# Why Does Almost Everyone Get this Question Wrong? **URL:** \ **Category:** Miscellaneous and Personal Stuff I Must Share\ **Created:** [April 21, 2020, 12:52am UTC](https://boards.straightdope.com/t/why-does-almost-everyone-get-this-question-wrong/852239 "2020-04-21T00:52:17Z")\ **Posts on this page:** 20\ **Page:** 2
**Author:** ![Telperion](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/telperion/32/509_2.png) [@Telperion](https://boards.straightdope.com/u/Telperion)\ **Post date:** [April 21, 2020, 12:01pm UTC](https://boards.straightdope.com/t/why-does-almost-everyone-get-this-question-wrong/852239/21 "2020-04-21T12:01:56Z")
> [@penultima\_thule](#): > > An old rural favourite; > If a hen and a half, lays an egg and a half, in a day and a half … so; > How many eggs do four hens lay in six days? > > The most common and deductive answer 24 is wrong because not all factors are additive. How is it wrong? My grandparents had hens and they got about one egg per day from each of them. ---
**Author:** ![Ynnad](https://avatars.discourse-cdn.com/v4/letter/y/4491bb/32.png) [@Ynnad](https://boards.straightdope.com/u/Ynnad)\ **Post date:** [April 21, 2020, 12:13pm UTC](https://boards.straightdope.com/t/why-does-almost-everyone-get-this-question-wrong/852239/22 "2020-04-21T12:13:42Z")
> [@guizot](#): > > … I don’t buy the premise of the OP that “everyone” gets it wrong. … I have not kept accurate records but I estimate less than 1 in 40 gets it right. I have asked a lot of people. Many of them supposedly “highly educated.” Also, I did say **almost** everyone. ---
**Author:** ![Telemark](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/telemark/32/372_2.png) [@Telemark](https://boards.straightdope.com/u/Telemark)\ **Post date:** [April 21, 2020, 12:14pm UTC](https://boards.straightdope.com/t/why-does-almost-everyone-get-this-question-wrong/852239/23 "2020-04-21T12:14:27Z")
> [@Telperion](#): > > How is it wrong? My grandparents had hens and they got about one egg per day from each of them. Because according to the setup it takes a day and a half for a single chicken to lay an egg. Therefore any individual chicken will lay 4 eggs in 6 days; meaning you get 16 eggs in total over a span of 6 days. The misdirection in the setup makes you think that a single chicken lays an egg per day, but that’s not what it says. ---
**Author:** ![Andy\_L](https://avatars.discourse-cdn.com/v4/letter/a/c67d28/32.png) [@Andy\_L](https://boards.straightdope.com/u/Andy_L)\ **Post date:** [April 21, 2020, 12:16pm UTC](https://boards.straightdope.com/t/why-does-almost-everyone-get-this-question-wrong/852239/24 "2020-04-21T12:16:35Z")
> [@Northern\_Piper](#): > > But that answer is contrary to the terms of the problem: «John spends a total of $1.10 for the two pencils.» > > If the total cost is $1.20, then the terms of the problem have been breached. Right. It’s a failure to check one’s results. But if an answer comes to mind easily, people tend not to check their results, but rather just go with the immediate answer. ---
**Author:** ![Ynnad](https://avatars.discourse-cdn.com/v4/letter/y/4491bb/32.png) [@Ynnad](https://boards.straightdope.com/u/Ynnad)\ **Post date:** [April 21, 2020, 12:21pm UTC](https://boards.straightdope.com/t/why-does-almost-everyone-get-this-question-wrong/852239/25 "2020-04-21T12:21:57Z")
> [@guizot](#): > > … I don’t buy the premise of the OP that “everyone” gets it wrong. … I have not kept accurate records but I estimate less than 1 in 40 gets it right. I have asked a lot of people. Many of them supposedly “highly educated.” Also, I did say **almost** everyone. ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [April 21, 2020, 12:22pm UTC](https://boards.straightdope.com/t/why-does-almost-everyone-get-this-question-wrong/852239/26 "2020-04-21T12:22:41Z")
Your grandparents got one egg per day from their chickens, but **penultima thule** gets one egg per day and a half from his chickens. Back on topic, while the off-the-cuff pattern-recognition method is quicker (but sometimes wrong), and the analytic, algebraic method is usually right (but usually slower), those aren’t the only options. You can also start with the off-the-cuff method, and then check your answer. This lets you start acting on the quick answer before you’ve verified it (thus mitigating the increased time cost), but still gives you a chance to fix it if the check doesn’t work out, only spending the time on the full algebraic method when needed. And in fact, for many more complicated algebra problems, this is how the algebraic solution works. You make an approximation, and then check to see if your approximation is good enough (and if it isn’t, then use your preliminary result to get a better approximation, until it is good enough, which usually only takes a small number of iterations). ---
**Author:** ![Telperion](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/telperion/32/509_2.png) [@Telperion](https://boards.straightdope.com/u/Telperion)\ **Post date:** [April 21, 2020, 12:23pm UTC](https://boards.straightdope.com/t/why-does-almost-everyone-get-this-question-wrong/852239/27 "2020-04-21T12:23:56Z")
> [@Telemark](#): > > Because according to the setup it takes a day and a half for a single chicken to lay an egg. Therefore any individual chicken will lay 4 eggs in 6 days; meaning you get 16 eggs in total over a span of 6 days. It says a hen and a half, but that’s not uncommon when talking about statistics. Obviously heart disease can’t literally kill 198.8 people out of 100,000, but that’s the commonly quoted number. ---
**Author:** ![Telemark](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/telemark/32/372_2.png) [@Telemark](https://boards.straightdope.com/u/Telemark)\ **Post date:** [April 21, 2020, 1:20pm UTC](https://boards.straightdope.com/t/why-does-almost-everyone-get-this-question-wrong/852239/28 "2020-04-21T13:20:23Z")
> [@Telperion](#): > > It says a hen and a half, but that’s not uncommon when talking about statistics. I’m not sure how that relates to the portion of my post that you quoted. The problem as stated is mathematically correct, if misleading to the casual observer. When you say _“a hen and a half lays an egg and a half in a day and a half”_ a casually observer is going to cancel out all the "a half"s and reduce the statement to _“a hen lays an egg in a day”_. But the whole point of the riddle’s misdirection is that you can’t reduce like that. You can only remove the first two, leaving “a hen lays an egg in a day and a half”, the time period doesn’t change. Most folks miss that and therein lies the magic of the riddle. It’s the same type of misdirection in the OP’s riddle. ---
**Author:** ![kayaker](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/kayaker/32/441_2.png) [@kayaker](https://boards.straightdope.com/u/kayaker)\ **Post date:** [April 21, 2020, 2:34pm UTC](https://boards.straightdope.com/t/why-does-almost-everyone-get-this-question-wrong/852239/29 "2020-04-21T14:34:06Z")
> [@Chronos](#): > > Your grandparents got one egg per day from their chickens, but **penultima thule** gets one egg per day and a half from his chickens. Your grandparents had Golden Comets, while **penultima thule** has Rhode Island Reds. ---
**Author:** ![hogarth](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/hogarth/32/1773_2.png) [@hogarth](https://boards.straightdope.com/u/hogarth)\ **Post date:** [April 21, 2020, 2:39pm UTC](https://boards.straightdope.com/t/why-does-almost-everyone-get-this-question-wrong/852239/30 "2020-04-21T14:39:31Z")
This reminds me of when my great-uncle visited and he told me the old puzzle about the three guys overpaying $30 for a $25 hotel room and the bellhop keeping $2 of the change – three people paid $9 = $27 and the bellhop kept $2 so WHERE’S THE MISSING DOLLAR?? I explained that it should be $27 - $2 = $25, not $27 + $2 = $30. My great-uncle paused and then said BUT WHERE’S THE MISSING DOLLAR?? I bet he went back to England and told people “I talked to a mathematician and even he couldn’t figure out where the MISSING DOLLAR is!!” ---
**Author:** ![TriPolar](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/tripolar/32/3008_2.png) [@TriPolar](https://boards.straightdope.com/u/TriPolar)\ **Post date:** [April 21, 2020, 2:43pm UTC](https://boards.straightdope.com/t/why-does-almost-everyone-get-this-question-wrong/852239/31 "2020-04-21T14:43:20Z")
> [@hogarth](#): > > This reminds me of when my great-uncle visited and he told me the old puzzle about the three guys overpaying $30 for a $25 hotel room and the bellhop keeping $2 of the change – three people paid $9 = $27 and the bellhop kept $2 so WHERE’S THE MISSING DOLLAR?? > > I explained that it should be $27 - $2 = $25, not $27 + $2 = $30. My great-uncle paused and then said BUT WHERE’S THE MISSING DOLLAR?? > > I bet he went back to England and told people “I talked to a mathematician and even he couldn’t figure out where the MISSING DOLLAR is!!” It is part of the joke to keep asking where the missing dollar is. Not everybody is asking that as part of the joke though. At least bellhop problem is something people get a little interested in since it doesn’t sound like a question on a middle school math test that shuts off their mind immediately. ---
**Author:** ![TriPolar](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/tripolar/32/3008_2.png) [@TriPolar](https://boards.straightdope.com/u/TriPolar)\ **Post date:** [April 21, 2020, 2:45pm UTC](https://boards.straightdope.com/t/why-does-almost-everyone-get-this-question-wrong/852239/32 "2020-04-21T14:45:22Z")
> [@Ynnad](#): > > I have not kept accurate records but I estimate less than 1 in 40 gets it right. I have asked a lot of people. Many of them supposedly “highly educated.” > > Also, I did say **almost** everyone. Sometimes it’s just as difficult to explain to a math-head why people get this wrong. They just keep saying, “Yeah, but it’s simple algebra, see let X be the price of one pencil…”, yet these highly educated people can’t grasp that most people don’t think that way. ---
**Author:** ![peccavi](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/peccavi/32/388_2.png) [@peccavi](https://boards.straightdope.com/u/peccavi)\ **Post date:** [April 21, 2020, 2:56pm UTC](https://boards.straightdope.com/t/why-does-almost-everyone-get-this-question-wrong/852239/33 "2020-04-21T14:56:01Z")
> [@Chronos](#): > > Back on topic, while the off-the-cuff pattern-recognition method is quicker (but sometimes wrong), and the analytic, algebraic method is usually right (but usually slower), those aren’t the only options. You can also start with the off-the-cuff method, and then check your answer. This lets you start acting on the quick answer before you’ve verified it (thus mitigating the increased time cost), but still gives you a chance to fix it if the check doesn’t work out, only spending the time on the full algebraic method when needed. When I read the OP, that’s how I did it. I started with the intuitive “oh, the expensive one is $1.00”, did the obvious check. Realized that was wrong, started to construct the algebraic equations in my head, but then realized I could do it iteratively (guess $1.01, check, guess $1.02, check…), then realized it would be quicker with successive approximation, then “guessed” $1.05, did the check and was done. The whole process took a few seconds and would have been faster if I hadn’t wasted time on the algebra. ---
**Author:** ![TonySinclair](https://avatars.discourse-cdn.com/v4/letter/t/49beb7/32.png) [@TonySinclair](https://boards.straightdope.com/u/TonySinclair)\ **Post date:** [April 21, 2020, 3:06pm UTC](https://boards.straightdope.com/t/why-does-almost-everyone-get-this-question-wrong/852239/34 "2020-04-21T15:06:45Z")
> [@Little\_Nemo](#): > > What do they call it? A five cent piece? A Royale with cheese. ---
**Author:** ![TriPolar](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/tripolar/32/3008_2.png) [@TriPolar](https://boards.straightdope.com/u/TriPolar)\ **Post date:** [April 21, 2020, 3:19pm UTC](https://boards.straightdope.com/t/why-does-almost-everyone-get-this-question-wrong/852239/35 "2020-04-21T15:19:16Z")
> [@penultima\_thule](#): > > You could include New Zealand, PNG, Singapore, Hong Kong etc amongst countries who have 5c coins that aren’t known as nickels. > > The composition of both US and AUS 5c coins is 75% copper and 25% nickel. > They are 5c and they aren’t nickel so we just tell it like it is. How did you and they buy things in the old days when everything used to cost a nickel? Ask any old person and they’ll tell you how you could buy anything with a nickel;, a hamburger cost a nickel, a bottle of beer cost a nickel, a car cost a nickel… It was the only unit of currency back then. Some people are so old they can remember when you could buy a dollar for a nickel. ---
**Author:** ![Andy\_L](https://avatars.discourse-cdn.com/v4/letter/a/c67d28/32.png) [@Andy\_L](https://boards.straightdope.com/u/Andy_L)\ **Post date:** [April 21, 2020, 3:34pm UTC](https://boards.straightdope.com/t/why-does-almost-everyone-get-this-question-wrong/852239/36 "2020-04-21T15:34:47Z")
> [@hogarth](#): > > This reminds me of when my great-uncle visited and he told me the old puzzle about the three guys overpaying $30 for a $25 hotel room and the bellhop keeping $2 of the change – three people paid $9 = $27 and the bellhop kept $2 so WHERE’S THE MISSING DOLLAR?? > > I explained that it should be $27 - $2 = $25, not $27 + $2 = $30. My great-uncle paused and then said BUT WHERE’S THE MISSING DOLLAR?? > > I bet he went back to England and told people “I talked to a mathematician and even he couldn’t figure out where the MISSING DOLLAR is!!” A method I’ve found helpful for the “missing dollar” problem is to find 30 objects to represent the dollars, and to go through the story with those objects. There’s no missing object at the end, so there’s no missing dollar. ---
**Author:** ![Thudlow\_Boink](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/thudlow_boink/32/320_2.png) [@Thudlow\_Boink](https://boards.straightdope.com/u/Thudlow_Boink)\ **Post date:** [April 21, 2020, 3:43pm UTC](https://boards.straightdope.com/t/why-does-almost-everyone-get-this-question-wrong/852239/37 "2020-04-21T15:43:19Z")
> [@TriPolar](#): > > How did you and they buy things in the old days when everything used to cost a nickel? Ask any old person and they’ll tell you how you could buy anything with a nickel;, a hamburger cost a nickel, a bottle of beer cost a nickel, a car cost a nickel… It was the only unit of currency back then. Some people are so old they can remember when you could buy a dollar for a nickel. In those days, nickels had pictures of bumblebees on 'em. “Give me five bees for a quarter,” you’d say. ---
**Author:** ![glee](https://avatars.discourse-cdn.com/v4/letter/g/b5a626/32.png) [@glee](https://boards.straightdope.com/u/glee)\ **Post date:** [April 21, 2020, 3:45pm UTC](https://boards.straightdope.com/t/why-does-almost-everyone-get-this-question-wrong/852239/38 "2020-04-21T15:45:00Z")
> [@Mangetout](#): > > 10 kids in a room and you call “Who wants ice cream?”. One kid hesitates to consider “What does this question really mean? What does it actually mean to want something? Is he asking whether we, in the room want ice cream, or whether people, in general want ice cream? Is he actually questioning the desirability of ice cream? Do people in general want ice cream? How could we measure that question without asking everyone? Does it depend on the flavour?” > Guess which kid is last in line. Now if you had 10 philosophers in a room, then the ice cream would melt whilst they pondered the question. 😉 ---
**Author:** ![CookingWithGas](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/cookingwithgas/32/485_2.png) [@CookingWithGas](https://boards.straightdope.com/u/CookingWithGas)\ **Post date:** [April 21, 2020, 3:58pm UTC](https://boards.straightdope.com/t/why-does-almost-everyone-get-this-question-wrong/852239/39 "2020-04-21T15:58:13Z")
> [@Novelty\_Bobble](#): > > Travel uphill for an hour at 30mph and then downhill for an hour at 60mph and indeed your average speed is 45mph because you’ve covered 90 miles in 2 hours > > In both cases your questions are set up as “gotchas” because the information is not complete. More precise wording would have been “Go up a hill 30 MPH and back down the same hill at 60MPH.” Which I think everybody would assume anyway. This is actually a very practical calculation for pilots and boat captains, where this effect comes into play with winds aloft and water currents/river flow. > [@glee](#): > > Now if you had 10 philosophers in a room, then the ice cream would melt whilst they pondered the question. 😉 And tried to figure out whose chopsticks to use. ---
**Author:** ![bump](https://avatars.discourse-cdn.com/v4/letter/b/7c8e57/32.png) [@bump](https://boards.straightdope.com/u/bump)\ **Post date:** [April 21, 2020, 4:08pm UTC](https://boards.straightdope.com/t/why-does-almost-everyone-get-this-question-wrong/852239/40 "2020-04-21T16:08:35Z")
I’ve always felt these sorts of problems are sketchy and annoying, not because they test your arithmetic ability, but because they’re testing your ability to parse out the deceptive part inherent in the way it’s phrased. I mean, the whole thing hinges on realizing that _“The expensive pencil costs $1.00 more than the cheap pencil”_ means that a ten cent cheap pencil and a $1 expensive pencil actually means that the expensive pencil is only 90 cents more than the cheap pencil, and that the actual equation is: (1 + x) + x = 1.10, where x is the cost of the cheap pencil. The whole thing hinges on the “more than”- most people read it as something more like _“The expensive pencil costs $1.00, more than the cost of the cheap pencil **(and the total is $1.10**)”_, where the “more than” is more of an adjective describing that the expensive pencil costs more than the cheap one. It doesn’t make a lot of sense, I know, but that’s the point- if you don’t read carefully and think about what it’s actually saying. [Previous page](https://boards.straightdope.com/t/why-does-almost-everyone-get-this-question-wrong/852239.md?page=1) [Next page](https://boards.straightdope.com/t/why-does-almost-everyone-get-this-question-wrong/852239.md?page=3)