[The Real Bill]

You people are cruel. I solve math problems for a living and I read H&R to forget.

[Meister]

And this is suppose to measure your risk tolerance how????????

[Matt Bruce]

I idly wonder what the correlation is between {people who are good at math and risk-neutral} and people who play a lot of poker.

[Shawn Smith]

Happy Jack,

If you offered $10 for my ticket, I would probably offer instead to give you $40 for your ticket (splitting the money evenly between us). I would recognize that your arrangement would have guaranteed you winning $65 and wouldn't consider that very fair. The mathemetician profiled in A Beautiful Mind demonstrated that people will be vidictive if they feel they're getting gypped by someone else as opposed to a computer.

[Jimbo]

The real question is...if one man could lose 30 lbs. in 30 days, how many lbs. could 5 men lose humping a carpet.

[R C Dean]

i can't decide which would be a more moral choice -- eating you or a chimpanzee.

Throw another chimp on the barbie, I say!

[dead_elvis]

As long as we're overly deconstructing the machine question, isn't the most important factor knowing whether or not the machines are unionized?

[Happy Jack]

Shawn - If I was involved, I would first ask if you went to Princeton or Toledo. Might change the answer I received. 🙂

[Phil]

Also, it seems that the lily pad one makes a lot of assumptions about the shape of the pad and of the lake and about how the pad is doubling in size. The pad could double in size forever and never cover the lake.

Er . . . the question itself stipulates that the doubling lily pad patch covers the lake in 48 days. If the patch doubles every day, and on day 48 the lake is covered, there is literally only one answer to the question.

[Shawn Smith]

Happy Jack,

Well, the University of Nevada at Las Vegas is probably closer to Toledo than Princeton on the academic scale, but because it's Las Vegas, I would probably be more of a risk taker than otherwise. The more interesting question to me was, "would you rather have a certain $100 loss versus a 50% chance of losing $300." That is a much tougher question to answer, at least as far as I'm concerned. If the experiment were run multiple times, I would probably choose the certain $100 loss, but if it were run only once, I would have a slight preference for the 50% chance of losing $300.

[Happy Jack]

Shawn - The scenario you (or they) posit is similar to surrender in blackjack. Just something to consider.

Another thing to think about. What if your employer gave you the choice of buying $5 of lottery tickets a week, or putting the money in an index fund. What would you choose?

[Ron Hardin]

My own favorite illustrates the economic effect called ``the velocity of money.'' The Fed does this all the time.

Three salesmen check into a hotel and share a room. The room costs $30. (old problem)

The clerk suddenly realizes that it's a $25 room, so sends the bellhop up to return $5.

The bellhop realizes that three guys can't split $5, so pockets $2.

The men paid $27 for the room, the bellhop kept $2 making $29, where's the other dollar?

[amazingdrx]

Figurin' r hard. Hehehey.

Would you rather have a leader who is proven to be corrupt and incompetent, or take a chance on a new leader who may prove to be even more incompetent...in time of war?

Don't bother to answer that, you alrewady have.

[Michael A. Clem]

Er, the men paid $27 for the room ($30 less $3), and the bellhop kept $2, which would have made it $25. Simple misdirection. Okay, not so simple, but still misdirection.

Found the article I was talking about. It's in the book: "Why The Reckless Survive: And Other Secrets of Human Nature" by Melvin Konner. No libertarian, but if there's a nugget of truth to be found, why not take it?

[Shawn Smith]

Happy Jack,

Sorry for taking so long to get back to you, but in your scenario, I would put the $5 into the index fund. Because I live in the Las Vegas Metro Area, I see gambling as inherently stacked against the player. We don't have a lottery here in NV because the casino interests don't want it, and we can't even have a state-wide progressive Keno game, because it's too much like a lottery.

I'm not aware of any lotteries that are expected to pay more money to the players than they pay in, so your scenario seems more like having two options where one has a very small chance of a very big payout, and another with a very big chance of a very small payout. So, in that case, I'm quite risk-averse.

[Steven Wright]

If it's zero degrees outside today and it's supposed to be twice as cold tomorrow, how cold is it going to be?

[Hakluyt]

Evan,

The point is whether you go with the obvious answer, or whether you invest time in making sure it's right.

Which this test may not accurately answer given the low incentive, risk, etc. level that necessarily comes with such tests.

[mediageek]

I can't believe how much dissecting is being done over these "trick" questions. They are all straightforward and undue analysis violates the spirit of what is so simply stated. If you guessed wrong, once you've been given the answer you should immediately see that it is correct (and feel foolish for being so easily tricked).

Thanks for making me feel like a moron, jackass.

[Ethan]

Er . . . the question itself stipulates that the doubling lily pad patch covers the lake in 48 days. If the patch doubles every day, and on day 48 the lake is covered, there is literally only one answer to the question.

That first sentence is right on. I was going by my memory of what the question was. Oops. But the second sentence isn't. A lake could be covered on day 48 and be half covered a day other than day 47.

[Sandy]

I glanced at these questions, got them all wrong, which would be embarrassing except that a) once I saw the answer to number 1 I thought about it and realized I'd been had, and then went back and thought about the others, and b) I have always sucked at math, and these are story problems, which are worse for me than anything. I don't know why--suffice it to say my IQ has been rated decently highly, but I have a problem in this area.

I must say it rings true, because I didn't bother to think much about them, and I have only slight tolerance for risk. I wouldn't overextend myself at the beginning of the housing bubble on the bet that my income would rise to the point where I was no longer housepoor, and I wouldn't buy in a bad neighborhood that is nonetheless likely to come up in value, even though I could afford it. For me the downsides of losing my job (I work in an industry that is not known for stable employment) and getting burgled far outweighed the gains.

But yep, don't ask me math questions. I program computers to do that shit for me. As long as I have adequate time to think about the problem, I can figure out a way to solve it. Yeah, yeah, other people might be faster than me at that initial step, but interestingly, few of them are significantly better at architecting an easily-maintainable system, partially because they attempt to quickly answer everything and not think about the downsides.

[Steve]

I loved these problems! I am a successful lawyer who is not allowed to work on any monetary calculations on my job, for good reason. As at work, I got every single one wrong!! I think I must have been dropped on my head as a child and damaged the (?) left side.

[Dr. Math]

Lots of discussion about (trick) questions 1 and 2. Not enough about 3:

Doubling 48 times isn't possible. The lily pad can't double in size 48 times.

2 to the 48th power is a big number. Very big.

They should have used a number like, say, 8, so the "obvious" would be 4 and there's still room for other silly answers such as 2.

[Kurt]

That first sentence is right on. I was going by my memory of what the question was. Oops. But the second sentence isn't. A lake could be covered on day 48 and be half covered a day other than day 47.

I don't get this. If it's half covered on day 46, what do you think it looks like on day 47?

[Ethan]

Hey Kurt,

In the discussion on this thread, the "patch" of lilypads became a "lilypad." And with respect to a single lilypad, of course, half the lake could be covered on one day, the pad could double overnight, and yet the lake could remain uncovered the next day, if the lake was shaped right. But it also works for a patch of lilypads, if you allow the patch to extend a little bit beyond the shores of the lake, which can happen and would almost certainly happen if the patch were doubling in size every single day.

Cheers!