Logic puzzle

Posted by: TigerJimmy

Logic puzzle - 09/12/2005 06:04

Since the "will the plane fly" thread got so much attention, here is my favorite logic puzzle:

Suppose you have two lengths of cannon fuse. Suppose that you know that each of these fuses will take exactly 60 minutes to burn, but they burn at a variable rate along the length of the fuse (you can't just cut a fuse in half to get 30 minutes of burn time).

Using only these fuses (and a box of matches), how would you use them to measure a 45 minute interval?

Good luck. This one took me a couple of days.

Jim
Posted by: pgrzelak

Re: Logic puzzle - 09/12/2005 10:39

Hmmm... I will take a shot at this one...

My thought is that take one fuse and light it on both ends. This way, you know the burn time for this fuse is 30 minutes, no matter how quickly it burns along any point of its length.

As soon as this fuse burns completely out and the two burning points meet, light the second fuse at both ends, and in the center. This should give you the last 15 minutes. Edit: Hmmm - is this 15 minute part valid? I am not so sure now...

Insert Edna St. Vincent Millay poem here...
Posted by: frog51

Re: Logic puzzle - 09/12/2005 13:58

awkward solution - light match at the same time as the fuse, light another one each time one goes out. Once the fuse goes out, count the number of burnt matches and multiply by 3/4.

fiddly, and probably not the answer you want

[edit] - and also assumes reasonable tolerance in match quality
Posted by: andy

Re: Logic puzzle - 09/12/2005 14:07

Quote:
and also assumes reasonable tolerance in match quality


and a very big box of matches
Posted by: lectric

Re: Logic puzzle - 09/12/2005 15:14

Solution attached, but solve it yourself! Great puzzle.
Posted by: andy

Re: Logic puzzle - 09/12/2005 15:20

Quote:
Edit: Hmmm - is this 15 minute part valid? I am not so sure now...



Don't think so, thanks to the unequal burn time along the fuses.

For example, imagine that the second fuse takes burns very quickly for 99% of its length and very slowly for the last 1%, such that the last 1% takes 59 minutes.

If you light it at both ends and the middle, then one half will burn in 15 seconds and the other half will take 27 minutes 45 seconds to burn (roughly).
Posted by: lectric

Re: Logic puzzle - 09/12/2005 16:47

So.... 17 views and no responses... Can someone tell me if i'm right?
Posted by: andy

Re: Logic puzzle - 09/12/2005 17:08

You're wrong, try again.
Posted by: wfaulk

Re: Logic puzzle - 09/12/2005 17:26

Spoiler (we need a ROT13 hover mode or something):

I don't see how he's wrong. I think we can both agree on the first part, and that that takes up 30 minutes. The second part is probably the contentious one, and it seems to me that that's correct, too. It's already burned 30 minutes, and burning from both ends means it's going to burn the remaining 30 minutes at double-speed.
Posted by: lectric

Re: Logic puzzle - 09/12/2005 17:48

That is exactly my thinking.... The only issue I can see is the timing it takes to actually light the fuse.
Posted by: Mataglap

Re: Logic puzzle - 09/12/2005 18:07

As with most of these things any truly scientific approach to the problem quickly highlights semantic tricks to the question.

If the burn rate truly is variable -- as Andy points out the legitimate but extreme case -- then that decouples burn time from fuse length, which invalidates the whole idea of being able to define 60 minute fuses but not 30 minute fuses

So it's a clever question for Mensa wannabes but not scientific theory.

--Nathan
Posted by: Robotic

Re: Logic puzzle - 09/12/2005 18:16

Quote:
Spoiler (we need a ROT13 hover mode or something):

I don't see how he's wrong. I think we can both agree on the first part, and that that takes up 30 minutes. The second part is probably the contentious one, and it seems to me that that's correct, too. It's already burned 30 minutes, and burning from both ends means it's going to burn the remaining 30 minutes at double-speed.

More Spoiler-
If you think of it in terms of % of time burned, then it certainly makes sense to me... 100%=60 minutes. Let 50% of the *time* burn and you don't have 50% of the length, but still the amount of fuse has been used that would have burned that percent of time anyway.
So, burning from both ends of fuse 1 doesn't give you the middle of the length of fuse, but will give you the middle of length of time (30 minutes).
If fuse 2 is lit from one end at the same time that fuse 1 is lit from both ends, then fuse 2 only has 30 minutes left to burn when fuse 1 is gone. Cut that time in half by starting the 2nd end of fuse 2.

/cheated by looking
//agreeing with the answer is still fun
///slashies!
Posted by: wfaulk

Re: Logic puzzle - 09/12/2005 18:37

Just a test:
V qba'g frr ubj ur'f jebat. V guvax jr pna obgu nterr ba gur svefg cneg, naq gung gung gnxrf hc 30 zvahgrf. Gur frpbaq cneg vf cebonoyl gur pbagragvbhf bar, naq vg frrzf gb zr gung gung'f pbeerpg, gbb. Vg'f nyernql ohearq 30 zvahgrf, naq oheavat sebz obgu raqf zrnaf vg'f tbvat gb ohea gur erznvavat 30 zvahgrf ng qbhoyr-fcrrq.
Posted by: lectric

Re: Logic puzzle - 09/12/2005 18:39

Holy crap, that's cool....
Posted by: JeffS

Re: Logic puzzle - 09/12/2005 18:47

I've heard this before and lectric's solution is what I came up with. I think he's right.
Posted by: andy

Re: Logic puzzle - 09/12/2005 20:09

Quote:

I don't see how he's wrong.


I got confused, I thought I was replying to Paul's incorrect solution still. My mistake.
Posted by: TigerJimmy

Re: Logic puzzle - 09/12/2005 20:42

You got it, and I like how you posted the answer. Its very rewarding when you figure it out!

Jim
Posted by: Robotic

Re: Logic puzzle - 09/12/2005 20:51

That's cooler than the original topic!
Character shifted by 13?
Posted by: wfaulk

Re: Logic puzzle - 09/12/2005 20:56

Yeah. I can do it because I'm a moderator and can post HTML (and JavaScript, as it turns out). I should petition Tom to add a [rot13] tag so we can all do it.
Posted by: AndrewT

Re: Logic puzzle - 09/12/2005 23:35

Another alternative is [spoiler][/spoiler] tags that the BBS renders using the DHTML mouseover event. They appear as a solid black block but upon mouseover the browser alters the foreground/background colours making the text readable.

A bit of Googling turned up a few very old user hacks for this on UBB.threads boards so perhaps your idea is better.
Posted by: gbeer

Re: Logic puzzle - 10/12/2005 01:30

On another BBS I see posters setting the FG and BG colors the same. Highlighting the text reviles the answer.
Posted by: larry818

Re: Logic puzzle - 10/12/2005 02:02

Quote:
Highlighting the text reviles the answer.


reviles...
Posted by: gbeer

Re: Logic puzzle - 10/12/2005 02:18

Crap, I hate spell checkers!
Posted by: wfaulk

Re: Logic puzzle - 10/12/2005 03:20

Well, naming the tag spoiler vs. rot13 is just semantics.

All the stuff about text color and whatnot has the problem that it will either not be concealed for some browsers or it will not be accessible by some browsers. Using rot13 means that those browers will continue to have concealed text that is still accessible, even if not directly in the browser.
Posted by: Robotic

Re: Logic puzzle - 10/12/2005 19:06

Quote:
On another BBS I see posters setting the FG and BG colors the same. Highlighting the text reviles the answer.

I don't see that the poster has control over the background color on this BBS, though.
Nifty ideas!
Posted by: matthew_k

Re: Logic puzzle - 10/12/2005 19:09

Quote:
I don't see that the poster has control over the background color on this BBS, though.

The viewer does though. You can chose your stylesheet on the setup page. I use a nice light one, which works until someone specifes light colored text.

Matthew
Posted by: andy

Re: Logic puzzle - 10/12/2005 19:58

Quote:
I use a nice light one, which works until someone specifes light colored text.



<AOL>me too</AOL>
Posted by: gbeer

Re: spoiler method, this may be too practical. - 11/12/2005 18:50

See the attachment. edit: You should be able to figure this one out without looking.
Posted by: wfaulk

Re: spoiler method, this may be too practical. - 11/12/2005 19:11

Spoiler:
Vg'f na njshy ybg bs rssbeg.
Posted by: RobotCaleb

Re: spoiler method, this may be too practical. - 12/12/2005 16:52

Tom, could you set it to put <pre> tags around the spoiled text? Rendering in a fixed-width font makes it so it doesn't jump around when you put your mouse over the tail-end of the size-changing text.
Posted by: RobotCaleb

Re: spoiler method, this may be too practical. - 12/12/2005 16:53

heh.
Spoiler text would be better, I suppose.
Posted by: RobotCaleb

Re: spoiler method, this may be too practical. - 12/12/2005 16:55

Oops, didn't see the dedicated thread.
Posted by: gbeer

Re: spoiler method, this may be too practical. - 13/12/2005 01:19

Quote:
<font class="small">Spoiler:<br/></font><span onMouseOver="javascript:rot13(this)" onMouseOut="javascript:rot13(this)">Vg'f na njshy ybg bs rssbeg.</span>


Ha!
Try hovering over the last few letters in the encripted message.

PS, Quoting breaks it.
Posted by: RobotCaleb

Re: spoiler method, this may be too practical. - 13/12/2005 02:47

Yeah, that's what my post above was about. The last few letters, that is.