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Topic: Sad orc (Read 768 times) |
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alien2
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There is a gigantic sad orc. He was elf once, taken by the dark powers, but he retained his elf soul. He despises this present form of life, so he decides to kill himself along with nine dwarfs he recently captured. They are all on the big flat square roof of a tall tower, currently in the middle. All have secured wrists with 9 handcuffs, so that every pair secures wrists of two persons. This orc is to powerful for dwarfs to keep him in place, and he is immune to their strikes as well. He says to them that in an hour, he will slowly approach the roof's end, and then jump in exactly three minutes, as he can still count seconds with elfish precision. Orc also says that he might jump early or a bit later, that is 58 seconds after the last dwarf picks up the key for handcuffs. The key is enchanted, so it will produce a sound when touched. But this particular key can unlock only the last handcuffs securing wrists of orc and the last dwarf. The key is currently in orc's pocket, and he will put it near the edge later, after which dwarfs should form a line so that 1st dwarf can get to it, all nine standing right between orc and the key. Orc has retained one of his magic powers as well, so he cursed all dwarfs with spell called slow hands. Regardless, there is sequence in order of events, so it will take exactly 7 seconds to pass the key to the next dwarf (w/o unlocking). The above last pair is also twisted, because it will take exactly 3 seconds for 9th dwarf to unlock himself. And they all know all of the above facts. Sad orc used to like riddles, so he unlocks himself and leaves the handcuffed dwarfs alone on the roof for an hour, so they can discuss the optimal plan.
a) What is the fastest solution that could save nine lives?
b) What is the safe solution that guarantees nine lives saved?
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Archae
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Re: Sad orc
« Reply #1 on: May 10th, 2007, 12:32pm » |
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How long would it take for the dwarves to wrap around, and the first dwarf (who picked up the key) to unlock the 9th pair of handcuffs (the ones attaching the dwarves to the orc)? Also, will the orc jump off alone if he is no longer attached to the dwarves?
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| « Last Edit: May 10th, 2007, 12:33pm by Archae » |
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denis
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Re: Sad orc
« Reply #2 on: May 10th, 2007, 12:51pm » |
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the 1'st dwarf who picks up the key (the last in the line) unlocks his handcuffs. Then instead of passing the key to the next dwarf, let the same dwarf holding the key unlock the next set of handcuffs thus saving 7 seconds.
In fact, let this dwarf unlock all the handcuffs in the same order that was prescribed by the rules. The rules don't say that he dwarf must unlock his own handcuffs (unless the "enchanted" part about the key producing the sound when touched implies someting that is not explicitely stated). In the worst case, each dwarf in order can touch the key to produce the sound without really taking the key from dwarf#1 and let dwarf #1 do all the work.
This way you save 63 (9x7) seconds by not having to pass the key around from dwarf to dwarf.
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| « Last Edit: May 10th, 2007, 1:46pm by denis » |
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Grimbal
wu::riddles Moderator
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Re: Sad orc
« Reply #3 on: May 11th, 2007, 2:34am » |
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The curse is slow hands, not slow feet. They push the key down the line with the foot, it takes an estimated 3 seconds per person, that is 24 seconds to the last one and 27 to freedom.
But frankly, they should use the one hour to go down the stairs and go home.
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alien2
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Re: Sad orc
« Reply #4 on: May 16th, 2007, 8:22am » |
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on May 10th, 2007, 12:32pm, Archae wrote:| How long would it take for the dwarves to wrap around, and the first dwarf (who picked up the key) to unlock the 9th pair of handcuffs (the ones attaching the dwarves to the orc)? |
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Looks to me you got it Archae. Yep, they move coordinated like a damn caterpillar. And Grimbal is right, as the curse wasn't slow feet.
on May 10th, 2007, 12:32pm, Archae wrote:| Also, will the orc jump off alone if he is no longer attached to the dwarves? |
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Yep.
on May 11th, 2007, 2:34am, Grimbal wrote:The curse is slow hands, not slow feet. They push the key down the line with the foot, it takes an estimated 3 seconds per person, that is 24 seconds to the last one and 27 to freedom.
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Yes.  And note that 1st they take a step back except for the 1st and 9th dwarf. 
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