Bomb Planning
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From asas:
You have two 4 min fuses and a bomb. You want to be able to time the detonation of the bomb for 1min. Like the ropes puzzle, neither fuse burns at a uniform rate throughout.
How do you time your act of senseless destruction?
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You can time one minute like this:
Light both ends of the first fuse and one end of the second. Once the first fuse has burnt out, exactly two minutes have passed.
When lit from the other end as well the second fuse will now take exactly one minute to burn.
I don’t think this is the right answer though as you can’t use a fuse that is burning from both ends to detonate a bomb.
If you had a third fuse you could light it and then use the first two as described above to time three minutes. This would leave a one minute fuse.
Don’t attach either fuse to the bomb.
Set fire to one fuse at both ends, and the other in the middle. When the one at both ends has burned out, you have two minutes. Extinguish the burning fuse. You now how two one minute fuses. Attach one of these to the bomb.
Just realised the above solution leaves you with two (or one, depending on how it burns) pieces of fuse that together burn for two minutes, but are not necessarily one minute each. Oops.
Take one fuse, cut it in half. Light one of the halves and the whole fuse from one end at the same time. When the half burns out, immediately light both ends of the remaining half fuse. When that burns out, extinguish the whole fuse where it is. The remaining unburnt portion will burn for 1 minute.
This solution assumes you can count-out a minute or that you have a clock.
Light one fuse, count-out 60 seconds, then light the second fuse. Once the first fuse burns through, put out the second one. You now have one 1 minute fuse.
If, as suggested in another solution, you can use a watch, then simply light one fuse, let it burn for 3 minutes and put it out. Use whats out for your minute fuse.
Cut the first rope in two, so you have three pieces of rope altogether (2 from the cut, and one intact). Light all the pieces at both ends.
When one of the pieces that is cut is complete (this will always happen before the uncut piece), extinguish all the other ropes.
Take what is left of the other piece of the cut rope, and cut that in two. You now have 3 pieces of rope again.
Repeat burning all at both ends/extinguishing/cutting in two and you will eventually approach a 1 minute fuse on the uncut rope.
You need to divide the fuses in 4ths and have them burn into the middle as in the ropes exercise.
since fuses burn in both directions when lit in the middle you need only light half.
I would lay out 2 squares (4 sides equal) with one side overlapping the other and the bomb placed in the middle.
Assuming the fuse burns in all directions, I would light the center points on the outer sides.
—x—
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x x
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—B—
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x x
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—x—
lit the ends of the 1st fuse, and at the same time lit one end of the 2nd fuse. When the 1st fuse is out, stop the 2nd fuse. You now have a 2nd fuse with 2 mins left. Lit both ends of the 2nd fuse and constantly position and center the bomb to the middle of the remaining fuse. The fuse will complete burning and ignite the bomb at the end of 1 min.
I believe there is a problem with this question. I’m pretty sure you would need a third fuse! (Or am I wrong?)
First, the solution (which has already been explained, just clarifying).
Light both ends of fuse #1, and one end of fuse #2 at the same time. When fuse #1 has burned out (which should be after exactly 2 minutes), kill the flame of fuse #2. Fuse #2 now has 2 minutes remaining on it.
You could light both ends of fuse #2 to get one minute, but there is no way to know which part of the fuse will be the “center” once one minute has passed. Therefore, there is no safe and sure way to place this “center” next to the explosive part of the bomb!
You would need a third fuse, repeating the previous steps (first stopping fuse #3 along with fuse #2, and then using fuse #2 as a reference point for when to stop fuse #3, like was done with fuse #1)
I think the following solution works. Start with Fuse A and Fuse B. Cut both fuses into two pieces. Giving 4 fuses for Set A light all 4 ends and for Set B light both ends of one piece and one end of the other.
When any piece of fuse burns out cut the remaining fuse in the set, and relight the ends of the set so that Set A always has 4 ends burning, and Set B always has 3 ends burning. Repeat this.
Set A will become infinitesimally small after 1 minute (A 4minute fuse always burning in 4 places will burn out in 1 minute). At this point recombine the remaining pieces of Set B. This will be a one minute fuse (a 4minute fuse burning in 3 places will take 1.33mins to burn out, after 1min you will be left with 0.33mins if burning in 3 places or 1min if burning in place).
Solving this problem requires the bomber to prepare beforehand. While the process will take more than a minute, when you’re done you’ll have a one minute fuse.
On fuse #1, light both ends of the fuse at the same time you light one end of fuse #2. When fuse #1 burns out, extinguish fuse #2.
Now fuse #2 has two minutes left in it. Now to have the one minute trigger for the bomb, light both ends of fuse #2 which will burn up in one minute.
What a senseless act I’m helping to perpetrate.
After reading the other answers, I disagree with any solution that cuts a fuse because you have no way of saying that the cut lengths will burn for equal lengths. Since the fuses burn at a non-constant rate, cutting them in half does not half the time of the burn. It may be that one side burns for 1:53 and the other 2:07. There is just no way to know.
Also, I agree with Andreas in that, “Therefore, there is no safe and sure way to place this “center” next to the explosive part of the bomb!” So even my solution suffers from this. I’m not sure if the answer is a third fuse or if there is something we all haven’t figured out yet.
Michael,
My solution does not require the fuse to be cut into pieces that burn at an equal raate. In fact it relies on the fact that the ropes will burn at different rates.
Fuse 1 and Fuse 2
Light at the same time:
both ends of Fuse 1 and one end of Fuse 2.
Fuse 1 will be completely burnt in half of the time: 2 minutes (when both ends meet).
When this happens, put Fuse 2 off. Fuse 2 still has 2 minutes on it.
Now, light both sides of Fuse 2, it will take a minute for it to finish.
If the fuses are extinguishable, you will just need one fuse and a watch since you can be sure it will burn off at 4 minutes exactly
Light up the fuse and extinguish the burning fuse in exactly 3 minutes.
Now you have a fuse that would burn in 1 minute. The most straight forward logic but I get to save one fuse for future use
At 0:00
light fuse 1 from both ends
light fuse 2 from one end
light fuse 3 from one end
At 2:00 (marked by fuse 1 being consumed)
light fuse 3 from the other end
At 3:00 (marked by fuse 3 being consumed)
put out fuse 2
Now fuse 2 is a 1 min fuse