# Math Challenge - why do people think this is hard? **URL:** \ **Category:** Miscellaneous and Personal Stuff I Must Share\ **Created:** [May 10, 2016, 2:36am UTC](https://boards.straightdope.com/t/math-challenge-why-do-people-think-this-is-hard/754457 "2016-05-10T02:36:34Z")\ **Posts on this page:** 20\ **Page:** 1
**Author:** ![aceplace57](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/aceplace57/32/3500_2.png) [@aceplace57](https://boards.straightdope.com/u/aceplace57)\ **Post date:** [May 10, 2016, 2:36am UTC](https://boards.straightdope.com/t/math-challenge-why-do-people-think-this-is-hard/754457/1 "2016-05-10T02:36:34Z")
The answer seems pretty obvious to me. [SPOILER]19 left, 17 got on. Net difference is -2 63 left on the train, add 2= there were 65 originally think of it like money. you find a $5 bill on the street, you paid $6.50 for lunch. There’s $11 left in your wallet. How much did you have to begin with? [/SPOILER] people were using algebra. or complicated sums. I don’t see why this wouldn’t be a question for a young math student. Am I missing something? 😕 My answer matches the article except they did it in a much more convoluted way. [Math question](http://www.dailymail.co.uk/femail/article-3580699/Can-solve-children-s-maths-puzzle-s-leaving-adults-baffled.html) > [@](#): > > A maths question aimed at year 2 pupils which involves figuring out how many passengers were originally on a train is the latest brain teaser to leave the internet confused. > > The question reads: ‘There were some people on a train. 19 people get off the train at the first stop. 17 people get on the train. Now there are 63 people on the train. How many people were on the train to begin with?’ > > Mother Louise Bloxham shared the test on Twitter as she couldn’t believe the tough teaser was aimed at children as young as six, and her followers were certainly left confused as they battled to figure out the correct answer. ---
**Author:** ![CatastrophicFailure](https://avatars.discourse-cdn.com/v4/letter/c/8c91f0/32.png) [@CatastrophicFailure](https://boards.straightdope.com/u/CatastrophicFailure)\ **Post date:** [May 10, 2016, 3:44am UTC](https://boards.straightdope.com/t/math-challenge-why-do-people-think-this-is-hard/754457/2 "2016-05-10T03:44:22Z")
I just did it with my 7-year-old to see if he could solve it, and once we wrote it out, he could do it. However, it is a trickier problem for that age group, I think. Not the actual calculations, but setting up the problem correctly. I do find it concerning that the teacher giving the test thought it was 46, and many adults couldn’t figure it out. ---
**Author:** ![mhendo](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/mhendo/32/3159_2.png) [@mhendo](https://boards.straightdope.com/u/mhendo)\ **Post date:** [May 10, 2016, 4:06am UTC](https://boards.straightdope.com/t/math-challenge-why-do-people-think-this-is-hard/754457/3 "2016-05-10T04:06:00Z")
The difficulty is not really mathematical; it is conceptual. As **CatastrophicFailure** says, it’s about setting up the problem. The math is incredibly simple. The fact that we are asked to begin the process of addition and subtraction without a starting number is probably the sticking point for some people. After all, how can you subtract 19 from a number that you don’t already know? What you have to do is accept that you don’t know the starting number, and simply look at your net gains or losses. In my head, for example, once i saw that 19 got off and 17 got on, i said to myself “OK, so you have a net loss of two people.” When i’m told, in the next step, that the number of passengers on the train is now 63, it’s a simple matter to add those two back on for the original number. I’m pretty good at basic math, so all of this happens pretty much automatically, but some people are more adept than others at quickly recognizing these sorts of conceptual arrangements. Of course, if you can’t do this quickly in your head, you could easily assign a letter to the unknown number, and work from there. x - 19 + 17 = 63 =\> subtract 17 from each side x - 19 = 46 =\> add 19 to each side x = 65 ---
**Author:** ![aceplace57](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/aceplace57/32/3500_2.png) [@aceplace57](https://boards.straightdope.com/u/aceplace57)\ **Post date:** [May 10, 2016, 4:58am UTC](https://boards.straightdope.com/t/math-challenge-why-do-people-think-this-is-hard/754457/4 "2016-05-10T04:58:26Z")
Understanding what occurred and what changed is key to solving these problems. Sometimes they throw in extra stuff to confuse the situation. Like the train departed at 10Am and 19 Got off at Elm Street station. 17 got on at Oak Street station. Lot of details too ignore. ---
**Author:** ![pulykamell](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/pulykamell/32/3166_2.png) [@pulykamell](https://boards.straightdope.com/u/pulykamell)\ **Post date:** [May 10, 2016, 5:25am UTC](https://boards.straightdope.com/t/math-challenge-why-do-people-think-this-is-hard/754457/5 "2016-05-10T05:25:24Z")
Good lord how I hate the Daily Mail. The SHOCKING subheads read: > [@](#): > > Maths puzzle posted to Twitter by mum Louise Bloxham > Challenge is to work out how passengers are on a train carrying 63 people > If 19 got off at first stop and 17 boarded, how many were there originally > Twitter users gave answers ranging from 46 to 63 but none were correct Yet all the answers they show from Twitter screen shots are the correct one, 65, minus the person who originally tweeted the question, who claims that it is wrong, and the answer book said it’s 46. ---
**Author:** ![mhendo](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/mhendo/32/3159_2.png) [@mhendo](https://boards.straightdope.com/u/mhendo)\ **Post date:** [May 10, 2016, 5:34am UTC](https://boards.straightdope.com/t/math-challenge-why-do-people-think-this-is-hard/754457/6 "2016-05-10T05:34:07Z")
> [@pulykamell](#): > > Yet all the answers they show from Twitter screen shots are the correct one, 65, minus the person who originally tweeted the question, who claims that it is wrong, and the answer book said it’s 46. Not only that, but the claim about it being 46 in the answer book is a second-hand claim, made by one person about something another person claimed on a separate Facebook page. No-one provides any real evidence that the answer book said 46, and even if they showed that 46 was indeed the answer provided by the answer book, the most likely explanation is that it was just an error in the publishing, not in the actual calculations. _Daily Mail_ in Shock Beat-Up of Non-Story. Again. ---
**Author:** ![Biotop](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/biotop/32/321_2.png) [@Biotop](https://boards.straightdope.com/u/Biotop)\ **Post date:** [May 10, 2016, 6:02am UTC](https://boards.straightdope.com/t/math-challenge-why-do-people-think-this-is-hard/754457/7 "2016-05-10T06:02:18Z")
A train travels from Point A to Point Z, stopping at the alphabetical stops in between and usually loading and unloading some passengers at each stop. Two thirds of the passengers who were on the train when it left Point A have already gotten off by the time the train reaches Point Z. There are 150 passengers on the train when it arrives at Point Z. Of these passengers, there are 100 more passengers who got on after the train left Point A than there are passengers who were on the train when it left Point A. No passenger who left the train has reboarded. How many passengers were on the train when it left Point A? ---
**Author:** ![Princhester](https://avatars.discourse-cdn.com/v4/letter/p/3e96dc/32.png) [@Princhester](https://boards.straightdope.com/u/Princhester)\ **Post date:** [May 10, 2016, 6:16am UTC](https://boards.straightdope.com/t/math-challenge-why-do-people-think-this-is-hard/754457/8 "2016-05-10T06:16:45Z")
> [@mhendo](#): > > …and even if they showed that 46 was indeed the answer provided by the answer book, the most likely explanation is that it was just an error in the publishing, not in the actual calculations… 46 is 63-17 so I suspect it wasn’t a typo. I suspect either (a) the person setting the answer sheet had a total brainfade and subtracted the 17 and forgot to add the 19, or (b) the wording was utterly borked and was supposed to say “how many people were on the train after the first stop”. I suspect (a) is more likely. ---
**Author:** ![Tabby\_Cat](https://avatars.discourse-cdn.com/v4/letter/t/6a8cbe/32.png) [@Tabby\_Cat](https://boards.straightdope.com/u/Tabby_Cat)\ **Post date:** [May 10, 2016, 6:21am UTC](https://boards.straightdope.com/t/math-challenge-why-do-people-think-this-is-hard/754457/9 "2016-05-10T06:21:37Z")
> [@Biotop](#): > > A train travels from Point A to Point Z, stopping at the alphabetical stops in between and usually loading and unloading some passengers at each stop. Two thirds of the passengers who were on the train when it left Point A have already gotten off by the time the train reaches Point Z. There are 150 passengers on the train when it arrives at Point Z. Of these passengers, there are 100 more passengers who got on after the train left Point A than there are passengers who were on the train when it left Point A. No passenger who left the train has reboarded. > > How many passengers were on the train when it left Point A? [spoiler]At Z, there are 150 passengers, of which there are 100 more new boarders (NBs) than original boarders (OBs). 150 = NB + OB, NB - OB = 100. Solve for NB and OB, it seems that there are 25 original boarders (OBs) and 125 new boarders (NBs). Since 2/3 of the passengers at A have already left the train, the 25 OBs at Z represents 1/3 of the total OBs at A, and so there were 75 OBs at A. [/spoiler] ---
**Author:** ![Tabby\_Cat](https://avatars.discourse-cdn.com/v4/letter/t/6a8cbe/32.png) [@Tabby\_Cat](https://boards.straightdope.com/u/Tabby_Cat)\ **Post date:** [May 10, 2016, 6:24am UTC](https://boards.straightdope.com/t/math-challenge-why-do-people-think-this-is-hard/754457/10 "2016-05-10T06:24:24Z")
> [@mhendo](#): > > The difficulty is not really mathematical; it is conceptual. As **CatastrophicFailure** says, it’s about setting up the problem. > > The math is incredibly simple. The fact that we are asked to begin the process of addition and subtraction without a starting number is probably the sticking point for some people. After all, how can you subtract 19 from a number that you don’t already know? What you have to do is accept that you don’t know the starting number, and simply look at your net gains or losses. > > In my head, for example, once i saw that 19 got off and 17 got on, i said to myself “OK, so you have a net loss of two people.” When i’m told, in the next step, that the number of passengers on the train is now 63, it’s a simple matter to add those two back on for the original number. > > I’m pretty good at basic math, so all of this happens pretty much automatically, but some people are more adept than others at quickly recognizing these sorts of conceptual arrangements. > > Of course, if you can’t do this quickly in your head, you could easily assign a letter to the unknown number, and work from there. > > x - 19 + 17 = 63 =\> subtract 17 from each side > > x - 19 = 46 =\> add 19 to each side > > x = 65 I did it the other way around. I’m told that I end with 63 people. I’m told that 17 people got on the train, so before they got on, there were 63 - 17 = 46 people. I’m also told that before THAT, 19 people got off the train. So add them back on, and you get 46 + 19 = 65. No unknowns or algebra needed. ---
**Author:** ![aceplace57](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/aceplace57/32/3500_2.png) [@aceplace57](https://boards.straightdope.com/u/aceplace57)\ **Post date:** [May 10, 2016, 7:19am UTC](https://boards.straightdope.com/t/math-challenge-why-do-people-think-this-is-hard/754457/11 "2016-05-10T07:19:57Z")
No one gave the simple method of recognizing the change in the number of people and adding to 63. They were using algebra and complaining it was too difficult for a 7 or 8 year old. When its easy grade school math. I did problems like this throughout my early school years. Long before taking algebra in 9th grade. ---
**Author:** ![Nava](https://avatars.discourse-cdn.com/v4/letter/n/da6949/32.png) [@Nava](https://boards.straightdope.com/u/Nava)\ **Post date:** [May 10, 2016, 8:01am UTC](https://boards.straightdope.com/t/math-challenge-why-do-people-think-this-is-hard/754457/12 "2016-05-10T08:01:38Z")
> [@mhendo](#): > > Of course, if you can’t do this quickly in your head, you could easily assign a letter to the unknown number, and work from there. > > x - 19 + 17 = 63 =\> subtract 17 from each side > > x - 19 = 46 =\> add 19 to each side > > x = 65 Yeah, but al-jibber isn’t taught in 2nd grade. It can be solved without it by working backwards, but thing is, for many people the setting up seems to be the hardest part of math. ---
**Author:** ![pulykamell](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/pulykamell/32/3166_2.png) [@pulykamell](https://boards.straightdope.com/u/pulykamell)\ **Post date:** [May 10, 2016, 12:26pm UTC](https://boards.straightdope.com/t/math-challenge-why-do-people-think-this-is-hard/754457/13 "2016-05-10T12:26:38Z")
nm. ---
**Author:** ![jtur88](https://avatars.discourse-cdn.com/v4/letter/j/e9c0ed/32.png) [@jtur88](https://boards.straightdope.com/u/jtur88)\ **Post date:** [May 10, 2016, 1:01pm UTC](https://boards.straightdope.com/t/math-challenge-why-do-people-think-this-is-hard/754457/14 "2016-05-10T13:01:23Z")
Sadly, children are taught “process” now instead of intuitive sense. Obviously, the number of people on the train decreased by two, so there must have been 65, while the other children are still laboriously writing symbols on fresh clean sheets of forest products. But if a child gives that perfectly correct answer, it is labeled as “wrong” and the child must be given a grade of zero and “corrected”. ---
**Author:** ![Nava](https://avatars.discourse-cdn.com/v4/letter/n/da6949/32.png) [@Nava](https://boards.straightdope.com/u/Nava)\ **Post date:** [May 10, 2016, 1:35pm UTC](https://boards.straightdope.com/t/math-challenge-why-do-people-think-this-is-hard/754457/15 "2016-05-10T13:35:08Z")
> [@jtur88](#): > > Sadly, children are taught “process” now instead of intuitive sense. Obviously, the number of people on the train decreased by two, so there must have been 65, while the other children are still laboriously writing symbols on fresh clean sheets of forest products. But if a child gives that perfectly correct answer, it is labeled as “wrong” and the child must be given a grade of zero and “corrected”. Same as when I was taking multivariate calculus and had problems with the geometry problems because I knew the answer via geometry. Or all those drawings of multicolored circles (well, loops would be a better description) around all those black dots and blue Xs, to learn how to count in bases other than 10… It’s not exactly new, and in fact being able to follow a process is quite valuable, so long as the process itself is well explained. ---
**Author:** ![pulykamell](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/pulykamell/32/3166_2.png) [@pulykamell](https://boards.straightdope.com/u/pulykamell)\ **Post date:** [May 10, 2016, 1:59pm UTC](https://boards.straightdope.com/t/math-challenge-why-do-people-think-this-is-hard/754457/16 "2016-05-10T13:59:01Z")
> [@jtur88](#): > > Sadly, children are taught “process” now instead of intuitive sense. Obviously, the number of people on the train decreased by two, so there must have been 65, while the other children are still laboriously writing symbols on fresh clean sheets of forest products. But if a child gives that perfectly correct answer, it is labeled as “wrong” and the child must be given a grade of zero and “corrected”. That’s weird. I would consider this a problem that is teqching conceptual understanding, not process. ---
**Author:** ![Nava](https://avatars.discourse-cdn.com/v4/letter/n/da6949/32.png) [@Nava](https://boards.straightdope.com/u/Nava)\ **Post date:** [May 10, 2016, 2:09pm UTC](https://boards.straightdope.com/t/math-challenge-why-do-people-think-this-is-hard/754457/17 "2016-05-10T14:09:50Z")
I understood as that being his complaint, that since the children have only been taught process, this would be unsolvable. Now, which specific process he thinks is taught, and why it wouldn’t work in this particular case, is beyond my ken. ---
**Author:** ![friedo](https://avatars.discourse-cdn.com/v4/letter/f/8edcca/32.png) [@friedo](https://boards.straightdope.com/u/friedo)\ **Post date:** [May 10, 2016, 2:15pm UTC](https://boards.straightdope.com/t/math-challenge-why-do-people-think-this-is-hard/754457/18 "2016-05-10T14:15:20Z")
> [@aceplace57](#): > > Am I missing something? 😕 Yes. You are reading _The Daily Mail_. ---
**Author:** ![pulykamell](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/pulykamell/32/3166_2.png) [@pulykamell](https://boards.straightdope.com/u/pulykamell)\ **Post date:** [May 10, 2016, 2:27pm UTC](https://boards.straightdope.com/t/math-challenge-why-do-people-think-this-is-hard/754457/19 "2016-05-10T14:27:37Z")
> [@Nava](#): > > I understood as that being his complaint, that since the children have only been taught process, this would be unsolvable. > > Now, which specific process he thinks is taught, and why it wouldn’t work in this particular case, is beyond my ken. I get what he’s saying. To me, traditional math teaching methods are about process, and the new fangled ones are the ones teaching the more holistic, intuitive, understanding way. It seems to me the people complaining that it’s too hard for a 9 year old because algebra are exactly the ones who do things by rote/process and the children for whom the question was aimed would know how to do it by recognizing the net difference or something like that. ---
**Author:** ![bump](https://avatars.discourse-cdn.com/v4/letter/b/7c8e57/32.png) [@bump](https://boards.straightdope.com/u/bump)\ **Post date:** [May 10, 2016, 2:40pm UTC](https://boards.straightdope.com/t/math-challenge-why-do-people-think-this-is-hard/754457/20 "2016-05-10T14:40:59Z")
I think it’s more or less a good example of what Lockhart’s Lament is talking about. The problem is dirt-simple in concept- how many more got off than got on? Once you know that, you just add that to the number still on the train to get the total original number. But most people are taught math in terms of dry and abstract symbols and numbers, so they try to set it up as N-19 + 17 = 63, and fuck that up, likely by trying to solve for N before they subtract 19 from 17, simplifying it to N-2 = 63, which anyone should be able to solve for N. But the fundamental problem is how they thought about it- it doesn’t need algebra- it just needs common sense.