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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.

A man spends a fifth of what is in his wallet, and then one fifth of what remained. He has spent a total of £72. What was the amount originally in his wallet?

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.

77 comments

  1. I’m not as clever as the other dudes who post on this site so it has taken me many hours to find an answer that I am still not fully confident with.

    1. SPOILER ALERT!!!! DO NOT READ THIS IF YOU DON’T ALREADY HAVE AN ANSWER.

      one fifth of one fifth is one twenty-fifth. one twenty-fifth plus one fifth is six twenty-fifths. seventy-two equals six twenty-fifths. six multiplied by four equals twenty-four. seventy-two multiplied by four equals two-hundred eighty eight. seventy-two divided by six equals twelve. two-hundred eighty eight plus twelve equals three hundred dollars. thirty seconds, no calculator, I am eight years old.

  2. Yeah, less than a minute I think, including a little chat with myself to have a go. Used a calculator though…

  3. You Brits are fast! it took me 5 minutes with a calculator and just plugged and chugged until I get it. American math system blows. Looking forward to the algebraic solution

    1. I’m surprised. I haven’t heard about plugging and chugging for a while. very reliable, though.

  4. <30 sec in my head after reading the problem. the wording is confusing…took me longer to read the darn problem than solving it…

  5. Played on a whiteboard, assuming £100 to start so the fractions would be easy. Then realised what the real answer would be. Now I just need to figure out how I could have done it with just brain power alone.

    1. I can NEVER do these without a pen and paper! I don’t know where I’d even start if I only had a calculator…

    2. Working it in reverse order, with just a tiny bit of initial logic, and it’s quite simple to do in your head.

  6. It’s a good one. Went wrong the first time and concluded that he had less money to begin with than he ended up with. Then I realised the error. Two minutes – with good old-fashioned algebra.

  7. Weird. Instinctively thought of an answer as I read it and it turned out to be correct.

    Evidently I’ve spent too long thinking about higher rate pension contributions with the 20% grossing up followed by the 20% PTR rebate.

  8. i am confused by phrase “and then one fifth of what remained” does this mean one fifth remained in his wallet? so he spend fourth fifths?

  9. At first I thought this would be a tricky maths question that I’d need a calculator for.
    Then I made an estimated guess in about 5 seconds, and rationalised that the first ‘one fifth’ would have to be exactly one fifth more than the second ‘one fifth’.
    Subsequent calculations revealed my guess to be correct!

  10. I ‘ready reckoned’ the answer in seconds then wasted about 10 mins filing the back of an envelope with gibberish.

  11. I think I worked it out, I just picked a nice, round number to start with and found I only had to double it! That took about a minute.

    1. Brilliant, genius. I’m sure you know how to tie your shoelaces as well, although I’m not sure I’d trust you to sit the rght way round on the toilet. Unfortunately you didn’t know how to read the bit about not giving the answer away.

    2. Same here. I tried it out with several values. I was sure thats a even number. But how is the correct formula ? What if the spent were 194654 Pounds ? Haha ?

      By the way: “Please do NOT post your answer,…solution on monday”

  12. This puzzle is lame, anyone with grade 9 algebra could solve it, I agree, the question takes longer to read than solve! Straight Algebra….where’s the puzzle?

  13. Got it, after reading all the hints and frigging with numbers for long enough. Still no clue what the formula should be. I probably shouldn’t be in university.

  14. I seem to remember there is a proper method for figuring these things out, but not being able to remember it I resorted to heuristics. Managed to get it in a minute or so.

  15. I took just too much time as compared to all the others 😦
    first tried with equations and got wierd results, then with a random number and got the correct value (by chance) and then went back to the equations and got it,…
    I am sure on Monday we ll see a different way of resolving it with much less paper and pencil….

  16. About 1 or 1-1/2 minutes using a calculator since one was right at my elbow. Probably could have just as easily done it using algebra and mental calculations.

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