coverPlease do NOT post your answer, but do say if you think you have solved the puzzle and how long it took. Solution on Monday.

Let’s play a little game.  Please snap your fingers.  Then, 1 minute later please snap your fingers again.  And so it goes on.  Each time you double the time between the snaps, so you snap your fingers again after 2 minutes (from the beginning).  Then snap your fingers after 4 minutes (from the beginning).
Then snap your fingers after 8 minutes (from the beginning).
How many snaps will you make in a year?
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. Not really, since the question is flawed. At no point would you “snap your fingers again after 2 minutes (from the beginning)”. Think about it.

      This isn’t really a puzzle anyway, just some maths that I really can’t be bothered to trawl through.

    2. Dave,
      I’ve thought about your comment and still can’t understand it – perhaps you would be kind enough to explain now (if would not constitute a spoiler) or on Monday (if it would).
      It took me a few seconds to work out the methodology and a minute to get an answer.
      Isn’t this based on an old Chinese puzzle about grains of rice on a chessboard?

    3. @The Masked Twit

      I’m with Dave here.

      “Please snap your fingers [0]. Then, 1 minute later please snap your fingers again [1]. And so it goes on. Each time you double the time between the snaps, so you snap your fingers again after 2 minutes (from the beginning).”

      Your second snap was 1 minute from the beginning. If you double the time between the snaps, then there should be a two minute gap before your next snap, making that one 3 minutes from the beginning.

      Maybe what Richard meant is doubling the time from the first snap each time. But I’m inclined to think it’s a trick because, over the course of a year, I’m bound to go to sleep rather than clicking my fingers.

    4. Thanks Ben
      Now I understand Dave’s comment.
      My feeling is it is a badly worded question rather than a trick.
      We will find out on Monday I guess.

    5. Yea, it’s not solvable because it’s not clear from the wording how often you snap. Do you double the time from the beginning or do you double the time between snaps? It says both.

  1. Some simple math will solve this. Maybe the answer will be surprising to some people. The solution is straightforward, but it’s not a quickie.

  2. I should add that I wish you had done it in terms of seconds because I’ve memorized that there are about pi *10^7 seconds in a year. That’s an important factoid if one is concerned about things like how many heartbeats one has in a lifetime.

    1. Oi, no… Some of us have enough to dwell upon without that additional factoid! :-S

    1. OK. I’ll offer the same deal to everyone here who wants it.

      There will be a small postage and handling fee, which will be a paltry penny per grain, doubling for each grain added.

  3. I agree it is fairly straightforward to solve but isn’t there an inconsistency in the way he has described it? The interval between the first and second click is one minute, and the interval between the second and third click is also a minute, so in that case you don’t double the time between clicks. After that, it’s fine: clicks 2 and 3 are 1m apart, clicks 3 and 4 are 2m apart, 4 and 5 are 4m apart.

    Or have I misinterpreted?

    1. I intepret the puzzle as follows:
      S = snap
      m = minute

      Time ————1 year (525600m)——————————————–>
      S–1m–S–1m–S—-2m—-S——–4m——–S—— etc until ——-S—

    2. Yep, looks like Richard’s snapped once too often. The bit ‘…2 minutes (from the beginning)…’ is where he’s confusing everyone.

      PS took me a year to get the answer.

    3. It’s not the interval that’s doubling, it’s the number of minutes from the beginning. So you go 1, 2, 4, 8 etc. No problems.

    4. Richard says: ‘Each time you double the time between the snaps’. So there is definitely a contradiction here. Problems.

  4. About ten minutes. Five minutes to work out how on earth I’d even start and then another five minutes to get an answer. Good puzzle.

    1. thanks, that actually helped. I couldn’t work out where to start, so I read the comments. For some reason, this one gave me an idea and I solved it in about a minute after that. I needed a calculator though. I wonder if it’s right!

    2. Julia: Well, I needed a spreadsheet! No shame in using the tools that we’ve been given, I hope.:-)

  5. 10 types of puzzles on this site, those that are solved very quickly and those that don’t have a solution at all. In this caseCalculating the number of minutes in a year, took a few seconds with a calculator, writing down a few powers of two, it took about 5 minutes before arriving at the quick way of solving it.after that it was done in seconds though I object to calling it a puzzle it is more of a maths question, but unless there is some twist I’m not seeing yet, but since it said please I won’t complain, I liked the politeness of the question. Most puzzles just order you to do things

  6. Even though I know the “reveal” in this one, it always comes as a bit of a shock when I work it out and find how few it actually is. A twist on the old “give me money every day for a month, £1 day one, £2 day 2, £4, £8 etc”.

    1. The character Spoilt Bastard in Viz pulled this trick with his mum in a recent issue. He convinced her to pay him 1p on day one, 2p on day two, 4p on day three etc. instead of a fixed amount of pocket money. … I agree that this answer to this puzzle has a similar surprise ending!

    1. 10 types of people in the world. Those that understand binary, and those that don’t.

    2. Sceptic_Tank: I used to manage an Education Department in a maximum security prison. In one of the computer classrooms there was a laminated sign on the wall that read exactly what you have written. It was – shall we say? – a joke that did not go unchallenged. It once caused a riot as it was torn from the wall and set on fire…. Happy days. I’m really looking forward to the binary solution on Monday because I did it a different way (and could be wwrong, of course).

  7. About a minute (if that) – one calculation to work out the number of minutes in a year (mercifully the answer doesn’t change if you count a year as 365, 365.25 or 366 days!) then a simple calculation / fill down to work out the intervals.Find the last value where x < n, and read off the row number.

  8. Wow, that’s interesting. I knew pi seconds was approximately a nanocentury, but I didn’t know about this other rather serendipitous alignment…

  9. Took about a minute with a calculator and came up with an interesting result. I can’t understand why some people are getting their knickers in a twist about the wording of the question, it seems pretty clear to me, and most others judging from the comments.

    1. You tell us then – do you snap at t = 0, 1, 2, 4… or t = 0, 1, 1, 2, 4… or t = 0, 1, 3, 7,15,…

    2. t=0,1,2,4,8…. like it says in the question. Why would you possibly think otherwise?

    3. Because he says ‘Each time you double the time between the snaps’. Your interpretation doesn’t follow this.

    4. ‘Each time you double the time between the snaps’

      1 x 2 = 2 2 x 2 = 4 4 x 2 = 8 etc. Basic maths, buddy.

    5. You haven’t doubled the time from between 0 to 1, and 1 to 2. The span is the same i.e. 1.

  10. i think if richard changes the wording to “Each time after the third snap, you double the time between the previous two snaps…” it preserves the exponential, but then it gives the solution away too easily.

  11. I Know How To Solve This And I Read A Book Called A Creation Of Rice That Is Like This, But I’m Just Too Lazy To Try And Figure This Out. I’ll Wait For The Answer.

  12. … and dont forget the dozens of snaps you do in the restaurant when you are trying to call the very busy waitress…

  13. Appears to me the puzzle as described is self-contradictory and cannot be solved.

    > “Then, 1 minute later please snap your fingers again…. so you snap your fingers again after 2 minutes (from the beginning).”

    … is true, then,

    > “Each time you double the time between the snaps”

    … cannot be true, and vice versa.

  14. Let me illustrate that contradiction a bit more, because I’m surprised more people are not seeing it (presumably the ones claiming to have solved the puzzle are missing the contradiction). It has to do with when the third snap occurs, and per instructions given there are two different and exclusive possibilities, each with a different answer.

    — “Please snap your fingers.

    Ok, I snap my fingers. Let’s call this snap a. And let’s call this moment A0. And we’ll run a count of total snaps and call this C1.

    — “Then, 1 minute later please snap your fingers again.”

    Snap b occurs at A1, and now C=2.

    A1 is one minute later than A0, so now we can set a time-between-snaps to increment, which we’ll call T and set at a value of 1.

    Also set another variable for time-since-A0, which we’ll call S. That also equals 1, ergo S=T right now.

    — “Each time you double the time between the snaps,”

    This tells us that T should multiply by itself every time C increments by one. We know that snap c occurs at A2 after T. Since we have to multiply T by itself, it now has a value of 2. Ergo A2 occurs two minutes (T2) after A1. And S (time since A0) now equals 3.

    Summarizing, this iteration:
    Snap c @ A2 results – T2, C3, S3.

    We now have enough information to forecast how we can determine the answer to the puzzle. It will be whatever the value of C is after enough T has passed, such that S is equal to (or greater than) 525949, the number of minutes in a year.

    Now on to snap d, which will occur at moment A3. We know A3 occurs after (T2xT2=T4) after A2.

    Summarizing, this iteration:
    Snap d @ A3 results – T4, C4, S7.

    Earlier Richard said…

    — “And so it goes on”


    Snap e @ A4 results – T8, C5, S15.
    Snap f @ A5 results – T16, C6, S31.
    Snap g @ A6 results – T32, C7, S63.


    — “so you snap your fingers again after 2 minutes (from the beginning).”

    And here is the problem.

    It’s not exactly clear what Richard means by “from the beginning” here. The only thing we can presume he means by it is our variable S, time since A0 when the originating snap a occurred, “the beginning”. So he’s saying there should be a snap that happens at 2 minutes from the beginning, but we can see that S has never had a value of 2.

    So this is wrong. It must be either that this statement is erroneous or one of the previous statements has been erroneous. There are no other possibilities.

    You can see the remainder of the statements (e.g., “… after 4 minutes (from the beginning)”, “… after 8 minutes (from the beginning)”) are all based on the same erroneous premise, and would result in values of S that we can see S will never have.

    Therefore the puzzle as described is self contradictory and cannot be solved.

    1. Thanks for mentioning this for at least the third time on this thread – and so succinctly too.

    2. Nobody in their right mind is going to find your notation any clearer than the puzzle itself. The first error you seem to make is when you state “double the time” equates to “T should multiply by itself”. Multiplication by two is *not* the same as squaring. I stopped reading after that.

      By my reading of the puzzle, the main mistake is that it talks about the time *between* snaps, but then discusses it as an absolute time from the first snap. So there is 1 minute between the starting snap and the 2nd snap, but in order for there to be 2 minutes between the 2nd and 3rd snap it would mean that 3 minutes would have to have elapsed from the beginning. The 4th snap likewise happens at the 0+1+2+4 = 7 minute mark, and so on.

      In essence, Richard incorrectly adds a snap at the two minute mark, and then has a one-off error for all the other values. No real fuss necessary; just add error bars to your answer. 🙂

  15. If Andy Murray hits a tennis ball at t=0, then it is returned at t=1 what time will Andy hit his second shot?

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