#271692 - 09/12/2005 06:04
Logic puzzle
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old hand
Registered: 15/02/2002
Posts: 1049
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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
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#271693 - 09/12/2005 10:39
Re: Logic puzzle
[Re: TigerJimmy]
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carpal tunnel
Registered: 15/08/2000
Posts: 4859
Loc: New Jersey, USA
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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...
Edited by pgrzelak (09/12/2005 12:36)
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Paul Grzelak
200GB with 48MB RAM, Illuminated Buttons and Digital Outputs
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#271694 - 09/12/2005 13:58
Re: Logic puzzle
[Re: TigerJimmy]
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pooh-bah
Registered: 09/08/2000
Posts: 2091
Loc: Edinburgh, Scotland
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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
Edited by frog51 (09/12/2005 14:00)
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MkIIa, blue lit buttons, memory upgrade, 1Tb in Subaru Forester STi
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#271695 - 09/12/2005 14:07
Re: Logic puzzle
[Re: frog51]
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carpal tunnel
Registered: 10/06/1999
Posts: 5916
Loc: Wivenhoe, Essex, UK
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Quote:
and also assumes reasonable tolerance in match quality
and a very big box of matches
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#271696 - 09/12/2005 15:14
Re: Logic puzzle
[Re: TigerJimmy]
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pooh-bah
Registered: 20/01/2002
Posts: 2085
Loc: New Orleans, LA
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Solution attached, but solve it yourself! Great puzzle.
Attachments
271801-solution.txt (177 downloads)
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#271697 - 09/12/2005 15:20
Re: Logic puzzle
[Re: pgrzelak]
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carpal tunnel
Registered: 10/06/1999
Posts: 5916
Loc: Wivenhoe, Essex, UK
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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).
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#271698 - 09/12/2005 16:47
Re: Logic puzzle
[Re: lectric]
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pooh-bah
Registered: 20/01/2002
Posts: 2085
Loc: New Orleans, LA
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So.... 17 views and no responses... Can someone tell me if i'm right?
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#271699 - 09/12/2005 17:08
Re: Logic puzzle
[Re: lectric]
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carpal tunnel
Registered: 10/06/1999
Posts: 5916
Loc: Wivenhoe, Essex, UK
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You're wrong, try again.
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#271700 - 09/12/2005 17:26
Re: Logic puzzle
[Re: andy]
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carpal tunnel
Registered: 25/12/2000
Posts: 16706
Loc: Raleigh, NC US
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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.
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#271701 - 09/12/2005 17:48
Re: Logic puzzle
[Re: wfaulk]
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pooh-bah
Registered: 20/01/2002
Posts: 2085
Loc: New Orleans, LA
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That is exactly my thinking.... The only issue I can see is the timing it takes to actually light the fuse.
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#271702 - 09/12/2005 18:07
Re: Logic puzzle
[Re: wfaulk]
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enthusiast
Registered: 11/06/2003
Posts: 384
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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
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#271703 - 09/12/2005 18:16
Re: Logic puzzle
[Re: wfaulk]
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pooh-bah
Registered: 06/04/2005
Posts: 2026
Loc: Seattle transplant
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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!
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#271704 - 09/12/2005 18:37
Re: Logic puzzle
[Re: wfaulk]
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carpal tunnel
Registered: 25/12/2000
Posts: 16706
Loc: Raleigh, NC US
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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.
Edited by drakino (10/12/2005 21:24)
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#271705 - 09/12/2005 18:39
Re: Logic puzzle
[Re: wfaulk]
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pooh-bah
Registered: 20/01/2002
Posts: 2085
Loc: New Orleans, LA
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Holy crap, that's cool....
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#271706 - 09/12/2005 18:47
Re: Logic puzzle
[Re: lectric]
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carpal tunnel
Registered: 14/01/2002
Posts: 2858
Loc: Atlanta, GA
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I've heard this before and lectric's solution is what I came up with. I think he's right.
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Rome did not create a great empire by having meetings; they did it by killing all those who opposed them.
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#271707 - 09/12/2005 20:09
Re: Logic puzzle
[Re: wfaulk]
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carpal tunnel
Registered: 10/06/1999
Posts: 5916
Loc: Wivenhoe, Essex, UK
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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.
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#271708 - 09/12/2005 20:42
Re: Logic puzzle
[Re: lectric]
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old hand
Registered: 15/02/2002
Posts: 1049
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You got it, and I like how you posted the answer. Its very rewarding when you figure it out!
Jim
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#271709 - 09/12/2005 20:51
Re: Logic puzzle
[Re: wfaulk]
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pooh-bah
Registered: 06/04/2005
Posts: 2026
Loc: Seattle transplant
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That's cooler than the original topic! Character shifted by 13? 
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#271710 - 09/12/2005 20:56
Re: Logic puzzle
[Re: Robotic]
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carpal tunnel
Registered: 25/12/2000
Posts: 16706
Loc: Raleigh, NC US
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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.
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#271711 - 09/12/2005 23:35
Re: Logic puzzle
[Re: wfaulk]
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old hand
Registered: 16/02/2002
Posts: 867
Loc: Oxford, UK
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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.
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#271712 - 10/12/2005 01:30
Re: Logic puzzle
[Re: AndrewT]
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carpal tunnel
Registered: 17/12/2000
Posts: 2665
Loc: Manteca, California
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On another BBS I see posters setting the FG and BG colors the same. Highlighting the text reviles the answer.
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#271713 - 10/12/2005 02:02
Re: Logic puzzle
[Re: gbeer]
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old hand
Registered: 01/10/2002
Posts: 1039
Loc: Fullerton, Calif.
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Quote:
Highlighting the text reviles the answer.
reviles... 
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#271714 - 10/12/2005 02:18
Re: Logic puzzle
[Re: larry818]
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carpal tunnel
Registered: 17/12/2000
Posts: 2665
Loc: Manteca, California
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Crap, I hate spell checkers!
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Glenn
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#271715 - 10/12/2005 03:20
Re: Logic puzzle
[Re: AndrewT]
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carpal tunnel
Registered: 25/12/2000
Posts: 16706
Loc: Raleigh, NC US
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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.
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#271716 - 10/12/2005 19:06
Re: Logic puzzle
[Re: gbeer]
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pooh-bah
Registered: 06/04/2005
Posts: 2026
Loc: Seattle transplant
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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!
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#271717 - 10/12/2005 19:09
Re: Logic puzzle
[Re: Robotic]
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pooh-bah
Registered: 12/02/2002
Posts: 2298
Loc: Berkeley, California
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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
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#271718 - 10/12/2005 19:58
Re: Logic puzzle
[Re: matthew_k]
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carpal tunnel
Registered: 10/06/1999
Posts: 5916
Loc: Wivenhoe, Essex, UK
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Quote:
I use a nice light one, which works until someone specifes light colored text.
<AOL>me too</AOL>
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#271719 - 11/12/2005 18:50
Re: spoiler method, this may be too practical.
[Re: wfaulk]
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carpal tunnel
Registered: 17/12/2000
Posts: 2665
Loc: Manteca, California
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See the attachment. edit: You should be able to figure this one out without looking.
Attachments
271953-spoiler.txt (139 downloads)
Edited by gbeer (11/12/2005 18:52)
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Glenn
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#271720 - 11/12/2005 19:11
Re: spoiler method, this may be too practical.
[Re: gbeer]
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carpal tunnel
Registered: 25/12/2000
Posts: 16706
Loc: Raleigh, NC US
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Spoiler:
Vg'f na njshy ybg bs rssbeg.
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#271721 - 12/12/2005 16:52
Re: spoiler method, this may be too practical.
[Re: wfaulk]
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pooh-bah
Registered: 15/01/2002
Posts: 1866
Loc: Austin
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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.
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#271722 - 12/12/2005 16:53
Re: spoiler method, this may be too practical.
[Re: RobotCaleb]
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pooh-bah
Registered: 15/01/2002
Posts: 1866
Loc: Austin
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heh.
Spoiler text would be better, I suppose.
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#271723 - 12/12/2005 16:55
Re: spoiler method, this may be too practical.
[Re: RobotCaleb]
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pooh-bah
Registered: 15/01/2002
Posts: 1866
Loc: Austin
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Oops, didn't see the dedicated thread.
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#271724 - 13/12/2005 01:19
Re: spoiler method, this may be too practical.
[Re: wfaulk]
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carpal tunnel
Registered: 17/12/2000
Posts: 2665
Loc: Manteca, California
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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.
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Glenn
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#271725 - 13/12/2005 02:47
Re: spoiler method, this may be too practical.
[Re: gbeer]
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pooh-bah
Registered: 15/01/2002
Posts: 1866
Loc: Austin
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Yeah, that's what my post above was about. The last few letters, that is.
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