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Topic: 1 ring, 100 locks (Read 993 times) |
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dojo
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1 ring, 100 locks
« on: Oct 22nd, 2004, 9:10pm » |
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You are given a circular rope (a ring) and 100 locks. The rope is as long as you want, and as thin as you want, yet it is very strong. You have to put the locks on the rope, in a way that it is impossible to remove any lock from the rope (while the locks are locked), yet, when any (one) lock is unlocked, all of the other locks can be removed without unlocking them.
anyone know the answer to this riddle? i forgot it and its really simple -_-
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Rezyk
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Here's one way (attached). Proof of correctness is omitted.
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Obob
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I don't think that solution works. If you were to unlock the 100th lock, it wouldn't free the other 99 from the loop.
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Icarus
wu::riddles Moderator
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Re: 1 ring, 100 locks
« Reply #3 on: Oct 23rd, 2004, 7:16pm » |
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No - without the 100th lock, you can simply pull the string out of the others. Look at his one-lock loop. You can pull the string out without unlocking. It is only lock 100 that stops you from doing this to the 99 loop, and then the 98 loop, and then ...
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dojo
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Re: 1 ring, 100 locks
« Reply #4 on: Oct 24th, 2004, 2:10am » |
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taking off any lock has to free them all not one that you suggest. *as in the last lock
or else you could just simply lock all the locks onto the one lock and lock that onto the rope -_-
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| « Last Edit: Oct 24th, 2004, 2:10am by dojo » |
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Icarus
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Re: 1 ring, 100 locks
« Reply #5 on: Oct 24th, 2004, 3:10pm » |
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Taking off any one lock in Rezyk's solution does free them all. I was addressing Obob's complaint about the 100th lock. Look again at Rezyk's solution, and you should see why removing any lock works.
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"Pi goes on and on and on ...
And e is just as cursed.
I wonder: Which is larger
When their digits are reversed? " - Anonymous
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Rezyk
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Re: 1 ring, 100 locks
« Reply #7 on: Oct 27th, 2004, 8:11am » |
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I wonder if there is a general solution for n locks where the required rope length doesn't grow as fast as [theta](2n).
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| « Last Edit: Oct 27th, 2004, 8:12am by Rezyk » |
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fatball
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Re: 1 ring, 100 locks
« Reply #8 on: Nov 25th, 2004, 10:40am » |
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Quote:| Taking off any one lock in Rezyk's solution does free them all. |
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I think different people have different meanings of what is the 100th lock? Is it the first lock that ties the folded rope into one piece? or is it the last lock that was locked to the rope? I would say only by unlocking the only critical lock (the other 99 locks ar egeneric in nature) can you free all locks without having to unlock them...Icarus, can you explain how you can unlock all locks by merely taking off one of those 99 generic locks?
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Icarus
wu::riddles Moderator
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Re: 1 ring, 100 locks
« Reply #9 on: Nov 25th, 2004, 10:21pm » |
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The locks are numbered by the order in which they are added according to Rezyk's scheme. The 100th lock is the one that is simply linked with the final loop. Removal of any of the lesser locks, and the loop that the lock completed is now open. All higher locks (added later in the scheme) can be threaded off the ends. Lower level locks are then removed in the same fashion as is possible by the removal of the 100th lock.
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"Pi goes on and on and on ...
And e is just as cursed.
I wonder: Which is larger
When their digits are reversed? " - Anonymous
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Grimbal
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Frankly, with a 100 locks, you need to pass the string 1030 times through the lock.
Attached is a non-exponential solution. Attach the locks as per the drawing. It is circular with the last lock linked back to the first one. Removing one lock frees all others in turn.
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