coverOn Friday I posted these puzzles.  If you have not tried to solve them, have a go now.  For everyone else, the answer if after the break…

1) How many times can you subtract the number two from the number fifty?

2) You drive a bus from London to Edinburgh. At the first bus stop, 43 people get in. At the second stop, 9 more people get in. At the third stop, 45 passengers step off and 12 people get in. After nine hours, the bus arrives in Edinburgh.  What is the name of the driver?

1) Once – after that you are subtracting from 48!

2) Your name – you are the driver!

Did you find other ways of solving the puzzles?

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. Roland, you’re right of course. Fifty is always fifty. It doesn’t turn into 48 (or any other number) no matter what operation you perform on it.

    2. @Roland

      You are making the same mistake that Steve made in his comments over the weekend,

      The blog here gives the correct answer. It is the same answer that those of us who are literate and numerate also arrived at.

      The comment posts over the weekend for another post carefully examine why your answer cannot be accepted. If you review them with an open mind your will realise the true answer is that as given.

      Many of the puzzles here are like optical illusions for the rational mind. The number of misunderstandings are an amusing insight into the way that our minds fool us into not seeing what is rationally the true reality.

      This is why I am an astrologer. The objective feedback from the stars helps hone my mind to a fine creative system.

    3. Bazza: At the risk of inviting you to say too much, could you explain what you mean by this ”over the weekend” bullshit, please? Keep it brief if you would. Richard doesn’t allow us to post answers on Fridays anymore, largely because of people like you.

    4. @Sampson Beegees

      Thank you for asking me to comment further. It is always a pleasure to be of help.

      Some people – notably Steve and Jonno and others too – used the post “Lovely dramatic stunt…” to add comments that were related to the Friday puzzle. What some of them posted was quite frankly of low quality. Therefore some others added clarifications to correct their mistakes.

      If you require further explanation of this on any past puzzle please do ask.

    5. Well, I have a Master’s Degree in mathematics so I’m probably not completely innumerate. It is a common error to confuse countable things with those that are non-countable.

      Coins, bottles, etc are countable. If you have a pile of 50 coins and take two of the coins away from the pile, you will be left with a pile of 48 coins. If you take another two coins, you’ll be taking them away from a pile of 48 coins so the logic of only being able to do this once holds in this example.

      However, “the number fifty” is not itself countable. It is an immutable concept which is used to count those things which can be counted. If, as the puzzle asks, you subtract “the number two” from “the number fifty”, even though the answer to the constructed equation is ’48’, the concept of “the number fifty” will still be ‘the number fifty’. You don’t need to get “another 50” in order to be able to subtract two from it again as there is only one “number fifty” in the first place – it is a universal concept but a single entity.

      Roland demonstrated doing it twice very clearly and could obviously repeat that for as long as he wished/until he died.

    6. Nonsense. The answer is clearly 25 times. Look:

      50 – 2 – 2 – 2 – 2 – 2 – 2 – 2 – 2 – 2 – 2 – 2 – 2 – 2 – 2 – 2 – 2 – 2 – 2 – 2 – 2 – 2 – 2 – 2 – 2 – 2 = 0

    7. So BG, you are an astrologer!. What it tells us is that you participate in the mass cultural delusion that the sun’s apparent position relative to arbitrarily defined constellations at the time of your birth somehow affects your personality.

      It all makes sense now.

    8. Larry Stoppard: If you were correct, you would have to keep counting into the minus numbers. You can’t arbitrarily stop at zero. That’s why the answer (if this method happened to be correct, which it isn’t) would be ‘infinite times’.

    9. @ Mike Benton,
      A request for clarification.
      As the number fifty is an immutable concept surely nothing can be subtracted from it? If you could subtract from it, it would not be immutable.
      Hence the correct answer to Richard’s question is no times?

    10. Bazza: Thanks for the clarification. I understand what you mean now.

      Mike Benton: I have to agree with Twit’s comment about mutability, I’m afraid.

    11. @The Masked Twit
      Well, not really. Immutable in this sense simply means that “the number fifty” doesn’t become (in this example) “the number forty-eight” when you use it in an equation, but remains “the number fifty”. It’s different from when we talk about taking something away from 50 objects. “The number fifty” isn’t a real object, it is simply a useful way for us to represent something in the real world. You could make a joke about real numbers here if you like…

  1. I feel so dim! I said ‘infinite times’ for question 1. Obvious, really.

    Got the second one. It’s been a staple icebreaker for ropey team-building training sessions for many a year now…:-)

  2. I also got “as often as you like” for question 1.

    I got question 2 instantly, but that’s only because a former maths teacher of mine once used it to fool an entire class (including me) in the finale of a mental arithmetic test. It was the last question in a 40-question test, so obviously we were all geared up for crunching the numbers in our heads. At the end, you could hear everyone go “huh”?

    1. Yeah, your answer to question 1 as it is worded is correct. Mike (above) gives a pretty decent explanation of why.

  3. I didn’t even think about question 1 – numbers aren’t my thing. 🙂 But question 2 was just TOO easy. Seen a hundred variations of that one.

  4. “how many times can you subtract the number two from” is the same as n*(-2), where n is a whole number. if you’re stopping after subtracting each (-2) and treating each individual result as your minuend, you’re either doing accounting or still in preschool.

    oh, and Dave, don’t forget that pi is exactly equal to 22/7.

  5. OK. How many different ways can you subtract 2 form 50?

    Also, learnt the new word ‘minuend’ today. Cheers ctj.

  6. Eddie
    Minuend reminds me of innuendo…..
    This woman goes into a bar and asks the barman for an innuendo. So he gave her one.

    1. I can see why you wouldn’t want to put your name to that.

      I think I must’ve gone to the same bar. I didn’t even ask for a double entendre but the barman still gave me one.

    2. Thanks Simon
      I knew that there was something not quite right as I made the post.

  7. Though the expected answer to the first question was, of course, one, that is neither the only nor the most correct one: as it has been said, above, you can subtract 2 from 50 as many times as you like. Depending on your liking, it may either go “50-2 = 48, 50-2 = 48, 50-2 = 48, 50-2 = 48, 50-2 = 48, 50-2 = 48, 50-2 = 48, 50-2 = 48, 50-2 = 48, 50-2 = 48, 50-2 = 48, 50-2 = 48, 50-2 = 48, …” or “50-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-…” Both could be repeated indefinitely with no error whatsoever…

  8. Looking ahead, does anyone have the answer to the question that Richard will pose this Friday. Barry G, what do the stars foretell?

    1. @Sheldon Cooper

      Astrology is not parlour mentalism of the sort that TV magician Darren Brown uses when he predicts the lottery numbers.

      It is a deep trans-rational way of knowing our innermost essences.

      There is more to explore here.

    2. You do talk some rubbish. “Trans-rational”? This is one of those weasel words used by charlatans such as yourself to try to protect the BS you spout from being attacked by logic. “Oh, you can’t use rational argument against me because what I’m talking about goes beyond rational thought”. There’s a word for something that is not rational – “irrational”.

      The stuff that Darren Brown does is a lot more real than the unmitigated crap that you’ve filled your head with.

  9. The number I can subtract 2 from 50 is not 1, but nor is it “infinity” or “as many times as I like”. The number of times is limited by the capacity of the human brain to imagine and carry out such a process; this time span is itself limited by the speed of the electrical and neurological processes in the brain, the boredom threshold of the individual, the lifespan of the person calculating, the eventuality of the human brain evolving to a different form, and the dissipation (below the threshold of viability) of the necessary energy levels due to the heat-death of the universe.

  10. There’s been a debate over whether 50 is an immutable object or a number or whatever, but if it is oranges then as Larry Stoppard says the answer must be 25 – because you can’t have negative oranges.

  11. I agree with those who say the answer is infinite or “as many times as you like,” becaise subracting 2 from 50 does nothing to alter the “50” any more than it alters the “2”; it just performs arithmetic with the two numbers producing a third, namely 48.

    A better way to word the puzzle (without losing the “gotcha”) would have been to make it less abstract. For example, how many times can you take two eggs out of a full carton of a dozen eggs? The answer to that would be only once, because after that it’s no longer a “full carton”.

  12. If we are to believe many of the “mathematicians” who had answered above then the answer must be a big fat zero. They say: it is not possible to even subtract 2 once from 50 because 50 is some sort of universal unmuted eternal object that can never change or be affected by simple human means such as arithmetic.

    That strikes of so much eternalistic yearning that it is hard to make much sense out of it.

    50 (let me show some proper mathematical sophistication for a moment) is a CONSTRUCT. It is constructed as the successor to 49. Therefore it is made of parts. That is standard maths theory. What can be constructed can be reconstructed deconstructed or renovated.

    To summarise. We can very easily subtract 2 from 50. Those who say otherwise are in a very peculiar ivory tower indeed. Those of us in the real world call to them to come out and see what life is really like.

    1. There is no need to put mathematicians in quotes – I do have a degree in mathematics (Masters). That is the sort of tactic that children use in an attempt to discredit whom they are arguing with, when their own argument lacks substance.

      The second common tactic used by those without anything to say is to set up a straw man for them to attack. If you actually read my explanation you will see that I didn’t say that the answer is ‘zero’, in fact it’s the opposite (within the real-world limits expanded upon by John Cartwright).

      A third common tactic is to pretend that the argument is about something else as you do when you say that you can subtract 2 from 50. Nobody said that you couldn’t. Perhaps you just misunderstood?

      Then you conclude your ramble by accusing those who disagree with you of living in ivory towers whilst you, of course, live in the real world. Another classic tactic of someone who is unable to rebut the argument at hand so instead chooses to label those on the other side as “out of touch”.

      Your third paragraph, apparently the meat of your argument, is a waste of space. Nobody said that you could’t divide 50 or subtract any number from it. Simply that it can be done over and over since “the number fifty” is not the same as “fifty objects”.

      Roland, the very first commenter, demonstrated very clearly doing this twice, and it is obvious to any rational being that it could be done a third, fourth, fifth,… time.

  13. “What can be constructed can be reconstructed deconstructed or renovated.”

    My garden shed? Yes
    My wife’s Eton Mess? Not so sure

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  15. Infinite! 100 times 2 = 200(true), 50 – 200 = -150.(true) 50 – (2 x n) =?
    Thus I can subtract whatever I want.

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