First, 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.).

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About 30 seconds. If I’m right. Clock’s still ticking if I’m wrong…

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)?

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.

Are we to calculate only whole inches or fractional parts? If fractional, how small a division is required?

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

About ten minutes but I think I’m cheating.

one “Mark” can do it.

No marks at all, and use a tape measure instead

No marks at all if the ruler is one inch wide.

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.

I cheated. Nice puzzle

Same as the 40lb nails problem…

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

Spoiler…

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.

Took me about two minutes to ascertain the minimum number of marks (Richard’s question).

Where they should be is another matter however.

I’ve got an answer, but I can’t prove it’s right.

There is an easy proof of the minimal number of marks required..

20 seconds. I am a slow reader, and I read it twice 🙂

the above proposal was a kind of tease – didn’t mean to send a spoiler.

A “serious” answer took me 10 sec.

Wasn’t timing it. Probably about five minutes with the hint from The Masked Twit.

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

15minutes from when I first read the question and couldn’t work it out. Just reread it and got it straight away.

I’m not familiar with inches. 😦

Cant find answer

I’m not familiar with inches,we use cm

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? 😉

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.

I took about 5 minutes and I think I have the correct answer but I’m not certain.

Got answer

Can’t get that answer

Inches? Really? Can we move into the 21st century?

Oh Jimmy Carter, where art thou?

I think iv’e got it.. but I’ll give a few more minutes before I check the Monday post.

I’m puzzled..