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I've just gotten a textbook (physics) for next year and I noticed that, like many other textbooks I've had, it contains solutions to only odd-numbered questions.

From my experience, this is typical, at least for texts at the undergraduate level.

If anyone is wondering, the text is "Fundamentals of Physics" by Halliday & Resnick 10th edition.

My question is, why do textbooks often include the solutions to odd or even numbered problems but not both? In my case, I don't think space is the answer because the answers section only takes up 7 pages.

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    For what it's worth, as someone who for several decades has looked through many hundreds of 1800s algebra, conics, trigonometry, calculus, etc. texts (I own hard copies of at least 20, I have digital copies of several hundred, I have looked at over 100 hard copies in a nearby university library, etc.), this was very common back then too, and the reasons are often given in the prefaces (and in published book reviews) as providing the instructor problems that can be used on tests and such. – Dave L Renfro Jun 19 at 7:36
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    It's rather odd isn't it? – Pryftan Jun 19 at 17:04
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    @DaveLRenfro: That’s fascinating! What (roughly) is the earliest text you’re seen this in? – PLL Jun 19 at 17:27
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    @PPL: I don't know, but if anyone is interested in looking into this, a simple way to begin is to try searches such as this google-books search for "algebra + treatise" for 1700 to 1800. Maybe change "algebra" to "mathematics" or other things, and try including "problems" or "exercises" or some other word that you see these referred to in the older books (just look at a few of them to see what terms are used for the exercises). – Dave L Renfro Jun 19 at 19:31
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    @DaveLRenfro I agree it was rather common also in other field of knowledge (physics and engineering undergraduate textbooks). There were (are?) also textbooks where no answer is given whatsoever. I always sincerely hated books that gave exercises with no solutions (I mean the final results, not the step-by-step procedure). My study method involved solving tons of exercises just to exert my "automatic" skills and acquire self confidence in the topic, but I had to have at least the numerical solutions as a feedback for effective self study. ... – Lorenzo Donati supports Monica Jun 20 at 8:55
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This allowance is a custom to allow instructors to give homework where the solutions to some questions were not provided directly to the student (at least not in the book - this was from a time where searching for solutions to homework was not so easy outside of personal social connections).

If an instructor just wants students to work on problems where the students can easily refer to sample solutions at the back of the book, the instructor can just assign "problems 1-7, odds only". If they want to assign only no-solution problems, they can assign "evens only". If they want to give a mixture to try to encourage students to mix up their solving strategies, they can assign both. To go farther, putting them at the back of the book was another way to try to make it take a little more effort to look for the solution, to encourage the students to try to solve it themselves rather than immediately looking at the solution.

Finally, it is a custom that the problems tend to go from easier to harder, with some texts making the highest numbered questions of a chapter require more knowledge or skills than is actually provided in the accompanying chapter.

As you can imagine, this isn't the only system of designing a textbook that would support these uses, but it just became a very popular and simple way to do it - so you can generally expect to see it in many of the textbooks you'll encounter.

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    This. I only know it from the US but it was in every textbook in my 10th grade, and the teachers used it exactly like you described here. For an actual assignment they gave us the odds, for an "hey, you might wanna exercise optionally" they recommended Exercise 5 evens. – Hobbamok Jun 19 at 8:52
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    For common textbooks detailed solutions to the other questions were often printed in a seperate "teacher's guide". It wasn't unknown for students to get their hands on copies of these guides – Chris H Jun 19 at 9:10
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    @ChrisH Yes -- it's just a book and people can buy books, even in the days when this required going into a bricks-and-mortar store and asking them to order a copy from the publisher. – David Richerby Jun 19 at 9:40
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    @DavidRicherby in my undergrad days there were photocopies of photocopies of photocopies... kicking around. In some of them you could even read the subscripts. The on-campus bookshop claimed not to know anything about the teacher's guides – Chris H Jun 19 at 13:01
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If I were to produce such a book, my reasoning would be a bit different from that of BrianH. In using any such book for a course, I would probably assign only questions that did not have answers in the answer key.

But I would encourage the students to use a tried and true learning technique: reinforcement and feedback. The extra problems, while not assigned, give those students who want the practice (all of them do need it, actually) the opportunity to work on some additional problems and then check their work. If they got the correct answer they have additional confidence in their learning. If they did not, then they want to come and see me to find out where they went wrong - additional reinforcement and feedback.

I would, of course, stress that there is a good way and a bad way to use the answers. Working toward a known answer is far less valuable than working out an unknown answer. Not every student would 'get it' but the opportunity is there for them.

And, of course, they get reinforcement and feedback for the questions that I do assign and for those, I get to follow their thinking somewhat to search for misconceptions.

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    How does this answer differ from BrianH's which says the purpose is so that questions can be assigned that don't have answers in the key (which you say would be your approach), and that having both questions with and without answers gives flexibility to the instructor (which includes your approach)? – Bryan Krause Jun 19 at 16:39
  • @BryanKrause It's different as I interpret it because it also suggests that they could use the questions with answers as a way to try and work it out and then check their answer so as to learn. Since after all people don't always have the best confidence when learning something new and different people learn differently. It might not say why the books have it the way they often are but it still adds to a possible use to it - whether or not that's actually the reason (and I imagine that it could be for some books). I didn't get this impression from the other answer though. – Pryftan Jun 19 at 17:10
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    @Pryftan Yes, the other answer already says "If an instructor just wants students to work on problems where the students can easily refer to sample solutions at the back of the book, the instructor can just assign "problems 1-7, odds only"...If they want to give a mixture to try to encourage students to mix up their solving strategies, they can assign both" which covers what you just described. – Bryan Krause Jun 19 at 18:05
  • @Pryftan BrianH says: "This allowance is a custom to allow instructors to give homework where the solutions to some questions were not provided directly to the student" Buffy says "I would probably assign only questions that did not have answers in the answer key" I am simply pointing out that these are the same reason, stated with different words. – Bryan Krause Jul 16 at 20:56
  • @BryanKrause Funnily enough I figured that much out but the fact you went to try and explain that fact demonstrates my point. As I noted there's a miscommunication: not of what you were trying to do but of my point. The best analogy I can think of is - well I don't know if you know German but let's say I were to start a sentence as 'Die' but then I fell asleep and accidentally hit enter. Would you think I was telling you to 'die'? It's a contrived example but it's the best I can think of in my tired head. It's possible I was commenting originally on more than that quote too. Don't know now. – Pryftan Jul 16 at 21:20
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The other answers cover what I think is the main reason, but I want to bring up something else: Putting solutions into a textbook is a lot of work; the editors have to find the solutions, write them up, typeset them, and someone has to proofread them. On the other hand, the additional benefit of another solution becomes pretty small once half the problems have solutions, especially in those textbooks that feature a lot of rather repetitive problems.

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    I find it weird that no one else said this. It seems everyone else thinks there's some deep philosophical pedagogical meaning, when it might really be (mainly) a matter of time and money. – Selene Auckland Jun 21 at 12:48
  • If it were mainly about money, I would expect even fewer answers, or no answers at all. Teachers could always provide their own answer keys. – chepner Jun 21 at 18:53

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