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

Imagine a water-cask and three different sized water-taps.  The smallest tap can fill the water-cask in 20 minutes.  The middle tap can fill the cask in 12 minutes. And the largest tap can fill the water-cask in 5 minutes. How long does it take to fill the water-cask with the three taps together?
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.

70 comments

  1. It took about a third as much time as the answer. Good question. I will pass this on to my daughter who’s just started GCSE maths.

  2. It took me about one ninetieth of the of the time it would take all three taps to fill the cask to solve the puzzle.

    1. About a minute in Excel, plugging in a value of 100 units for the volume of the cask. As others have said, the different flow rates were deliberately chosen to ensure a nice round number when combined.

  3. Undoubtedly, I’d drop the d@mn cask in the middle of it all and ask myself why I’d bothered hunting down the three mismatched taps… 😀

  4. took me a few (<5) minutes – from first principles (let 'x' be the amount of water in the tank etc), checking whether the formulae I'd got actually made sense (that took the most time!), and then confirming it by imagining x was really 100 litres.

  5. Good thing I worked it out before I looked at the comments. Yet again it seems some people think it’s appropriate to give the answers away and spoil it for others. There shouldn’t be a comments option on the question page, there should only be one on the Monday morning answer page.

  6. mr wiseman’s puzzles are unfair to those of us who canno’t solve them. i must post only how long soln took. but this one o canno’t solve so my posting voice is silence.

    unfiar, mr wiseman!

    1. Obviously you need more practice at being silent. Tell you what, see how long you can manage from now on. We’re all rooting for you.

  7. WHY do people continue to insist on posting their answers – or obvious clues to the answers?? It’s fun to read people’s comments and see what they think of these puzzles – but don’t they understand that it spoils it for others just because they have a need to show off?? And don’t they understand the English that Richard uses to ask them NOT to post their answers?????

    1. I think that they post their answers just to wind up people like you and me Alma.
      Works every time too.

  8. so glad I didn’t read the comments today!

    I enjoyed this puzzle. I needed pen and paper and had to imagine that it’s a 60-litre cask. Took me about two or three minutes to solve.

  9. It took me less time than the answer, longhand, as taught for the eleven-plus maths exam back in the 1950s. Nostalgia isn’t what it used to be.

    Totally agree with comments re people posting the answer. I never look at the comments before solving the puzzle for myself (or giving up, which I did last week!).

  10. Fractions revisited, an answer appeared on the back of my old (and favorite) envelope in about 1/9 of the time it takes to fill the vessel.

  11. Couple of minutes. Somewhat ruined by reading comments before attempting (rookie error as ever – but why do people insist on posting answer or “cryptic suggestions”, enough of the willy-waving). But reached an neat answer on a post-it note, no excel or anything needed.

  12. It took just a few seconds to make a good guess.. The way I did it was that I figured it had to be less than 5 min and that made me think about a formula for adding resistors. That gave the same answer as the others who sadly gave away the answer. My way wasn’t as good as theirs that was more principled than my way which was just a guess. But it’s interesting that the principle is actually the same. So now I have deeper insight into that formula for adding resistors.

  13. I was thinking that finally there was a reason to have studied calculus (which I don’t remember because I never use it,) but you all only used fractions so even though I didn’t get the hints, I have no excuse not to try it. I always use the trial and error method.

  14. yeah! I guessed the first comment right!

    1) I read and work out the puzzle
    2) According to the answer, I try to guess the first spoilery comment (the very first one actually)
    3) THEN, I read the comments…

    Got it right this time!

  15. Took me about 15 seconds, mainly because I could see what was going on so I started calculating as I read through the question. I must have swallowed an extra maths pill tonight…

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