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        riddles >> hard >> 1 ring, 100 locks
        
(Message started by: dojo on Oct 22^nd, 2004, 9:10pm)

Title: 1 ring, 100 locks
Post by dojo on Oct 22^nd, 2004, 9:10pm

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 -_-

Title: Re: 1 ring, 100 locks
Post by Rezyk on Oct 23^rd, 2004, 11:45am

Here's one way (attached). Proof of correctness is omitted.

Title: Re: 1 ring, 100 locks
Post by Obob on Oct 23^rd, 2004, 2:47pm

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.

Title: Re: 1 ring, 100 locks
Post by Icarus on Oct 23^rd, 2004, 7:16pm

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 ...

Title: Re: 1 ring, 100 locks
Post by dojo on Oct 24^th, 2004, 2:10am

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 -_-

Title: Re: 1 ring, 100 locks
Post by Icarus on Oct 24^th, 2004, 3:10pm

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.

Title: Re: 1 ring, 100 locks
Post by william wu on Oct 24^th, 2004, 5:10pm

Wow! That's neat :)

Title: Re: 1 ring, 100 locks
Post by Rezyk on Oct 27^th, 2004, 8:11am

I wonder if there is a general solution for n locks where the required rope length doesn't grow as fast as [theta](2ⁿ).

Title: Re: 1 ring, 100 locks
Post by fatball on Nov 25^th, 2004, 10:40am

Quote:

Taking off any one lock in Rezyk's solution does free them all.

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?

Title: Re: 1 ring, 100 locks
Post by Icarus on Nov 25^th, 2004, 10:21pm

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.

Title: Re: 1 ring, 100 locks
Post by Grimbal on Nov 26^th, 2004, 2:01pm

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.