The REAL answer to the riddle everyone is talking about
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- Опубліковано 20 вер 2023
- A boy was playing with a book and tore out the pages 7, 8, 100, 101, 222 and 223. How many pages did he tear out?
Riddle
heavy.com/entertainment/2020/...
www.republicworld.com/enterta...
www.hitc.com/en-gb/2020/04/20...
gadgetgrasp.com/my-son-was-pl...
Numbering
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Page definition
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Les grandes heures de la reine Anne de Bretagne etl'aterlier de Jean Bourdichon
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Tale of Two Cities
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Book of Kells
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Child reading illustration
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System 1 and 2 thinking
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This riddle only exists because of a terminology problem. In typical saddle stitching, one sheet contains two leaves, each of which contains two pages. A person cannot tear out a page, but can tear out a leaf (page pair) or even a sheet (leaf pair). Depending on the number of pages, removing one sheet could account for multiple pages listed.
Yeah, there are multiple different factors that each lead to different answers. When you tear out a page, is it a single front and back page, or is it connected to another page on the other side of the book that also falls out? Also, are 7 and 8 two sides of the same page, or are they actually 6 and 7, and 8 and 9? If it's connected to another page on the other side of the book, are those connected pages also the 222/223 or different pages? It becomes less about math, and more about book making and what style of book it is.
so it can be 4 sheets, 8 leaves, 16 pages
1. if we assume 1,2,3,4 are in one sheet «7/8, 100, 101, 222/223». or
2. if we assume A,1,2,3 are in one sheet (A is an additional page) - 4,5,6,7 are in one sheet «7, 8, 100/101, 222/223». or
3. if we assume A,B,1,2 are in one sheet (A,B are additional pages) - 3,4,5,6 are in one sheet «7/8, 100/101, 222, 223».
or it can be 3 sheets, 6 leaves, 12 pages if we assume A,B,C,1 are in one sheet - 2,3,4,5 are in one sheet «7/8, 100/101, 222/223»
Unstated assumptions are made in the question which makes it impossible to correctly answer without first correctly guessing the unstated assumptions.
If you're interviewing for a position that isn't related to printing, I think it's safe to assume that knowledge of math and problem solving is all that should be needed to solve this puzzle, not knowledge of bookbinding. It's not "wrong" to consider how pages/leaves can double up like that, but no realistic interviewer should expect that to be factored in.
Well tearing is usually incomplete and leaves a little past the bindings, so it's sheet pair doesn't usually fall out.
This puzzle doesn't test our thinking.
It tests our ability to guess what the person writing it intended.
Or the ability to write a solution for every possible interpretation of said words.
And regardless if we interpret the second pages as single pages or sheets, we still need to assume whether only half a sheet gets torn out (2 pages) or the whole sheet (4 pages), as most, if not all, books I ever held in my hands where bound in a way that had 4 pages printed per sheet.
This puzzle I'd call a guessing game at this point.
I have to agree with you. It says pages 100, 101 - which makes someone think those are to SEPERATE pages. It then says page 222 and 223. 222 and 223 could mean:
1: That only that sheet is double-sided (which makes no sense).
2: That the writer/speaker didn't use an Oxford comma and misspoke (so it should have been 222, and 223).
3: That the writer/speaker misspoke by failing to specify what 223 means - AKA the person tore out page 222 AND then tore out 223 more pages after that.
On top of that some books have sheets that start with Even or odd numbers. If there's a forward in a book the first page of the first sheet you read may be labeled as 1 or a 2 which changes the question entirely. You can't give an answer because you can't possibly know if the first page of the first numbered sheet starts on the left or the right and if it's double-sided.
The riddle isn't a riddle because it requires thought; it's a riddle because it's poorly worded and lacks critical information.
I think you could have included the solution where the second word "pages" mean page numbers. So for example if we consider odd numbers being on the right side the missing pages will be 7/8, 99/100, 101/102, 221/222, 223/224. That's a total of 10 missing pages.
As an interviewer, I'd love for someone to present this as one of the solutions. Assuming the definition of pages is how we end up with IT solutions that don't match the needs of the user
That was my solution 😅
Yep. Why are there two distinct "page numbers" on a sheet if each side does not qualify as a separate page?
That was my thinking too.
Or it could be 6/7, 8/9, 100/101 and 222/223, for a total of 8.
The answers given in the video are correct if we agree that a page is a sheet, but usually a page is only a side of a sheet. In this case, the number of pages the child tears out is 10 (on 5 sheets) or 8 (on 4 sheets)
or 3 (edit: sheets) if the numbering isn't consistent, as is sometimes the case when there are pictures in between text pages, or multiple novels in a single book
It is confusing. With standard numbering it means you cannot tear out one page. Only even numbers. But most people would be fine if you said “one page is torn out of this book”. And we usually refer to pages as half a leaf “read 5 pages, from 12-16).
if you use the definition of a sheet and a sheet of paper is a whole piece of paper, so 1 piece of paper could actually include up to 4 pages in a flat book (ie if the book is exactly 323 pages long with odd numbers on the left side, then pages 100, 101, 222 and 223 would be on the same piece of paper) in which it would be possible for the boy to have only torn out 3 sheets of the book
@@Mediocre_Soup most mass produced books (on a press) print 32 pages per sheet now. That would 16 on one side and 16 on the other. The sheet is then folded to give you 32 pages on 16 leaves. Classically they could be 8 pages (Quatro) , or 16 pages (Octavo). That is the sheet. Each page is one block of text, after folding, each leaf will have a page on each side. If you want to talk about tearing out whole sheets, you'd loose at minimum 4 pages per sheet. The terms sheet, leaf and page are quite clearly defined. (edit: after trimming, you could say that they are all 4 pages per sheet now, as the connective bits are chopped off)
@@beauwilliamson3628 this youtube channel is too smart for me
The two uses of the word “pages” occur in the same paragraph, but more important is that they occur in the context of a riddle. Playing on multiple senses of a word is a very common practice in riddles. In this context you really can’t assume the meanings are different, and many people practiced in riddles won’t.
I rarely take issue with the analyses in this video channel, but I will here. The answer is ambiguous specifically because one accustomed to riddles will not, rationally assume the ambiguity of meaning is unintended.
There is Type 3 thinking -- knowing such things. My mother is a typograph, and when I was a child, she was sometimes typesetting and page formatting at home, not at the computer, but with actual pages and actual galley proofs and scissors and glue. And I was talking to her and asking how it works. So I know from experience how a book is numbered. And in typesetting, there is a strict distinction between pages and leaves. The first page is always on top of the stack of leaves. If you open a book, the even pages are on the left, and the odd pages are on the right. If only one page on a leave is printed and numbered, it is not a book, but a brochure or a booklet or something else, and it differs in the way it is bound together. You won't find an actual book with such a numbering scheme. Even if someone eccentric is willfully not using the typesetting numbering scheme and uses another way of numbering pages, for the actual print process, it is still the normal typeset numbering, whatever is printed on the actual page.
this puzzle is more about knowing what the questioner wants you to answer rather than logical thinking imo. for example, not all books number every page (from and back leafs), or if like traditional books the first page is just numbered 1 on the back of the page, which determines which side the odd numbers will be on. in this case you have to have experience with books, so if you dont this puzzle doesn't include all the information needed. to me this puzzle sucks because it relies on info outside the puzzle to be solved, and therefore has multiple answers depending when in history this riddle is asked.
edit: i guessed 5, assuming unnumbered pages dont count, and 1 starts on the back of the first page, making left pages odd and right pages even.
I think the idea is to verify if the interviewee is going through a careful and measured thought process.With questions like these there usually is no right answer, rather, they form a basis for the interviewer to observe the applicant's thought patterns and judge if their style of thinking is an approach that is suitable for the position that they've applied to.
Even if the interviewee provided an incorrect response, the sophistication and consideration of the methods they used to arrive at the answer should matter more to the interviewer, because, in reality there really is no situation where an employee is going to be solving specific puzzles like these. However there will regularly arise situations where in calm and reasoned thinking will be essential to the success of a project or proposal.
If left pages are odd numbered and right pages are even numbered, then the number of torn out pages would be 4, not 5 .
Moreover, traditional books have the right pages as odd numbered, and the left pages as even numbered, not the other way around.
"When in history this riddle is asked" -- you don't know in which year you're living right now?
FYI: Your example of The Book of Kells is, almost certainly, a misordered digital scan. By the placement of the numbers (which are typically on the outer edge if not centered) and the margins (where larger margins will always be on the outer and bottom edges) it's clear from the pages shown that it's meant to be ordered in the usual "odd right, even left" way.
Yes, well spotted! This is a "Digitized by Google" copy, which is available on-line. If we'd look on page 47, there is a wrinkle at the top of the page, which doesn't show up on page 46, but it does show up at the top of page 48 (in mirror-reverse, of course). This shows that the page numbering on the original (physical) copy is "odd/even" per leaf (i.e. even left, odd right), and not "even/odd" per leaf (odd left, even right).
True, but if someone printed it out and stapled it together; I wouldn't hesitate to call it a book; even if the pages are oddly numbered.
@@dtkedtyjrtyj Nothing would stop me from printing it out with _two pages_ or _four pages_ per page (and stapling it together), or collating it in reverse order (so that sheet #2 is "in front of" sheet #1, and reading starts at the physical "rear end" of the book) before stapling it together, or randomly printing some of the pages double-sided and some single-sided, or adding a few pages of my own in between just for the fun of it, or adding in purple ink my own page numbering which starts with 0 and skips any number that contains the digit "1" (so the first consecutive pages would be numbered 0 , 2 , 3 , 4 , 5 , 6 ,7 , 8 , 9 , 20 , 22 , 23 , 24 , 25 , 26 , 27 , 28 , 29 , 30 , 32 , 33 , 34 , ...), or whatever odd fun I can have with page numbers -- and you would still call it a book.
I must be really slow then. Pages tore out - 7/8 99/100 101/102 221/222 223/224
So either 5 pages (pieces of paper), or 10 pages (sides of a page - ie Page 7, Page 8, Page 99, etc)
Very important to differentiate between sheets and pages, even you fell into that trap in the summary!
Exactly
There are yet more complications. Some books have pictures interspersed with the pages of text. Often these pictures may be in color, printed separately from the text, often on special paper, such as glossy. These insertions can invert the even/odd left/right at the point where they are inserted. This could change the answer from 4 to 3 (if picture was after page 8), or 6 (if 2 pictures were present, one before page 7, & another after page 8, but before page 101). Other cases could make the answer range from 3 to 6. A book printed reduced, can have multiple "pages " (numbered panels of text) per physical page. Many copiers have the capability to print such "pages". What is the book were printed in microfiche?
Bottom line: THIS IS A BAD PROBLEM. Virtually any answer can be explained away, from one to the number of pages in the book!
"Interspersed pictures" on "special pages" do not alter the numbering like that... just because you don't see a number doesn't mean it doesn't refer to that page, so you might see something like (- / 1, P / 3, 4 / P, P / P, 8 / - ), but not ( - / 1, P / 2, 3 / P, P / P, 4 / -). Also, I've never seen an instance of a book printed "reduced" as you describe it actually being vendored as a book... not to mention the fact you even tried to pass "microfiche" off as a legit counterexample...
@@erikkonstas
I've seen many books with inserted images that do not affect the numbering of surrounding pages. i.e. you see 3 / P / 4.
Skipping the numbers on pages that have "full page" pictures are actually more common when the pages aren't on special paper. And, yes, this can and often does shift the numbering of the pages.
Yes, and also chapter endings affect pagination.
That's going a little too far. I think making an assumption that the book is not skipping any page numbers or doesn't have multiple page numbers per page is a fair assumption to make.
However, assuming that page 1 starts on the right hand side or knowing if "one page" counts as only 1 side of a sheet or both sides isn't a good assumption. The way the question is worded is unclear.
Add in the option for "This Page Left Intentionally Blank" pages and you're in a real pickle. The question should have distinguished between "Sheet" and "Page."
Such a page would still be numbered...
@@erikkonstas Not necessarily.
@@xnadave So, there's a chance it goes (7, blank, 8) instead of (7, blank, 9)?
My immediate thought was, what's the catch? Any puzzle like this raises suspicions that the obvious answer isn't correct for me. I arrived at the answer 5 leaves which is 10 pages based on the page numbering of most books after thinking about it and before watching your solution. Thanks!
If the list of page numbers is complete, and additional numbers not implicitly included, I think the answer is 3or 6. Otherwise additional page numbers would have been pulled.
There is also the fact that books are not made of individual pages, but booklets of folded sheets bound together. There is the chance pages 100/101 and 222/223 could be the same sheet. To truely answer the question and get one unambiguous answer, you would need a lot more information about the construction of the book.
Oooo i see what you mean. Then it would be just 2 pages!
Many books sold today are perfect bound, i.e. the pages are single, unfolded sheets that are clamped together, glued where the spine should be (e.g. paperbacks, sketchpads, et cetera). Since the question does not inform us about book construction, I doubt they had binding signatures (the booklets) in mind. And it is very easy to rip or cut out a page of a sewn book without removing the other half, as long as you don't cut/tear across the stitches.
@@mikouf9691 I hate modern books made like that. Pages come out so easily, especially if someone mistreats them like breaking the spine to keep the book open, or laying it open page down on a table.
Going with the "two numbered pages per leaf" assumption (no matter which sides are even) leads to the conclusion that the original desciption "tore out pages X,Y,Z" cannot be a complete enumeration, because at least some (altough not all) backside numbers where not included in it.
Therefore i think it's perfectly valid to reach the answer: "The child could have torn out any amount of pages - very clearly only partial information is provided"
The only valid answer is that the child tore six pages and the book had only one single page per leaf.
It's just a badly worded question. Any answer can be considered correct. There are books where when a chapter ends the reverse page is blank and not numbered, therefore, you cannot know if the book uses Odd first, Even first, or if the pages are determined by chapter length. But to further poke holes in the missing information presented in the problem, the question doesn't specify if the boy tore out any more or less pages by number. You could logically come to the conclusion that the answer is still 3 because if the answer were any number higher, the amount of page numbers wouldn't make sense given that again, blank pages with no numbers do appear in books. Since 6 numbers are listed, that means that we could conclude that those were the only pages removed from the book. If we assume the pages are all 2 sided, and we assume they are odd first or even first, then that would also mean assuming the question doesn't say that pages, 6, 9, 99, 102, 221, and 224 because they aren't also a part of any of the previous pages mentioned in the question. So to me, the only logical answer that can't be wrong is 3 pages, otherwise the purposed question doesn't have a real answer because the person asking could change the answer to fit their missing information as they wish.
It would be like if I asked you 'What time is it?', and when you gave the answer I just clarify later by saying 'No I meant: What time is it where I live?' or 'I meant: What time is it when I asked 3 minutes ago?'
Not enough information means no real answer.
On my first reading, I expected both words to mean one side of one sheet. I also pondered about the following: if I tear a sheet out, does it affect another sheet through the binding? If true, there are more cases to distinguish.
I thought a page is one side of the sheet. Don't you mean 5 sheets, for the first case? Which would make 10 pages.
In every interpretation of the riddle this video presents, the riddle is inconsistent/incomplete in the enumeration of the pages. If your coworker presented you with such an enumeration and some sheets are odd first, like with 7/8 and some seem even first as in 100/101, 222/223 you would strongly suspect an error. Why would the riddle list a sheet by both page numbers for 7/8 but not do so for (99/)100 and 101(/102) and just list them as 100 and 101 respectively (and misleadingly consecutive on top of that)?
But if the riddle and enumeration is assumed correct and *complete*, then there is a simple 3 pages solution: 7/8 (odd first) then 100/101 and 222/223 (even first).
After the first sheet with page numbers 7/8 there is simply a one-sided sheet in the book with one page completely empty and unnumbered, so that the numbering switches from odd first to even first for the remainder of the book.
Choose your favorite ambiguity. Either the pages are numbered such that all 6 sheets are separate, or the numbering is inconsistent such that all the pages are paired on 3 sheets, or pages 6, 9, 221, 224 etc are omitted from the problem when they were also removed from the book.
Or even more pages that weren't mentioned were removed too...
I guessed 5 (10 individual page numbers). Because we start on odds. So 7 and 8 share a page, 99 and 100 share a page, 101 and 102 share a page, 221 and 222 share a page and 223 and 224 share a page.
We'll see if I'm even close to right (I'm never right).
10 individual pages instead of 8 in that case
@@mohannad_139 Whoops thanks. I dunno why I have such a hard time counting today. I also wrote 9 at one point.
This is the issue with modern dictionnaries. The word "page" in fact is used to refer to one side of the leaf. Hence "To turn a new page" means to either turn the leaf over and start writing on the virgin side of it or to go to a new page of a new leaf, for it would be a new page either way. As for the expression "to tear out a page", it is only similar to saying "to tear out a leaf" because if you tear out a page you automatically tear out the entire leaf. But "page" still means "page". This is seemingly a simple matter but we have to be attentive to what words really mean as most arguments of the modern age happen because of misunderstandings of what certain words mean.
7 and 8 are opposite sides of the same sheet, but each of the other page numbers are on a different sheet. So five sheets were torn out, containing 10 pages.
3 pages - there is a non numbered picture page sometime after page 8. Also the instructions only mention 6 page numbers so they must be front and back unless they didnt tell us all the pages and in that case any answer is correct as long as its over 3.
It’s impossible for it to be 3 pages no matter if page 1 starts on the right (odd number pages on the right) or page 1 starts on the left (odd number pages on the left).
@omg4life234 This even works with any odd number of unnumbered (skipped) pages between page 8 and 100 and any even number of unnumbered (skipped) pages between page 101 and 222 so that 7, 100 and 222 are on the right side.
All that without the respectively opposite pages that are on the same sheet, which could make it up to 12 leaves or 24 page numbers with up to 6 sheets being ripped out, depending on the configuration of the book.
Generally, non-numbered pages are still numbered, but their page number is just not printed on them.
@@yurenchu Yes, generally, although I have seen unnumbered pages with page numbers skipped, which makes it not impossible
If we use a consistent definition of "page", the answer is either 8 or 10.
So, it could be more than 6. If you count each single number as a page, then you’d also be counting out the pages on the other side. So the standard would end up being 10 pages; 7/8, 99/100, 101/102, 221/222, and 223/224
My first thought was It's 10 pages of content that were ripped from the book. 7/8 99/100 221/222 223/224.
This does not take into account page numbering systems only the actual leaflets assuming that the book has content printed on both sides of all of its pages.
This was a surprising amount of additional information to a seemingly simple riddle. Thanks!
5 pages, if and only if the very first page in the book is labelled page 1. If the book has other pages before 'page 1', we cannot know the answer so long as we dont know how many actual pages of paper came before 'page 1'.
came here for this comment - thank you
It doesn't matter how many pages preceded page 1. The convention is that page number 1 is on a _recto_ page (which in Western books are pages on the right), as are all odd page numbers; and page number 2 is on a _verso_ page (which in Western books are pages on the left), as are all even page numbers. So the torn out pages are 7/8 , 99/100 , 101/102 , 221/222 and 223/224 , which are 5 leaves (or 10 pages).
Or else we could just as well hypothesize that the page numbers weren't given in the decimal system, but rather in some other base (for example: base 9).
@@yurenchu nah bro.
@@theastuteangler LOL, you explicitly wrote "if and only if"; have you actually checked any book that has pages before page "1"?
I interpreted this as the two instances of the word "pages" meaning the same thing - ie, a page is one side of a sheet. The question doesn't ask "how many sheets did he tear out?", it asks "how many pages did he tear out?". I also assumed odd numbers were on the right and even on the left. In this context, pages 7/8 are torn out together, that's 2 pages. When page 100 is torn out, however, that also tears out page 99 that's on the other side of it. Ditto for page 101 (page 102 on the other side is torn out), 222 (221 is also torn out) and 223 (224 is also torn out). So in my case, I got none of these answers in the video, I actually got an answer of 10.
This is the fundamental problem with word problems. They are more often English problems than math problems.
If they are listing all the page numbers torn out then only the bottom answer works. If they are failing to mention page numbers torn out, 4 and 5 pages torn out could work.
99, 102, 221, and 224 were not said to be torn out. 6, and 9 were not said to be torn out. Since they are not listed as missing, the top two answers don't work.
The problem would have one answer if they told us all the page numbers that were removed. And the only solution that fits if all the pages removed are listed in the bottom answer with1 page number per page.
…That’s complete nonsense. Just because I said “I punched John” doesn’t mean I didn’t punch Jimmy too. Cope harder.
@@abcdefghilihgfedcba by that logic, the kid could've torn out 15 pages or 20 or any number equal or greater than 4. Because saying the kid torn pages 7, 8, 100, 101, 222 and 223 doesn't mean the kid didn't also tear out page 16, 28, 40, 73 or 86.
@@alam5055 Sure, but at least the statement "The kid tore out 5 pages/leaves from the book" can be made truthfully, even when it tore out more than 5 pages/leaves out of the book.
In contrast: the statement "The kid tore out 15 pages from the book" for example, cannot be made with certainty of truth.
That's why "5 pages" is a verified answer, and "15 pages" or "20 pages" is not.
@@yurenchu So "5 pages" is an incorrect answer, as that is not verified. Another incorrect answer is "4 pages". That also isn't verified.
The correct answer is "4 or more pages", as that is verified.
@@MrSlothJunior
Even that isn't a verified answer.
If the book has no non-numbered (blank) pages then the child tore out at least 4 sheets[1] with 8 pages on them; if the book has non-numbered (blank) pages[2] then the child tore out between 3 and 6 sheets containing the 6 pages.
That is the verified answer...
[1]4 sheets assumes the odd pages are on the left: eg, the first numbered page occurs on the reverse of the cover, as can quite easily happen with home printing a booklet where the first page (page 1) is printed on the reverse of the front cover.
[2]The onlyvway the child can tear out only the given pages is if the book contains non-numbered blank pages, and thus the given page pairs are either on the two sides of a single sheet, or on a sheet with a non-numbered blank back.
I'm going to concur with others here and say the correct answer is in fact 10. The riddle considers one side of a sheet to be one page, so you should count pages 99, 102, 221 and 224 as well.
I haven't watched the video yet, but I think I can already predict that the answer will not be clear-cut and indisputable. A problem with the problem, as it were, is that we tend to use the word 'page' in at least two distinct senses. On the one hand, we may mean a leaf in a book, but on the other, we may mean just one side of one of those leaves. (There are other senses of the word, but those two are enough to lead to ambiguity.) If, for example, we say 'page 5', we are referring to one side of a specific leaf in a book, magazine, or other publication. Naturally, page 6 must be on the other side of that leaf. Tearing out page 5 will therefore tear out page 6 by default, even though only one 'page', in the sense of 'leaf', has physically been removed. By convention, odd-numbered pages are always on the right-hand side of an opened publication, although there may be a few exceptions around the world. That's why page 6, and not page 4, is automatically removed when page 5 is removed.
However, there is another important detail that should not be overlooked. In most books, magazines, newspapers, and other publications that open and close in a book-like manner, the actual physical sheets cross the binder (or, in the case of most newspapers, cross the crease). So, if page 5 is torn out, then not only is page 6 torn out by default, but also another 'page', in the sense of 'leaf', is loosened elsewhere in the publication. Of course, that other page can also be thought of as two 'pages', in the sense of 'sides of a leaf'. Whether that loosened leaf should be considered torn out is debatable.
In conclusion, I think it's going to be difficult to find two people on the same page (geddit?) with regard to this problem's solution.
BTW, "pages" can loosely mean the sheet as it comes off the printer prior to folding & binding the signatures, which reduces both the odd & even left page solutions to 4 the only difference then is the layout ordering prior to folding. This works for signatures of 8,16 & 32. So far I've not seen larger signatures.
i.e. for a 16 page signature with odd on the right the leaf numbering on a page going left to right, top to bottom as viewing from in front of the printer is: -
FRONT
05,12,09,08
04,13,16,01
REVERSE
07,10,11,06
02,15,14,03
Thanks Presh. Great explanation.
I thought of one other complication that depends upon the number of pages and the method of binding.
There is the possibility that either pages that are part of one pair would also be part of another pair. If, for example the entire book was printed with one biding through the centre, and the book was 230 or 231 or 232 pages long, then page 7 or 8 could also be page 222 or 222.
Or, if done in two bindings, 7 or 8 could be 100 or 101, or, 100 or 101 could be the same as 222 or 223.
I stopped there.
It might even be possible that 100 is the same sheet as 223 and 101 is the same as 222, but I haven’t gone down that rabbit hole.
Each sheet contains two pages. If the pages are odd on the right and even on the left the 7 8 - 99 100 - 101 102 - 221 222 - 233 234 will have been torn out. The answer must be 10,
I'm proud of myself. I went through all of these logical steps in under 30 seconds, arriving at the answer 4 or 5. Though I didn't come up with your justification for the answer 6; I immediately dismissed it as a trap. I suppose that was my own sytem 1 thinking on display.
My brain went into so much overdrive on this one I eventually concluded "The slow solution is impossible." as the child could not have torn out the pages listed without tearing out other numbered pages.
I pulled a book off the shelf and counted.9 pages gone. It was a Japanese map book (a form of atlas, 1cm = 100m) showing the streets of a city. There are two page 7s and two page 8s, the first page 8 is on the back of the second page 7. So if "page" is defined as a leaf attached to the binding of a book, tearing out pages bearing the numbers 7 and 8 requires the removal of three pages/leaves from the book. Continuing in this manner, I get nine pages/leaves.
So the answer to the riddle, is "It depends on the book and how you define your terms."
As usual the way you work out the answer is more important than the answer itself
Pages are enumerated by sides of a sheet of paper rather than by sheets themselves. 1 is printed (or rather, usually implied; most books start actually numbering at 3 or 7) on the right side of the first spread (ie when you open a book, the inside of the cover isn't a page, but the sheet next to it is), so any odd number and the consecutive even number is one sheet of paper (or two pages). 7 and 8 are therefore on the same sheet (two pages so far), 100 is on a different sheet from 101 (so that's four more pages, not two more; we're up to six) and 222 and 223 are likewise on different sheets (and now it's ten _pages_ in all, or five sheets).
Assuming a book that starts numbering from the inside of the cover (because there is no rule saying you CAN'T do this, it just generally isn't done), it's actually 8 pages on 4 sheets that are torn out. And lastly, I've never seen this before and it seems like an odd idea, but if pages were numbered per sheet (as in the front and back of a sheet were considered one page and "sheet" and "page" were considered synonymous) it would obviously just be 6 pages.
And of course a book can start on the right and proceed to the left like a Japanese comic book, but this does not affect numbering; It will still follow one of those three conventions.
An important question to consider: What do we exactly mean by the term "pages" here?
If we apply an ultra slow thinking and take the description literally and complete the pages has to be single numbered and not double sided since any other case would be inaccurate in the description of what page numbers was torn out as it would have to omit page numbers that must have been torn out together with its listed backside number.
I.e. in the case of the 5 pages answer the pages 99 and 102 would have to be omitted as being torn out together with 100 and 101, despite the fact that they in such case must have been torn out as well.
Then again, this assumes that the description implies that the listed page numbers were the only ones torn out. Since the description does not actually explicitly state that these were the only pages torn out, but just that they were in the set of pages torn out, we could argue that the description does not give enough information to answer the question in any definitive way.
Leaving out the case of single paged sheets (which feels very rare to me) the problem would be better if the question added, for example, that pages 53 and 54 have also been torn, since then the answer would be the same whether you consider evens right or evens left
Five. Most books have the odd page on the right so 7/8, 99/100, 101/102, 221/222, and 223/224.
There are also books with counted, single-sided, illustrated, "plate" pages. Around each of these, page numbering can switch sides.
5 sheets or 10 pages
So does that make this riddle with 2 correct answers?
I think it really makes it a poorly-worded riddle.
Shouldn't it be 10 pages? I know he ripped off 5 sheets, but those 5 sheets contain 1 page per sheet. So the kid tore out pages 7, 8, 99, 100, 101, 102, 221, 222, 223 and 224.
Yes, I'm with you. But as Presh noted near the end of the video, we intuitively consider that "pages" in the context of the second use of the word means the same as sheets....
@@Mesa_Mikewouldn’t call it intuitive if the first use of the word had a totally different meaning… the real intuitive answer would be 6 pages, because it asks how many pages the child tore out and it lists 6 pages the child tore out
Don't make it more complex 😖 or else I'm the child who will just rip up and burn the book to tell whomever saw me playing with the book and wondering where all the pages went. I'll say, "I dunno!" (I do know but act like I don't know)! 😂
Yes. The wording of the original problem seems to imply the definition of pages as the single side of a sheet.
@Mesa_Mike The answer, if given a modern book with standard pagination, is 5 sheets and 10 pages of the book. You cannot tear out page 7 without tearing out page 8, etc. Will another sheet fall out, given the size of the book and the nature of the binding? Maybe, though not necessarily. But in any event the child did not tear those out.
The puzzle ultimately combines the knowledge of page numbering in books, linguistics and maths. There would be, considering the linguistics, at least one more answer, which would again depend on the page numbering (which can be skipped in some ways of numbering - a blank page, or an illustration). If you tear out page 7 or 100 (depending on the numbering), and it so happens to be the way, that there is page 6 or 99 on the same sheet/page*, then you technically tear out that many more pages'. So if you don't know the proper terminology/linguistics at play in a specific scenario, the answer would be "anything between 3 and 12".
If we only refer to the text, it’s impossible to pull out page 7 without also pulling out page 8 in most boxes. However there’s a problem in that if we have the regular odd number on the right and numbering on both sides, the child pulled out more pages under the first definition used and stated in the problem.
If the problem had stated the child only pulled out those pages, then it follows that there’s only numbering on one side and the child pulled out six sheets.
depends on your definition of "page" and - assuming it's something like "a sheet of paper with an indexical integer on both faces, sometimes referred to as a 'leaf'" - whether pages labeled with odd integers are on the reader's right or left with the book open
so either 6, 5 or 4
NOTICE: I haven't watched the whole video yet.
I arrived to the answer "10 pages" by the following pattern:
Each even number, due to the numbering system of most books, is the back of the leaf. Using this, just notice 7 and 8 are on the same leaf, so, that would be just one leaf. Multiplying 2 by 50, we get that 100 is the back of a leaf, but 101 is a front of a leaf. So this would be 2 leaves more. Now doing the same with 111, we get same the same result: 2 leaves more, for a total of 5. 5 leaves = 10 pages.
We could state that we get 2 pages tore out if in the sequence, on ascendent order, we get firstly an even number, and then, an odd number. We could say that we get 4 pages tore out if viceversa.
This was a fun riddle.
Even after you explained it, I still feel like there's something off about every answer besides having the 6 pages be one page per leaf, though. The problem is that if the odd numbers are on the left side, then they failed to account for Page 6 and Page 9 in the original problem... the child can't have torn out "just" page 7 and page 8 without tearing out page 6 and 9 in a configuration where the odd numbers are on the left side of the book. Therefore, if that were the situation, they would have given us incomplete information and no way to arrive at the correct answer. Same applies if they're on the right side. In that case, 7 and 8 could be a single sheet, but now 221 is unaccounted for (because tearing out 222 removes 221 also), and 224 is also unaccounted for (because removing 223 means 224 is gone as well). So the only configuration that allows the original sentence to be accurate, is one where the pages are only printed on one side. Otherwise, they've omitted vital information about what pages are actually missing from the book, that might have allowed us to infer the structure of the book and whether it's one page per leaf, odd numbers on the right, or odd numbers on the left... that is to say, if they had included either 5 and 6, or 221 and 224 in the list given, then and only then could we assume the book ISN'T one page per leaf. There's literally no other way it could work if we assume we're given complete information, unless of course they basically admit they were lying through omission about precisely which missing pages were missing just to mess with us. Based on the information given, the only answer I think we could count as "wrong" is 3.
There's an answer you don't cover. That is, your page 100 would also be tearing out page 99 (the previous page printed on the other side of the "sheet"). The same logic applies to 101 having 102 on its other side, 222 having 221 on its other side and 223 having 224 on its other side. This logic makes a total of 10 pages. In fact, it's probably closer to the most accurate solution because you can't tear out page 7 and then tear out page 8 because they are one and the same but the question treats 7 & 8 as separate pages and so the 10 page solution I'm mentioning is as viable as any in your video.
But that IS his answer - 5 sheets a.k.a 10 pages. Look at the 3:00 mark.
@@froreyfire Wrong. The question doesn't mention the word "sheets" at all. The ambiguity is with the word "pages" but if someone asks you to look at page "x", you look at one side of a 2-sided piece of paper. So there are 2 pages inseparably connected. The proper answer must be 10.
@@TheDradge Sure, I concur with you that the correct answer is "10 pages". But when Presh says, I quote, "so in total there are 5 sheets torn out of the book", then by common knowledge that is the same as 10 pages. Yes, I would prefer to say 10 pages, but 5 sheets is just equivalent.
@@froreyfire I know what you mean and agree with you if we're talking "sheets" but the terminology is really part of the comprehension of the question and solving the riddle. It's so easy to think "sheets" but the question explicitly uses "pages" in the plural. The numbering is crucial to understanding the solution as some torn pages are unconnected (but will result in tearing out another unmentioned page) or the pages in the question are one and the same (7 & 8 for example - assuming standard numbering with page 7 on the right and 8 the next, left-facing page). Good puzzle though.
@@TheDradge You went from "just as viable" (I agree) to "the proper answer must be" (hmm)
Presh already showed that the terminology is ambiguous. There can't be a proper answer that revolves around ambiguous phrasing.
Not to mention now you're discarding books that have even numbers on the right side.
What about a abnormal numbering system where some pages are not marked (stickers) or where there are I,II,III… in the front of the book. For example 100 page could be connected to a sticker page and not numbered and then 101 page being connected to the other side of the sticker page. 100-sticker-sticker-101.
I'm not sure what you're talking about. But as far as I'm aware, "sticker" pages are either part of the page numbering (they just don't have their page number printed on them), or they aren't part of the page numbering, but then _both sides_ aren't numbered so their presence doesn't actually affect the answer to this riddle.
In conventional page numbering, the pages that are removed by the child would be pages 7/8 , 99/100 , 101/102 , 221/222 , and 223/224 . Presence of "Roman numerals numbered" pages in the front, or unnumbered "sticker" pages, wouldn't affect this answer.
And that's how lawmakers justify crimes against humanity
depending on how the book is printed, 4 or 5 sheets of paper
6/7, 8/9, 100/101, 222/223 = 4 sheets --> 8 pages
7/8, 99/100, 101/102, 221/222, 223/224 = 5 sheets of paper --> 10 pages
I thought about this carefully and I did take into account the distinction between "pages" and "leaves"
There are two parts to the question and the word used in both is "pages"
The words "a page" "a leaf" and "leaves" are not used anywhere, so the correct answer is 6.
Sometimes, the most obvious answer is the correct answer.
I answered 8 or 10 at first
My intuition for 'pages' is front or back
The same word should mean the same thing throughout the same question
Cannot understand the so-called 'intuition' and never heard of books with page numbers on one side only
Giving the riddle a go, I assume 10 pages. This isn't because he simply pulled out 6 pieces of paper from the book, but we have to remember the pages are double sided, thus making each paper he pulled out 2 pages. If we start from page 1, we see that there's a pattern of the right page in a spread being odd, which then goes to the next even number.
So by pulling 7, we also pulled out 8 at the same time; with 100, he would have also pulled out 99; with 101, he pulled 102; 222,221; and finally 223 came along with 224.
So counting those we can see he pulled 10 pages by tearing out 5 pieces of paper.
And let's see how I did...
Close, but it seems the narrator only thought of pieces of paper, and not the actual printed pages.
He switched definitions when "solving" the riddle. The most common definition by far is "one side of a leaf in a book, magazine oe newspaper, or the material printed on such a side." The next mosr common refers to the actual sheet considered by itself, as in adding a page to a book, but even that one is hazy because it's impossible in most cases to add a page to a book without adding an entire leaf.
Books are almost always printed with two sides for each page, and with pages stitched so it's actually 4 printed sides per sheet. Also, there's no set standard for where page 1 will actually be, since there might be title pages, crediting pages, bio pages, chapter heading pages.... so all we know is that pages 7 and 8 MIGHT be two sides of the same half-sheet, or might be adjacent, and thus tearing them out would also remove pages 6 and 9 as a side effect. Same goes for the other pairs. You'd think you might be OK figuring out that the first pair starts with an odd number and the other two start with even numbers.... but again, there can be unnumbered pages like chapter headings, or full page illustrations.
My preliminary guess at it: If it's a typical book with double sided pages, and odd numbers starting each page, that'd be five pages required to remove those six page numbers, along with a couple more page numbers of collateral damage, making ten page numbers over five pages.
Oops, I misread, editing... I'm not sure how I mixed up and thought the middle couple of numbers were opposite sides of a sheet, but I did that, initially. Edit to add, I'm a minute in now, and haven't reached the answer yet, but I guess it may be a fast/slow conflict sort of thing, that lead to that. I don't know. Over three minutes in, and I gotta admit, I did not see that coming, I totally didn't consider the Book of Kells at all! About five minutes in, and I'm wondering if we should consider a case with the meanings flipped around. The kid may've torn out the 7th, 8th, 100th, 101st, 222nd, and 223rd leaves of the book, taking twelve page numbers out of it? I feel like I'm even less sure than I was a minute in, and should consider every odd possibility.
I was gonna say 10 for a while, or maybe 5 if we sneakily changed the definition of page across sentences. After all, you can't tear out page 7 without tearing out page 8, and similarly, can't tear out page 100 without tearing out page 99. But no. No no no. That is all wrong! Here is my ULTIMATE COSMIC BRAIN level answer!
6 pages were torn out. Why? Remove the "Sealed for your protection" seal from say, a jar of peanutbutter. Very often, you will succeed in tearing off the top face of the "leaf", while the bottom face remains perfectly in tact. Thus, it is indeed possible, though difficult I know, to tear off page 100 from a single leaf, while leaving page 99 in place. Therefore, the child has indeed torn out exactly and only the pages listed: 7, 8, 100, 101, 222, and 223. Six pages.
[edit a bit later]
Actually, might the answer even be 20? The way some books are made, the sheets contain 4 pages each: a front and back side like what page 7 and 8 appear on, but also a left and right side, with a bend in the middle where the spine of the book goes. Though depending on how many pages are in the book, the right side's front and back pages might be on the same sheet as the one that contains pages 7 and 8... but otherwise, at a glance, there might have been 20 pages torn out, depending on how you think about it.
Assuming that facing pages are odd, and backing pages are even (sometimes numbering is dependent on blank or introductory pages),
pages 7 & 8 requires ripping out a single page, 100, 101, 222, & 223 require two pages each, so I would think the correct answer is 5 sheets.
(four, if facing pages are even)
The problem with the premise of this puzzle.. is that unless we assume that the child tore out more "pages" than are actually listed... you have to assume that the second word pages has to apply the same way as the first. IE page 100, 101, 222, and 223 have back pages attached to them.. and those are not mentioned. I would be forced to assume the pages have no backside.. therefore the answer should be 6
Exactly. If you assume that it's possible for the child to have actually torn out more pages than are listed, then the question becomes truly unanswerable. If you say that tearing out page 222 could have also torn out page 221, but that it somehow didn't make the list of pages in the first sentence of the problem, then page 138 could just have easily been torn out and not made the list. ALL the pages may (or may not) have been torn out, and yet only this partial list was provided to us.
it’s 4, 5, or 6 depending on page structure and definition. if a page is a sheet and even numbers are grouped to the number above them, it’s 4 because it’s sheets 6+7, 8+9, 100+101, and 222+223. if a page is a sheet and even numbers are grouped to the number below them, it’s 5 because it’s sheets 7+8, 99+100, 101+102, 221+222, and 223+224. if a page is the individual side of the sheet, then it’s pages 7, 8, 100, 101, 222, and 223, also how did that kid perfectly split that/those sheet(s) in half
The first part of the question explicitly refers to NUMBERED pages - which defines a page as a single leaf of the book for the purposes of the so-called "riddle". In the absence of any statement to the contrary there is no reason to assume that the a different usage of the word "page" should be applied to the question itself.
It is crucial that any problem should be presented in a clear and self consistent manner. If there is a potential source of misunderstanding then the problem should be rephrased accordingly. In this case simply by asking how many "leaves" or "sheets" had been torn out.
I raised 5 kids. My assumption was that if a boy enjoyed ripping out pages, he's going to keep going. Yes, he ripped out the pages mentioned, and maybe 700 more. The riddle does not specifically state that those were the only pages the boy ripped out. Media uses this same trick by sharing certain facts that support a particular narrative while ignoring other facts that don't, knowing full well the public will assume that the facts provided are the only relevant facts.
What they tell you, and the more relevant, bigger, and much more important things they don't!
And here I went the extra bit and assumed that this might not be the only time the child played with this book and could have torn out other pages in previous paly sessions of the book.
A single piece of paper in a book has 4 pages on it. You can't physically remove a single page without effecting at least 1 other. 7/8, 99/100, 101/102, 221/222, and 223/224 all could have an other pair of pages that they are connected to that may also fall out.
The answer is between 4 and 12 depending on how the book was constructed and the number of pages in the book.
Presuming that this book is printed with Page 1 as the facing page, then the child would have to tear out 5 sheets (or pages):
7 and 8 are on the opposite sides of one sheet
100 has 99 on the opposite side of its sheet
101 has 102 on its opposite side
222 has 221 on its opposite side
223 has 224 as its opposite side
There are 10 pages of text missing out of this book as a result.
So you could either interpret the answer as 5 or 10, depending on how you wish to interpret the word "pages" in the stated puzzle.
If we assume odd-even share a leaf, tearing out 7 inadvertently takes 8 with it, so you can't say you tore out 7 then tore out 8, so you would have to say you tore out 7 and 8 if you include both. Given that, why then mention you only tore out 100 which would also tear out 99? It's a logical incongruity to suggest you tore out 7 and 8, then tore out 100 (including 99), then tore out 101 (including 102), etc. Logical consistency would require the language to be equivalent, so if you tore out 7 and 8, you can say you tore out 100 and 101. This notion essentially refutes the assumption that the book has only numbered pages with odd-even or even-odd on each leaf without it switching at some point. So, it would stand to reason that either pairs of page numbers were removed which would require the assumption of unnumbered pages existing to shift the pairings, giving 3 as the answer, or individual page numbers were removed and there were no pairs within the numbers mentioned, giving 6 as the answer.
It would be more logical to suggest 6 as the correct answer, followed by 3 if we accept the premise that there are unnumbered pages within the numbered pages; however, it's not at all reasonable to suggest 4 or 5 as the answer unless we assume that one or two of the numbers couldn't be torn out because they were already torn out when tearing out another number, which I feel is less sound logical reasoning.
There is also possiblity that both "pages" are referring to same thing means "how many sides have been torn off"
That really depends on the page order of the book.
If the book, when open, has page order [ODD] | [EVEN], then the child tore out 6 sheets.
But if the order is [EVEN] | [ODD], then only 3 sheets were torn out.
I remember I solved this on a poll question of yours and I got it correct
It feels like the asker of the question deliberately left certain numbers out; you can't have a book with a page that has 7/8 on it, and also have pages that have 100/101 and 222/223 on them.
Let's stick with the average book, odd on ledt even on right: Unless you can somehow separate the opposite sides, you can't take JUST those 6 pages. So the question is just faulty.
(This is likely why I don't do well in job interviews.)
5, 4, or 6.
5: the book's pages are numbered "even/odd", so 7/8 is just one page, but 100/101 is two and 222/223 is also two. Page = physical piece of paper
4: the book's pages are numbered "odd/even", so 7/8 is two pages, but 100/101 and 222/223 are one each. Page = physical piece of paper
6: Page = the unit by which books are measured. Each piece of paper contains two.
(+ I'm not very knowledgeable in bookbinding, but it can probably get wilder if you consider the actual construction of books which can include "double length" pieces of paper folded and bound in « cahiers »)
Has it been considered that if the book was bound as a booklet (effectively, folded sheets with 4 half-sheet pages each), and that 7/8 and 222/223 occurred, then that could affect the overall count as well? The child could remove as few as 3 sheets to remove the pages mentioned!
Well, the question states that the child tore out exactly these 6 pages, i.e. 3 sheets. If they hadn't been on the same sheets, other pages would have to be torn out as well. The question must be, what kind of book this is. It could be a book with at least two parts, where parts are numbered individually (I have seen this in the real world with Bibles which start with page 1 both in the Old Testament and the New Testament).
However, the first part with pages 7 and 8 starts on a right hand side page (so it has odd numbers on the right), and the part with the other pages starts on a left hand side page (so it has odd numbers on the left). (I haven't seen that in the real world, but it may well exist.)
I immediately thought of how books are bound. In the simple case of a few sheets folded into a pamphlet and stapled together, tearing out the first page causes the last page to also come out. (Like when you tear a page from a lined exercise book at school to use the paper for something else)
Printed books are bound differently, and there are probably many methods of book binding.
My first answer was 10 pages across 5 papers (using the typical book of odd numbers on the right), the question set the standard that page meant numbered page.
Every leaf contain 2 pages, and it is usually starts with odd number. In this case, only 7 and 8 are in the same single leaf. So it would be like this :
7/8, 99/100, 101/102, 221/222, 223/224.
There are total 10 pages teared out.
Great Video. This one I got completely before the solution.
The question is written in English, and gives a list of six items it calls pages. This tells us that the items (pages) are individual, torn out individually and separately (the commas indicate that, otherwise slashes would have been appropriate). Thus the hypothesis that a leaf consists of two pages, one odd one even, is wrong, and a page is a leaf. "How many pages did the child tear out" is not the same as "How many leaves did the child tear out", unless a page means a leaf, and this confirms that 1 page = 1 leaf. Therefore the answer is 6.
5:18 You seem to be implying equivocation. Are you suggesting this was intentional?
There are so many assumptions one could make that there are many possible answers, each correct in their domain of discourse.
Most books use odd/even on the same sheet, and when you rip a sheet from one side of the book another one gets loose so you rip sheets by pairs (and pages by quads) so he rips up to 20 pages.
The other loose page doesn't necessarily come _out_ , so it doesn't necessarily mean that tearing out page 7/8 also means tearing out the other page. Moreover, the other page that comes loose may actually be page 101/102 or 221/222 .
Get the boy an e-book in future to pre-empt his naughty conduct of tearing up pages!
Here's the problem with that question: I needed to know YOUR definition of "page." When said "leaf" I saw that each page was on each "side" of the "leaf" which meant I needed to account for the ("n+1" n=odd number) part of the riddle,, The odd number begins the first side of the leaf, then "n+1" means the next number would be on each leaf. When the leaf began with an "even" number, then the "next leaf" would be involved, but ONLY after you introduced the word "leaf": 2 pages, starting with "n" being odd and the next page on the leaf being "n+1."
If a book was to have 100 pages, and you were to rip out 50 pages, you would tear half the book.
But tearing out half the book is only 25 sheets. So the child would tear out 10 pages, which is 5 sheets
It's kinda funny how I went through these steps one by one in 30 seconds when I saw the thumbnail.
I'm proud that I figured this one by myself 😁
I can also justify the 3 pages as it started with odd numbers on the right and even numbers on the left, and part way through the book there's an intermission or sorts with a blank unnumbered page, and it flips to be even numbers on the right and odd numbers on the left. i can't actually think of a time this has occurred, but technically possible.
Great, but there is another issue... pages of a book may have a specular page attached to it depending to the binding... this implies that in this case the final number should be multiplied by 2 (depending on the total number of pages...)
A what...?
... or page 101/102 or 221/222 is actually the other page, attached to page 7/8 . Or maybe the other loose page didn't physically come _out_ , and hence doesn't qualify as having been "torn out" from the book by the child.
I originally said 12, because even if page 7 and 8 are on the same page, they are considered separate pages. This being said, I never even realized that they were torn out 1 apart for each 2 pages, so really it could be 8 or 10 pages as well if you think of it that way. The reason I like this better is because if you were to observe the book after the pages had been ripped out, you would notice that there is a gap between page 6 and page 9, and you wouldn't say, "one page is missing there." Rather, it makes more logical sense to say that there are 2 pages missing, 7 and 8. (This alters with the whole even/odd or odd/even numbers)
Edit: Now that I have finished the video, I see what he means about this being a good interview question. My way makes sense in theory, but then I was reminded that the question was how many pages the child TORE out, not how many pages are missing. Very interesting.
In a modern book, you cannot tear out page 100 without tearing out page 99, 101 without 102, etc., but 7 and 8 are torn out together. Five tears of double-sided sheets, 10 pages of the book. Bringing in archaic or photography books is just silly.
@@l.w.paradis2108but what about the sheets connected to the sheets torn out through the binding? Depending on the nature of the tearing more pages could have been removed.
@Aerxis We are looking at what is necessarily the case. You're right about what's possible.
The correct answer is that, if there is a single, objectively correct answer to the question as phrased, it must be 6, but that the question is too ambiguously phrased to know whether that is the case (such that the answer could - in strictly logical terms - range between anything from 4 leaves containing 8 different page numbers, to infinity leaves containing double that infinity number of page numbers). The key point of ambuguity is that it is unlear whether or not the child tore out numbered pages 7, 8, 100, 101, 222 and 223 alone, or whether the child tore out pages including those numbered pages.
If the child tore out those numbered pages alone, then (assuming the book's page numbering is consistent) she or he must have torn out exactly 6 pages as tearing out odd or even numbered pages without also consistently tearing out the immediately preceding/following page number in each case reveals that the leaves of the book are not numbered on both sides.
By contrast, as the video points out, there could be a scenario where the leaves of the book are numbered on both sides. But in that case (assuming again that the page numering is consistent throughout the book) the child cannot have only torn out pages numbered 7, 8, 100, 101, 222 and 223, but must also have torn out pages with other numbers too: a mininum of 4 leaves containing the 8 page numbers 6, 7, 8, 9, 100, 101, 222 and 223 if the pages on the right hand side of the open book have even numbers; and a minimum of 5 leaves containing the 10 page numbers 7, 8, 99, 100, 101, 102, 221, 222, 223 amd 224 if the pages on the right hand side of the open book have odd numbers. But for either of these scenarios to be the correct answer, we have to allow that when the question says the child "tore out the pages 7, 8, 100, 101, 222 and 223" it actually means that the child tore out pages that included those page numbers but also tore out pages with other numbers. Since the question poses no upper limit and gives no information that allows an upper limit to be definitively identified, the correct answer (if it is not 6) could be anything from 4 to infinity.
An equivalent would be the question, "at lunchtime, a child ate a sausage. How many things did the child eat at that lunchtime?" If the question is capable of having a single, objectively correct answer, that answer must be 1: the child ate 1 sausage and 1 sausage only. But the question is too ambiguously worded to know for sure if the question is only capable of a single, objectively correct answer based on the information provided. If one interprets the first sentence of the question as meaning that the child ate a sausage at lunchtime but that that was not necessarily the only thing the child ate at lunchtime, then one must allow that the child may have eaten more than a sauaage - and in the absence of further information one must also concede that on this premise, as a matter of logic, the child could have eaten an infinitely large number of things in addition to one sausage.
So the correct answer to the question is, if there is a single, objectively correct answer that is capable of being identified from the information provided, it is 6 leaves of the book containing 6 numbered pages. Otherwise, the answer could be anything from 4 leaves of the book containing 8 numbered pages, to infinity leaves of the book.
Here's an idea: take out a modern book and look at it: If you tear out page 7, you have by that very act torn out page 8. Now, can you tear out page 100 without thereby tearing out page 99? No. Similarly:101 and 102; 221 and 222; 223 and 224. _Now, when the next reader picks it up, how many PAGES are missing?_
Nine. Nine pages he can't read because they are missing. I guess one could call it an engineering approach.
Could be two possible scenarios (solutions). Some books starts to count pages from left book side (physical page 1), some books from the right (physical page 2). So we have scenario 1:
Page 7 shares same sheet with page 6
Page 8 shares same sheet with page 9
Page 100 and 101 shares same sheet as well as
Page 222 and 223 shares same sheet.
In this scenario child tore out 4 sheets
Scenario 2:
Page 7 and 8 share the same sheet
Page 100 shares same sheet with page 99
Page 101 shares same sheet with page 102
Page 222 shares same sheet with page 221
Page 223 shares same sheet with page 224
In this scenario child tore out 5 sheets
Presh, there’s another answer, which could have been the intent of the puzzle. If the book in question was numbered with only one page number per page as in leaf (not two, either on the right or it’s obverse, the left) then the puzzle could be interpreted as follows, if transmitted VERBALLY and understood by students as follows: “Seven, eight, one-hundred, one-hundred-one TO twenty-two, and two hundred twenty-three”. In this case and specific reading would interpret “101, 222” as the RANGE “101-22”. It is a riddle after all, one permutation of the confusions caused by all riddles would allow this answer if the riddle was HEARD instead of READ. The correct answer in this case would be 26.
there are also books that have pictures occupying a single page - not numbered in the middle of a book which allows for a SWITCH, So:
correctly applying system 2: all we can say for certain is that the answer is between 3 and 6 - inclusive assuming we interpret the second meaning of pages as 'sheets', and as other have pointed out its up to 10 if we continue to interpret it as pages...
You can also get the answer 10 or 8 if your definition of a page being one side of a sheet. Since 1 sheet has 2 pages you can also answer 2 times the number of sheets pulled out
As a non native English speaker I did not at all think of the 2 meanings of page, and was about to comment that it is either 6, 8 or 10 pages torn in total