Ok, a nice simple one today….

Linda is the CEO of a big company. One day she walked out of her modestly sized boardroom and said to her secretary, ‘Here is a report about the company accounts for last year. I would like you to make a copy of this report for all of the board members, plus one copy for me and one copy for my mother’. Linda’s secretary, John, jumped up and ran to the photocopier. He returned exactly 11 minutes later, after photocopying 169 sheets of paper. How many board members are there?

As ever, please do NOT post your answers, but do say if you think you have solved the puzzle and how long it took. Solution on Monday.

I have produced an ebook containing 101 of the previous Friday Puzzles! It is called PUZZLED and is available for theKindle (UK here and USA here) and on the iBookstore (UK here in the USA here). You can try 101 of the puzzles for free here.

92 comments

  1. OK took a minute to get an answer but another couple of minutes to double check it was the only solution. I think the wording of the question is slightly confusing (but it may be that is deliberate)

  2. It took me three hours, I averaged out the size of company accounts reports and printer page capacity -I did assume that the photocopier was in the same floor for simpllicity 🍰

    1. You forgot to take into account the weight of the paper, its size, the smoothness of the surface, and its brilliance. You also forget to have a good look at the type of toner the copy machine was using and the amount of ozone it releases in the atmosphere.

      giggle

    2. There’s no need to estimate the size of company accounts – there were 169 pieces of paper to be copied. Almost certainly double sided, 11 minutes for the job…you just need the speed of the machine.

  3. I can’t tell.
    The secretary photocopied 169 sheets of paper, implying that the report about the company’s accounts is 169 pages long (or maybe 377 or 378), but the question doesn’t say how many copies were made.
    Perhaps I’m too square to answer this.

    1. “implying that the report about the company’s accounts is 169 pages long”

      In no way is this implied, you can disregard that.

      “the question doesn’t say how many copies were made”

      That’s why it’s a puzzle 🙂

    2. No, he’s right. It says that 169 sheets of paper were copied, and not that 169 copies were made. That is, it implies that the original report is 169 pages long.

      Where X is the length of the report and Y is the number of copies made, you’re meant to interpret it as X*Y = 169, but as worded it says that X = 169, Y = ?.

  4. It took me 3.52 seconds, I asked my ma to time it for me.

    Her thumbs are quite fat so I’m not sure of the accuracy down to the one hundredth?

  5. Isn’t there an element of confusion in the wording about “every member of the board” and me – surely she is also a member of the board – so do you want her to have two copies?
    Also, most p.a.s would use the original as one copy to save paper!

  6. Am I the only one worried that the CEO of a company is leaking sensitive infomation to her mother? Surly this could give her an advantage in trading the company stocks?

    1. The mother is not a member of the board though. If she was, Linda would have only said “make a copy for each member of the board, and one for me.” Also from the question, we must assume Linda is not a member of the board.

  7. I’m sure I’ve got it. The wording doesn’t fill me with confidence though, especially when the first sentence is “Linda is the CEO is a big company.” BTW for posterity the first sentence does say “Linda is the CEO is a big company.” in case of a future html edit.

  8. something is missing from the puzzle otherwise the answer is three.

    “a copy of this report for all of the board members (that’s ONE), plus one copy for me (that’s TWO) and one copy for my mother (that’s THREE)”

    it means some pages must be spoilt. i have bad photocoper like that too.

    1. Then the answer wouldn’t be three, it would be ‘unknowable’. The question wasn’t how many copies were made, but how many board members there are.

    2. That’s a very good point. When given a problem like this, one has to assume that all information necessary to solve the problem is explicitly and/or implicitly included in the wording of the problem.

  9. There seem to be two valid answers, one of which would, admittedly, involve an extraordinarily large board.

    1. Or extraordinarily small board members! I’m now confident I got it straight away, but was led astray by some of the other comments.

  10. Dharmaruci definitely has a point. The wording implies 3 copies, though that is clearly not the answer looked for. Either I am too square to get the twist, or this was really easy.

    1. If only one copy was made for all board members, then the question would be unanswerable and not easy at all. How would you know the number of board members if they all shared one copy?

  11. I found a mathematical answer in a few minutes (yeah, I suck at math, I know), but I may be wrong as I get a feeling the wording may be a trick (he photocopied 169 sheets of paper technically =/= he made 169 photocopies).

  12. I think a lot of people are misreading the problem. A total of 169 sheets of copy were produced. The 11 mins info is irrelevant. Only the 169 figure is important and makes the problem very easy to solve. Took me about 10 seconds to do the trivial arithmetic.

    1. Giving clues isn’t really in the spirit of the puzzle, I think. Also, not everyone is good with numbers — what took you 10 seconds took me a good few minutes to work out.

    2. I think clues are valid when i) there is perceived to be ambiguity in the question; and ii) when the clue is not misleading. Niva’s comment fulfilled both of those criteria for me.

      Then, admittedly, she ruined it all by crowing about how she found it trivial.

  13. Am I the only one to think that we are the subject of a big experiment by Mr Wiseman? Why else does he keep setting brainteasers with massive ambiguities? He’s probably poring over our replies and laughing maniacally to himself!

    Ps I assumed 169 pieces of paper came out of the copier! Happy now?

  14. I have 2 answers. I don’t think the question is worded very well. It should specify something about multiple pages.

    1. The implied answer is obvious, but the wording is ambiguous. Modestly sized just means not too big. However is that not too big for a small number of people or not too big for a large number of people?

      The implied answer can be worked out with logic. For there to be only one unique answer then the relationship between the number of copies and the number of sheets per copy must be…
      Basic maths helps too though!

    2. Dave
      Does that mean that the answer might be different if the question said “large board room” or different again if it said “tiny board” room?
      I’m struggling with this one so a little help (not a spoiler obviously) would be useful.
      Yours in perplexion (or is it perplexity?)
      SG

  15. PS to Anna Berber – totally agree with your comments – thank you! Some days my brain fades to black as I read the puzzle and I don’t even try, I know I “should” but, hey, I’m really here to have some fun…

  16. I agree that the question is very ambiguous. I would normally understand “photocopying 169 sheets of paper” to mean that there were 169 sheets in the original report, but if that is the case then there isn’t enough information to answer the question. I don’t see how the time can be relevant without knowing the speed of the copier and the time taken for John to run there and back, either. And then there’s ambiguity in the way she requests the copies. I just can’t see how there’s enough information to answer the question.

  17. “photocopying 169 sheets of paper” – is this a british term for “made 169 photocopies”?

    also, while possibly giving away the answer, it’s worth noting that the problem does not specify what happens to the original.

  18. If the report had 169 pages, and John had to make more than one copy, then it would be a very impressive copying machine if the whole thing could be done in 11 minutes, including the time it takes to get to and from the machine. If there is just one board member, it is 507 copies in 660 seconds less the “travel time”, which is pretty unrealistic. It’s about one second per sheet.

    So I think from a purely practical point of view, “photocopying 169 sheets” has to be read as “making 169 copies”

  19. I cannot answer this one! How many sheets of paper are there in a report about the company accounts of a big company? Surely not just the one? And yes I can divide 169 sheets by 11 minutes but that is not an answer to the question asked!

    1. If you bear in mind that the report everyone is given must have the same number of pages, it should become easier.

  20. Thinking as secretary process… if the report has 1 sheet, one is original, (no counts), and one of copies is for the mother…we have the solution…but the 11 minuts? is a confusing information for solve puzzle or not? but the other way, we don’t know how many sheets has a report, then is impossible solve it? .. :S

  21. I assume that the report has more than a sinlge page.. hehehe
    Resulting in the Question if teh CEo is part of the board or not– I guess only a few people in the board for such a big company—

  22. If if understand the intention of the puzzle, I think it could use some rewording. I think that there are two words that could be changed clarify what the puzzle is intending to state:

    “Linda is the CEO of a big company. One day she walked out of her modestly sized boardroom and said to her secretary, ‘Here is a report about the company accounts for last year. I would like you to make a copy of this report for EACH of the board members, plus one copy for me and one copy for my mother’. Linda’s secretary, John, jumped up and ran to the photocopier. He returned exactly 11 minutes later, after PRODUCING 169 sheets of paper. How many board members are there?”

    Does anyone disagree with me here?

    1. I disagree. EACH rewords the puzzle – makes it a different puzzle. ALL implies the board members are going to share it, if there is more than one. PRODUCING also makes a different puzzle than PHOTOCOPING. Richard isn’t that careless. He;s given a misdirection somewhere.
      And no, I don’t see the answer, if it is more than one. A “large company” would imply more than one.
      Can’t wait ’til Monday!
      BillWhite36

    2. I agree with you Karl. I think your suggestion is what Richard meant to ask.

      Bill – I don’t agree with your contention that Richard isn’t “that careless”. In the past he has not posted an answer to a question and also posted an incorrect answer and later corrected it.
      I do agree that Richard gives misdirection however.

      My guess, however, is that Richard has a life and doesn’t spend as much time on the Friday puzzle as some of us do.

    3. Not only has Richard been that careless with puzzles before, he has been that careless with answers to the puzzles before and had to post corrected answers to puzzles when his errors were pointed out. Frankly, that makes the puzzles even more fun in a way.

  23. I had to re-read it carefully. No where does it say that it’s a multi-page report. It might be a single page report in which case there are 167 board members. But I don’t think that’s the answer you’re looking for.

  24. I got the answer instantly.
    God told me what it was – although he did also volunteer that the question was very sloppily worded.

  25. Not enough information. It may or may not depend partly on whether Linda and/or her mother is/are (or not) members of the board, as well as duplication is allowed or required for those persons who are in more than one category.

  26. I got it. Admittedly, it took me some time though. Still curious as to what role Mom plays in all this. I guess Linda is very close to her mom and shares everything with her.

  27. It took me 10 seconds to get the answer then 42 weeks to set up a small company, rent a photocopier, hire a lady called Linda to take over the running and produce a set of accounts.

    While it proved I had the correct answer, sadly I had to let Linda go when it became clear she was passing confidential accounts information to her mother. Without her leadership the sales dropped and the company went into liquidation. The photocopier, a really good model capable of a page a second, was one of the first assets to go.

    I am now 147,000 GBP in debt and classed as bankrupt. I will see you in court Mr Wiseman!

  28. Took me about 10sec to recognize the equation. Took about 2 min to grind out the numbers fair and square. “Modestly sized boardroom” would seem to preclude a 169 member board of directors. No?

  29. This threw me at first because a) I’m really bad a arithmetic – I used to be practically innumerate although, weirdly I was good at statistics, algebra, calculus, trig and geometry. So I didn’t immediately know which numbers 169 was divisible by and b) I wasted several minutes what relevance was of it taking 11 minutes – was this a clue? Was it playing on the double meaning of, ‘minutes’ so that eleven ‘minutes’ were handed out to the board? No, that was just meant to confuse. Once I’d decided that the time was irrelevant (annoyingly!) and used my calculator to find that 169 was divisible by 13 the answer was obvious.

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