On Friday I posted this puzzle.

A shop sells chocolates for £1 each, and you can exchange 3 wrappers for 1 chocolate. If you start off with £15, how many chocolates can you buy?

If you have not tried to solve it, have a go now.  For everyone else the answer is after the break.

You can buy 22 chocolates!  Did you solve it? Any other answers? I have a funny feeling this is going to cause some debate.

I have produced an ebook containing 101 of the previous Friday Puzzles! It is called PUZZLED and is available for the Kindle (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.


  1. 21, right?

    15 pounds = 15 wrappers
    15 wrappers / 3 = 5 additional wrappers
    5 wrappers / 3 = 1.something
    The .something is irrelevant as you need a whole number of wrappers.

    Total = 21

    What am I missing?

    1. With 5 wrappers you exchange 3 for a chocolate leaving you with 2 wrappers. Eat the chocolate, and you have an additional wrapper to add to the 2 you had, thus you can get one last chocolate.

    2. After taking 3 wrappers from that remaining five, you get one more wrapper which you can add to the original two to make 22.

    3. You get a wrapper back with the one you exchanged for three of the five original bonus sweets. You can then combine that with the two unused wrappers from that original five.

    4. Amazing how quickly a load of similar replies can be composed before any are shown!

    5. After the third step, you have 1 chocolate plus the 2 extra wrappers. After you eat the 1 chocolate, you then have 3 wrappers for one last chocolate.

    6. When you have 5 wrappers in total… can buy one chocolate with the first 3 wrappers. Now you will have 3 wrappers left with you. These three can now be used to buy the 22nd one.

    7. Well I have read several answers and I disagree with everyone for the simple fact that the statement reads, “you can exchange 3 wrappers” it did not say “exchange 3 wrappers.” So therefore, logically the answer will be 15

  2. I disagree. You can *buy* 15 chocolates. You can *exchange* for a further 7. You may have had a total of 22 chocolates, but you only actually bought 15.

    1. Larry: There are *lots* of messages on that blog post, directly addressing Bazza by name. Get your facts right, wee man.

    2. I agree also. I got both solutions. If you approach this as a word puzzle then the 15 answer is more correct. If you approach this as a math puzzle then the 22 is correct. Richard posts both types of puzzles so I’d say either works.

    3. You are making the mistake of thinking that the term “to buy” is limited to purchasing something with a specific kind of currency, rather than the broader act of exchanging goods for payment of some kind.

      The imaginary store accepts pounds as currency. (I assume the imaginary store also accepts dollars, euros, maybe bitcoins… you get the idea.) We have been told this store also accepts chocolate wrappers as a valid form of currency to buy (exchange for payment) more chocolate.

      You can buy 22 chocolate bars. The price of a chocolate bar is 3 chocolate wrappers or 1 pound. (Not sure how many bitcoins you would need.)

  3. Same answer. See hardly any reason for debate
    Buy 15 chocolates, get 15 wrappers.
    Give 15 wrappers, get 5 chocolates and 5 new wrappers.
    Give 3 wrappers (keep 2), get 1 chocolate and 1 new wrapper. Now you’ve got 3 wrappers
    Give 3 wrappers, and get another chocolate.

    15 + 5 + 1 + 1 = 22.

    Only thing that can cause debate is, is “exchanging wrappers” really “buying”. So one could argue that you can only “buy” 15 chocolates with £15. But that is nitpicking.

    1. Since the wrappers can be exchanged for more chocolates, that effetively makes them a second form or currency for purposes of getting chocolates. Therefore, trading wrappers in for chocolate is, effectively, “buying” them. 22 is the right answer.

  4. So obvious when you know how! I knew it couldn’t be as simple as 20 but that’s as far as I went anyway. I feel like a muppet.

  5. The correct answer was given on Friday by @dave and I posted a warning to genuine solvers not to read his solution.

    For that I received a number (8) of increasingly vitriolic responses somehow doubting my humanity as I had tried to warn others of the spoiler below.

    I am not disheartened as I know that those who responded in that way are only a tiny minority of those who contribute to these weekly puzzles.

    Dave was right but his timing was wrong. I was somehow a subhuman for simply trying to solve the problem that Dave had set for other solvers (ie revealing the solution).

    It is a strange muddled mixed up world we live in.

    1. I wonder how many people have already figured out that .arry .o..ard (Barry Goddard/Larry Stoppard etc.) = Dave (‘s mothers friends neighbours grandfathers uncle)

    2. Except there isn’t a single comment on there aimed at you.

      I think you have some kind of paranoid schizophrenia, Baz.

    3. Larry: There are *lots* of messages on that blog post, directly addressing Bazza by name. Get your facts right, wee man.

      (I posted this up above in the wrong place. Sorry about that. This comment is for the wee man Larry Stoppard.)

    4. Barry Goddard is lying again. You didn’t post a warning. You gave the answer away where everybody could see it. What a good troll you are.

    5. It’s funny how your idea of solving problems is the same as other people’s idea of causing them. Your post ensured that any spoiling was done by you since your post was higher up the list. It’s not the first time that you’ve done this and I predict that it won’t be the last.

      The only tiny minority here is you and your self-delusion that nobody can see you for what you really are. There’s only one person living in a muddled mixed up world but you’re too conceited to see it.

    6. Thank you to everyone who has supported me above and in other replies. It is good to know that not everyone has succumbed to the “attack the messenger” response that has become common here of late.

    7. This “attack the messenger” of which you speak – I don’t suppose that there is any chance that you have been guilty of this yourself? Say, when you had digs at anyone who wishes to debate the sometimes dubious wording of these puzzles, or when you put mathematician in quotes to try to discredit someone whose grasp of mathematics was clearly superior to yours?

      No? I thought not.

    8. Barry, do you actually read these responses of which you speak? If you did, and you were also able to comprehend them, you would see that they all pretty much say the same thing, and that is to take you to task for the frequent hogwash that you assail us all with.

      They attack your message because it is usually hypocritical, mostly wrong-headed, and always unwanted. You ignore what others have said, instead preferring vague sophistry and to thank imaginary friends for their non-existent support. It would actually be quite sad if you weren’t so annoying.

    9. @Jonno

      I choose to overlook the negative comments and look deeper at the ways we all agree.

      In my heart I am a healer and in my mind I always seek clarity. This means although I may see the negative I always seek out the more positive aspects. Even with some of the posts here there are positives. It is almost as if people want to (perhaps in their depths need to) agree with my perceptions yet their egos stay their hands and out come harmful words.

      Yet harmful words that come out were harmful words on the inside. And they did far more damage and hurt there than they can ever do to me.

      Dialogue is important even with people who want to derail the discussion. That is my insight and also the message of this blog.

    10. More utter nonsense. You didn’t answer my question – who are all these people supporting you?

    11. Steve and Jonno. Take a deep breath…….count to ten…….and relax. There, there. There, there.

    12. uuuuuuuh 1 2 3 4 5 6 7 8 9 9.1 9.2 9.3 9.4 9.5 9.6 9.7 9.8 9.9 22/2 bugger haaaaaaaaa.

      Thanks Anon. I feel much better now.

  6. How many chocolates can I buy? Loads. I’ve got my credit card. (Question says you can EXCHANGE wrappers for chocolate, but asks how many can you BUY. I am a founder member of the British Pedantic Society, soon to be renamed the British Society of Pedants, as it is the members who are pedantic, not the society)

    1. I really hope there truly exists a British Pedantic Society that is soon to be renamed the British Society of Pedants. That is so awesome. I want to join.

    2. @Pat Harkin

      I predicted your brand of pedantry on Friday and received vitriol for doing so. Your linguistic error is to assume that PAY means PAY WITH MONEY. There are other ways to pay for things. Barter/exchange is payment thus the puzzle solution works as stated.

      There is no need to make these puzzles any less simpler than they need to be. Like at school just read the wording of the question and answer the question. If we question the question there is no end to that.

  7. If you sum the series 1+1/3+1/9+1/27… you will find it comes to 1.5. Using that as a multiplier against the number of bars you purchase (rather than exchange) gives you the upper bound of the number of bars you could receive. In the case of this example, 15 x 1.5 = 22.5. The offer doesn’t allow for partial bars (and partial wrappers), so you could never get more than 22 bars in total (with one wrapper left over). Note that this is a necessary, but not sufficient condition, but it’s easy enough to demonstrate you can get to the 22 bars with one wrapper left by a number of different buying and exchanging steps. They all finish with the same result.

    However, if the vendor had offered incomplete bars and wrappers equivalent to one third of the whole-bar equivalent wrappers submitted, you would, after an infinite number of transactions get your 22.5 bars. Or would, if bars were infinitely divisible.

  8. While you’re eating chocolates, you get 1 wrapper for each one you eat. Once you’ve eaten 3 you turn in your wrappers for another chocolate.

    After the first 3, each time you eat 3, you turn in your wrappers, get another chocolate and eat it thus getting another wrapper. So each time you eat 3, you get 1 back meaning you only need to eat 2 more (not 3) to get another chocolate (and another wrapper).

    So once you’ve eaten the first 3, you get another chocolate for every 2 that you eat. Starting with 15, you get an extra chocolate after you’ve eaten 3 (12 remaining plus the new one = 13), then after every 2 – 11, 9, 7, 5, 3, 1. That results in 7 extra chocolates for a total of 22.

  9. No no no no NO! The question never said that they had to be chocolate wrappers, so you could just get as many wrappers from the trash and exchange them for as many chocolates as you want.

  10. Why is everybody saying 22?
    Why is everybody assuming that there is only one wrapper on each chocolate?
    There might be more than 1.

    If there are 2 wrappers per chocolate, I reckon you can buy 43.

    If there are 3 or more, you can buy as many as you like (ad nauseam, rather than ad infinitum) subject only to the productive capacity of the chocolate company, the boredom / exhaustion / sickness of the consumer, and the eventual heat death of the universe.

  11. I have looked at the personal language used in the responses to this thread and it is disquieting. All these terms of abuse used at least once:

    ad nauseam, annoying, conceited, dubious, foolish, hogwash, hypocritical, idiot, lying, muppet, paranoid, pedant, poor, slugsie, tincy-wincy, trash, trick, troll, wee man, wrapper, wrong-headed.

    This should be a simple joyful exploration of a puzzle not an opportunity to express deep feelings inappropriately to strangers. I fear some contributors emotional depths lack the necessary emotional maturity. Throw chocolate into that mix and it has become very rowdy indeed.

    If even someone like Tony Blair can be a peace envoy then surely we can at least be politer and kinder in our interactions?

    1. Am I doing an idiotic thing by rising to this?
      Several of those words quoted were in no sense terms of abuse – ‘ad nauseam’, ‘pedant’, ‘slugsie’, ‘trash’, ‘trick’, ‘wrapper’.

      Even as I type this I am thinking ‘why bother?’

      Barry, perhaps you would be on the end of less of the words that were terms of abuse if you were more emotionally mature yourself. I used to enjoy the alternate viewpoints that you often brought to the Friday/Monday discussions – but there’s no excuse for spoiling things by telling people the answer in a comment that purports to warn of spoilers.

    2. Barry G. I’m with you on this. I may not always agree with your rambling, musings but they do add a bit of colour and personality, which is in stark contrast to much of what is written here

      These puzzles are meant to be entertaining diversions and not the forum for spiteful comment.

    3. @Gabby Bollard

      Thank you.

      It does seem that there are two distinct classes of people here. Those who want to solve the puzzles and those who want to troll the solvers.

      I see myself simply and humbly as a puzzle solver. Also as someone always willing to help those who are having trouble solving the puzzle. For that I get attacked by the other class of people. It is such a shame that they have no shame in what they do.

    1. Eddie, you’re right. The South Bank’s always nice at this time of year. It might stop a few people bickering, but even if it didn’t, a pint by the river is good.

    2. You’re on! Dave (+ relations), Barry (+ all spoonerised variants), TMT, Steve Jones, Ken, ctj, Emmanuel, how about the Horniman and Hays some Friday evening in July.

  12. dollars = 15
    chocolate = 0
    wrappers = 0

    while dollars != 0:
    dollars -= 1
    chocolate += 1
    wrappers += 1
    print chocolate, wrappers
    if wrappers == 3:
    chocolate += 1
    wrappers -= 2
    print chocolate, wrappers

  13. You can only buy 15 from 15£.the rest will be free.
    I request all those who oppose my view to reply me their reason.I also request richard to answer my question plzz

  14. The answer is 7. Here’s why. 1) We have to assume that removing the wrappers exposes the chocolate since if you were just redeeming an outer wrapper or sleeve, then shoplifters would remove the outer wrapper from all of the chocolate bars on the shelf except the one on top and get a bunch of free chocolate. Therefore, 2) You’ll start by purchasing three bars and greedily eat them so you can redeem the wrappers for a fourth bar. 3) Then you’ll purchase a fifth and sixth bar so you can get a free seventh bar. 4) As you work your way through the 4 chocolate bars left, unless you are a professional glutton, your stomach will cramp up and you will stagger from the store feeling bloated. The remaining 10 pounds will be spent on medicine. Either that or the blood sugar rush will cause you to pass out on the floor of the shop, and you will awake hours later in a nearby park missing the remaining 10 pounds and chocolate bars, your wallet, cell phone and shoes.

  15. I missing 10 lbs this thirty day period and i am pretty very pleased of myself for that… but I’m not looking at a massive variation within the mirror and i’m anxious I’m going to be discouraged this thirty day period. I’m sure I’m dropping chinese bee pollen for that proper motives (to be in a wholesome BMI), I assume I believed 10 lbs would make far more of the distinction in how I appear, so now I am dissatisfied. Any information?

  16. 15 chocolate bars = 15 wrappers
    15 wrappers / 3 wrappers = 5 chocolate bars.
    15 chocolate bars + 5 chocolate bars = 20 chocolate bars.
    5 wrappers – 3 wrappers = equals 1 chocolate bar and 2 wrappers
    20 chocolate bars + 1 Chocolate bar = 21 Chocolate bars and +1 Wrapper
    2 wrappers + 1 Wrapper = 3 wrappers
    3 wrappers = 1 Chocolate Bar
    21 chocolate bars + 1 Chocolate bar = 22 Chocolate bars and 1 wrapper left over.

  17. I agree but you shouldn’t never get exchange mixed up with buying…The question is how many can you buy…I think it was an idot who came up with this in the first place!!

  18. You can only get 15. As the question reads, it doesn’t say the chocolate you buy is wrapped, and it doesn’t say what kind of wrappers. If you answer anything else you are making assumptions about the chocolate being wrapped and the wrappers.

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