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Fuse on Fire

Hi
  Can we have a solution of something like the bomber folds one of the fuse into half and attaches it to the other fuse. So whenever he burns it would take a total of 45 seconds.

  A second solution I thought was placing the two fuses in the shape of "T"  that ways when he burns the tail of T it will take 30 seconds to go to the head and then 15 seconds to go to the end of whatever he wants to detonate.

Any suggestions are welcome.

--Harpreet

Harpreet
Tuesday, July 16, 2002

I think you've missed the point -- each fuse is of "varying thickness", presumably causing the fuse to burn at varying rates through its length.  So the fuse is not guaranteed to burn for 15 seconds from either end to the midpoint (or vice versa).

Having said that, I have to say that this is another poorly stated problem -- I'd put several more !!! after the "aha" in the rating -- because the interviewee is likely to try to come up with a solution that the bomb-maker can set up and walk away from.  That's the whole friggin' point of a fuse, for crying out loud.  If you have to light a fuse and stand there waiting for it to go out so you can light the 30-second fuse, that's a 30-second fuse, not a 45-second fuse.

If I were given this question as stated and then penalized for missing the "answer", I'd thank the interviewer for making it clear to me that I don't want to work there.

J. Michael Hammond
Wednesday, July 17, 2002

Here is a solution:

Take 3 fuses and tie them together, making a chain, so that the first fuse is knotted to the second fuse, and the second to the third. Make sure that the next fuse's knot is tied around the middle of the preceeding fuse.

The fire will burn halfway down the first fuse, which is 15 sconds then down the second, and then the third, for a total burn of 45 seconds.

Joey Kelly
Wednesday, July 24, 2002

Aargh. That won't work, will it?

Nevermind.

Joey Kelly
Wednesday, July 24, 2002

Why not just light one of the fuses, wait 15 seconds and put it out. Then tie them together blah blah.

Vlad
Wednesday, July 24, 2002

Vlad, that makes sense, but only for a sane bomber.  We're discussing a MAD bomber here.

Excellent straightforward solution otherwise, though.  ::applause::

Stephen Hoffman
Wednesday, July 24, 2002

Firstly, I agree that this problem is not worded well at all.  I also made the (seemingly logical) assumption that the bomber must act 45 seconds before the bomb is to go off, and after that he is not allowed to manipulate the fuses.  Then, because of what I think is poor phrasing ("how can he arrange the fuses...?", I concluded that he could simply fold one fuse in half and use it in addition to a full fuse in order to get his desired delay.

Another part that threw me was "he has two fuses... of varying thickness..."  I thought this meant that the two fuses were not of the same thickness, but that each fuse burned at a constant rate.  Re-reading the problem, I realize that this doesn't make sense, and I'm willing to conceed that this logical error was my fault - although I'll argue that it should have been made more clear.

One issue I have with Vlad's approach is that I read the problem to imply that the bomber had no way of timing just 15 seconds other than that mentioned in the suggested answer.  Otherwise he could simply wait 15 seconds (no need to light a fuse to time it) and then light one of the fuses and let it burn for the full 30 seconds.

In summary, I don't think it's valid to not somehow inform the reader that the bomber can manipulate either of the fuses after the 45-second mark.  However, how this can be done without making the problem significantly easier is probably a fairly challenging (semantic) problem in itself.

Drew Boyles
Saturday, July 27, 2002

clearly the problem is unsolvable based on the reasons you all just gave.

therefore i propose a new problem:

you have 3 fuses (variable widths blah blah). each has 30 seconds. you desire a 45 second fuse.

WHAT DO YOU DO?

Paull Pot
Monday, July 29, 2002

Nice amendment to the question, Paull.

Tie fuses A and B together to make 1-minute fuse AB. Light fuse C at both ends, and at the same time light fuse AB at one end. Once C has burnt itself out, fuse AB has 45 seconds left to go?

This gets around Drew's complaint that the bomber might not have a stopwatch. Drew, your other point (that you might as well just wait 15 seconds then light the 2nd fuse) doesn't stand up so well, because at least Vlad's solution allows the bomber the full 45 seconds to get out of the building.

Oh, am I allowed to suggest cutting the fuses in half along their length and tying them together again with one length reversed? This would guarantee symetrical burn-rates from each end, so you could use the "tie one fuse to the middle of the other" trick...

Adrian Gilby
Monday, August 05, 2002

SOLUTION:

fuses are of variable THICKNESS. so just split one of the fuses down the middle sideways so you have two skinnier fuses of equal length. then you have 1 fuse of 30 seconds, and 2 of 15 seconds.

in response to the "official" solution. the question says the bomber is MAKING bombs, not detonating them. the official solution requires the bomber to be at the site of detonation, which totally destroys the purpose of making the bomb. if the bomber is able to be at the site of detonation, then all the bomber needs is a timer. that destroys the purpose of the question.

rather, i think the purpose of the question is to get you to think outside of the standard of "halving" something right down the middle into 2 pieces, but halve it the other way. it's the only logical solution given the phrasing of the problem.

f00
Friday, February 21, 2003

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