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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.

The other day my friend sent me this note:

‘I’ve changed the calibration dial on my bathroom scale, and so the readings are off by a consistent amount. When I am on the scale it reads 170 pounds, and when my wife is on it, it reads 130.  When we stand on it together the scale reads 292 pounds. How should I adjust the scale?’

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.

53 comments

  1. You need to adjust the scale by the little twiddly knob on the bottom.

    p.s.
    It only took a couple of seconds to work out by how much.

    1. Only took me a minute ctj, just like you.
      This means that I can spend the rest of the day waiting for you to elaborate on your intriguing comment on Richard’s puzzle from 4th October 2103.
      In case you have forgotten it, here it is again:-

      “ctj
      OCTOBER 4, 2013 AT 10:40 AM
      there are two valid solutions.

      without explaining what is special about eric’s children, yes, parents of that kind of children really do think and talk that way.”

    2. richard’s solution to the problem of the ages of three children was 1,1, and 9. he incorrectly assumed that the parent of twins does not distinguish between the twins as older or younger. in truth, all parents of twins know who is older, even though the difference is often mere minutes. the distinction can lead to absurd results, particularly in cultures that place heavy emphasis on the oldest child. i know chinese parents of twins who actually admonish the “older” child of her responsibility to supervise and take care of her sister, who is a mere 6 minutes younger.

      of course, the 6-year-olds in the puzzle need not be twins. it is possible to have children who are slightly less than one year apart.

    3. Thank you for this ctj.
      I think, however, that there is a problem with your answer. If you (and the Chinese parents) are going to measure ages to the nearest minute you need to determine how old all three children are to the nearest minute. These three ages will then, when multiplied together, generate the number 36. Good luck with that.
      In addition the sum of their ages will need to be “exactly the number of biscuits we just consumed.”
      In effect your solution uses two numbering systems – one to the nearest year and one to the nearest minute.
      I realise that I have not expressed this very eloquently, but I hope that you “catch my drift”.
      SL

  2. Get off the scale and adjust it with nobody standing on it (as it should then give you the ‘off’ weight). No need for algebra (although, yes, it only takes about 2 minutes in this case – but then you still need to adjust the scale…..).
    And then throw it out the window. Horrible things, scales.

    1. Somebody got out of bed the wrong side this morning then…?

      I meant the trick in the question. It’s a very easy mistake to make if you don’t think about it.

    1. Roy, after re-reading the question, the same for me. What threw me was the word “calibration” which, by definition, requires at least 2 known points on a straight line graph through the origin, so I first tried some fairly complicated algebra in search of a percentage error. When that failed the penny dropped. Had the question stated “zeroed” rather than “calibrated” ……..

  3. Of course, being a modern man, I first of all converted the pounds to metric measures, then carried out the algebra, got the answer, then converted it back to pounds. Hmm, the answer ends in .99999 pounds. I wonder if that’s right.

  4. Took about five minutes to get to the answer. Even had to resort to doing it in excel.
    Tried to draw a graph but couldn’t find my scale rule!

  5. Evidently the problem was set in the US, given over here we either use Kilogrammes (if we want to be metric like our continental neighbours) or a combination of Stones and Pounds (1st = 14 lb) if we want to be truly British.

    Of course, adjusting the scales to give accurate results is completely different to adjusting the scales to give results both you and your wife are happy with… 😀

  6. I came up with my answer in less than a minute. Of course, I don’t know if my answer in right.
    (What I really like about the Friday puzzle is that I know which day of the week it is.)

  7. Please let’s have less maths problems and more logic puzzles! I can never do the maths ones, being thick at that subject. 😦

  8. When 2 dogs and 1 snail are on the same scale, it reads 73 pounds.
    When 1 dog and 4 snails are on the scale, it reads 58 pounds.
    When 3 dogs and 6 snails are on the scale, it read 128 pounds.
    What is the weight of a dog?
    *Note- They are on the same scale, so you will need to solve the above puzzle first.

    1. As you should have already found out the scale is 8 pounds too high.
      Now for the answer to my question.
      If the scale is too high by 8 pounds, the correct reading should be –
      a) 2dogs 1snail = 65 pounds
      b) 1dogs 4 snails = 50 pounds
      c) 3dogs 6 snails = 120 pounds

      the solution to the question is
      1. Take (A+C)-(B+C) you will get the weight of 1dog and -3snails which is 15 pounds.
      2. Take C divide by 2 and you will get weight of 1.5dogs and 3 snails which is 60 pounds.
      3. Add up the above two steps and you will get the weight of 2.5dog which is 75 pounds.
      4. 75/2.5 and one dog weight 30 pounds.

    2. OK but a bit long-winded answer as there are only two variables:
      A: 2D + 1S = 65
      B: 1D + 4S = 50
      So 4A; 8D + 4S = 260
      and 4A – B : 7D = 210 => D = 30

    3. Great, ChrisR, this question just came out of my mind from nowhere, thanks for a better answer. It’s seem much easier now.

  9. Trick question, people. The answer to “How should I adjust the scale?” is “To whatever negative off-set is necessary for your wife to believe she is her ideal weight”.

    1. or alternatively, to whatever offset causes your wife’s lie about her weight, based on what she sees on the scale, is in fact her true weight if the scale had not been adjusted.

  10. I do agree with all the ideas you’ve presented in your post. They’re really convincing and will certainly work. Still, the posts are very short for beginners. Could you please extend them a bit from next time? Thanks for the post.

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