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Sun 10 Sep, 2006 05:15 pm
Grimy cement floor....black iron door....air heavy with....death ....you are alone....
In front of you 3 cardboard boxes - numbers chalked onto each - a lighter - a rusty tin trunk secured with a Master lock. Then a speaker crackles to life - a cold sinister voice penetrates the dank cell:
"You are here because you have wasted you're life solving riddles. There is one chance to escape. The key to the door is in the trunk. Do not tamper with it or try the wrong combination - it is packed with explosives. The numbers to the combination are on the three boxes. To find the correct sequence solve my riddle. The boxes contain fuses sorted according to the time they take to burn: 20 min, 1 hr and....the other seems to have slipped my mind - say about 1 hr. The sequence is according to the numbers on the 1 hr, 20 min and remaining fuse box in that order."
Your mind races ahead - 20 min fuse - a cinch....then 3x20.... that chain of thought stops dead - only one fuse in the first box, and 2 in each of the remaining. And no indication which box contains which fuses. How to solve the riddle?
What do you mean the air was heavy with......death....?
was it really stinky or something?
It's not a word riddle - the description is just to set the mood:)
Quote:the other seems to have slipped my mind - say about 1 hr.
Didn't you just say the numbers were written on the boxes?
Quote:Your mind races ahead - 20 min fuse - a cinch....then 3x20.... that chain of thought stops dead
What do you mean?
Why did you mention this if the tiddle is not supposed to involve tampering?
Quote:And no indication which box contains which fuses.
You said the fuses were sorted and put into marked boxes though?
Quote:only one fuse in the first box, and 2 in each of the remaining
Is this part of the given or is it supposed to be obvious from what the speaker said?
Quote:How to solve the riddle?
I don't get it...what exactly is the question?
The lighter is to light the fuses.
You can't tamper with the metal trunk - try to pry it open etc. Your only chance is to open it with the combination lock but you have one chance only - any mistake and you're blown to bits.
There is one 20 min fuse in one box, 2 one hr fuses in another and 2 approx 1 hour fuses in the remaining box. But you can't tell which is which.
The numbers on the 3 boxes are the the 3 parts of the combination, but you don't know the order in which they are used to open the combination lock. You can only find out the right sequence when you know which box contains which fuses. Obviously you don't have a watch.
How to find out - that is the question.
about an hr means it could be more or less than an hr
do the fuses burn uniformly? like half of the 1hr fuse burns for 30min?
About one hour means more or less. Say +- 5 minutes.
They don't burn uniformly.
a) all the fuses burn at the same rate, but have different lengths?
b) all the fuses are the same length, but burn at different rates?
c) the fuses could be any length and burn at the same or different rates?
d) how much of the length of the fuses can be observed?
The fuses all look identical. The length is not important.
One burns for 20 minutes, two burn for one hour and the other two for about one hour.
They are sorted according to how long they burn by the boxes and can take the fuses out can see them completely.
The fuses all look identical. The length is not important.
One burns for 20 minutes, two burn for one hour and the other two for about one hour.
They are sorted according to how long they burn by the boxes and you can take them out and see them completely.
Ok...light them all and wait until one of them is halfway done. The 20 min fuse burns the fastest so it will reach halfway the soonest.
At this point, the 60 min fuse will be the length of 5 times the shortest fuse.
The odd fuse will be slightly off in length.
How do you know when one is halfway done? - they burn unevenly.
I"ll be back in 1 1/2 hours if you have any more questions.
But I've given everything you need to know - don't assume anything else.
If they don't burn at constant rates, and we don't know their lengths, then we can't do any tricks with burning them like folding them up or comparing lengths or times because we only gain information when one is completely burned. But I assume from the problem that if a fuse burns completely, we lose because it's attached to a bomb and we can't detach it. Clearly the context of this problem, which bears little resemblance to any plausible circumstance, is obscuring the real question...so you might as well just state the actual question mathematically.
Do I have this right?
You have:
- a box with one fuse that you know is 20 minutes.
- a box with two fuses that are either both 60-minutes or both 60-ish minutes.
- another box with two fuses that are whatever the fuses in the second box aren't.
You need to determine which of the last two boxes contains the 60-minutes fuses.
Who said the fuses were attached to the bomb?
No. You have one box with a fuse could be 20min, 1 hour or approx 1 hour fuse.
And two boxes with 2 fuses each - also could be 20min, 1 hour or approx 1 hour fuses.
The fuses in each box burn for identiacl times - i.e. the fuses are sorted by box according to how long they burn.
If my previous post is correct AND the two 60-ish fuses have the same duration, here's the procedure:
T = 0
Light the 20 at one end. (fuse A, 20 minutes)
Light one from box 2 at one end. (fuse B1, X minutes)
Light the other from box 2 at both ends. (fuse B2, X minutes)
Light one from box 3 at one end. (fuse C1, Y minutes)
Light the other from box 3 at both ends. (fuse C2, Y minutes)
T = 20
Fuse A is gone.
Fuse B1 has X-20 minutes remaining.
Fuse B2 has X-40 minutes remaining.
Fuse C1 has Y-20 minutes remaining.
Fuse C2 has Y-40 minutes remaining.
Light the other end of fuse B1.
Extinguish one end of fuse B2.
Light the other end of fuse C1.
Extinguish one end of fuse C2.
If X=60, then B1 and B2 will finish burning at the same time (T = 40).
Otherwise, they will finish burning at different times.
So, the two fuses that finish burning at the same time are the 60-minute fuses.
You're assuming there is only 1 twenty minute fuse.
If there is only one 20-minute fuse, then it is easily identified as it is the only fuse without a mate.
KuRmA wrote:The fuses all look identical. The length is not important.
One burns for 20 minutes, two burn for one hour and the other two for about one hour.
They are sorted according to how long they burn by the boxes and can take the fuses out can see them completely.
It's not an assumption. It was stated as fact.
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