coverFirst, if you are up at the Edinburgh Festival, I am speaking about strange stuff on Saturday.  Details here.

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.

What’s the fewest number of marks you could put on a 12-inch ruler and still be able to measure every distance from 1 inch to 12 inches?
UPDATE: By ‘every distance’, I mean every inch (1 inch, 2 inches, 3 inches etc.).
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.

34 comments

  1. Are you allowed to move the ruler? If not, what is the length of the ruler (I only ask because the one I have in front of me is actually 12.25 inches in length)?

    1. I interpret this to mean: After you’ve made the marks, every integral distance between 1 and 12 inches exists–either between 2 marks or one of the marks and an end of the ruler.

  2. I think we are to assume we have to measure whole inches from 1 to 12.

    It’s easy to show it’s impossible with up to a certain number n marks, and in about 10 minutes I found 3 ways to do it with n+1.

    Mark

  3. The assumption must be that you can measure from 1 to 12 inches in one go, either from the end of the ruler or from one of the marks – no measuring, remembering, moving, measuring again. This reminds me of the puzzle about the fewest number of coins needed to pay any amount exactly up to one dollar.

    1. You mean the answer is 4 – same as with the 40lb weight problem – or do you mean that similar principles apply?

    2. You mean your post was a spoiler?
      It doesn’t bother me but some of the contributors to this thread get near apoplectic over this kind of thing.

  4. Took me about two minutes to ascertain the minimum number of marks (Richard’s question).
    Where they should be is another matter however.

  5. Dear Mr. Wiseman

    I’ve tried three times, unsuccessfully, to unsubscribe from your postings. Is there some secret to do it? I’m following the instruction, but it doesn’t seem to work. Thanks.

    John Belz

    1. What’s the fewest number of marks you could put on a 30.48 cm ruler and still be able to measure every distance from 2.54 to 30.48 cm?

      UPDATE: By ‘every distance’, I mean every 2.54 cm.

      Better? 😉

  6. Two comments:
    1. Measurement would be so much easier if Americans were smart enough to adopt the metric system!
    2. I’ll only post this because I don’t think it’s the answer you’re looking for, but to measure “every distance from 1 inch to 12 inches” would take the exact same number of marks as would “every distance from 1 inch to 2 inches” or from 1 inch to 1.01 inch… which would be an infinite number of marks to measure “every distance” in any case.

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