40 replies to this topic

[Silas Nunnery]

the 3 slaves cant open the door this way.......

As far as mechanics go, they can. They all would have a key that was identical with a cylinder shaft, a flap on one side to twist and another flap that goes in the the lock to turn the mechanics. the lock would have to have an extra large cylinder hole to accommodate the three keys as they would have to be turn in unison. It is a completely viable answer. No one said what type of lock it was. So I went ahead and used a lock from the far past that only required something that fit in the whole and move the internal mechanics. I will from here on assume they are using modern locks.

[Arjit Saraswat]

Mathematical explination

Spoiler for The impossible riddle!!!

The mathematical key cam after you gave the vizier all the keys but one. With the remaining number of unknown locks you needed to have 2 keys for each lock among the remaining slaves. In order to not allow only 2 to have the right combination of keys, each lock had to be assigned to a differnt combination of slaves. (ie. Lock A to slaves 1 and 4, Lock B to slaves 2 and 3, etc) that would leave 3! extra locks in addition to the lock the vizier does not control. Hence 7. If there were 5 slaves there would have to be 4!+1 locks and so on.

thnx man....... that was the answer i was looking for
gr8 job....

[Arjit Saraswat]

Spoiler for Try this alternative

Perhaps the treasure has only one lock that must be opened by a sectioned, symmetrically notched cylindrical key. The key would be sectioned lengthwise in multiples of 120 degrees, so that the visier would have a two-thirds section and all four slaves would have identical one-third sections.

As far as mechanics go, they can. They all would have a key that was identical with a cylinder shaft, a flap on one side to twist and another flap that goes in the the lock to turn the mechanics. the lock would have to have an extra large cylinder hole to accommodate the three keys as they would have to be turn in unison. It is a completely viable answer. No one said what type of lock it was. So I went ahead and used a lock from the far past that only required something that fit in the whole and move the internal mechanics. I will from here on assume they are using modern locks.

In this way you are distributing the parts of key to the slaves while the question says that the king distributed the keys to the locks of treasure to the slaves

[mickjc75]

From my interpretation of your problem, at least three slaves should be required to open the treasure. How are you going to distribute 3 keys among four slaves so any three will have a full set but no two will have a full set? If your answer is to give slaves 1, 2 and 3 a key each and not give any keys to slave 4, then you have changed the problem since slaves 4 with any other 2 could not open the treasure.

I interpreted the question the same way, that ANY combination of 3 slaves should be able to open the door.
If this were the problem, then I wonder what the answer would be?

Spoiler for The first step

Find a combination which allows any 3 of 6 slaves to unlock the chest, (if this is possible), then, stitch two slaves together (like a human centipede) and give them the job of vazir. Then you have a vazir who can open the chest with 1 more of 4 slaves.

[Silas Nunnery]

In this way you are distributing the parts of key to the slaves while the question says that the king distributed the keys to the locks of treasure to the slaves

My method has two keys (divided up: vizier+slave[key A], 3 slaves[key b]) and one lock. The riddle says the "king protected his treasure by giving the keys (I did figure in two keys) to the locks of the treasure." It never once states whether or not the keys where divided into pieces. If you want to fault me on semantics then simply say the riddle says locks (plural) so one should automatically be assumed not to be the answer. I admit my answer is wrong because of that fact. It is; however, the simplest answer as to how it would work with one lock. I was to eager to answer my first riddle on here. Next time I will pay closer attention to the riddle itself. Happy solving }: -)

[plainglazed]

Spoiler for an alternative, perhaps?

Instead of a series of hasps with a lock and key for each, what if the treasure chest is locked with a chain-like configuration? Within the links of the chain are nine larger rings (1-9). Each of the four slaves (A,B,C,D) and the vizier (V) have their own lock and key. Lock A goes through rings 1,2,3,4,7,8. Lock B goes through rings 1,2,3,5,6,8,9. Lock C goes through rings 1,2,4,5,7,8,9. Lock D goes through rings 2,3,6,7,8,9. Lock V goes through rings 3,4,5,6,7.

1-ABC-2-ABD-3-AV-4-CV-5-BV-6-DV-7-ACD-8-BCD-9

So if the vizier and any one slave or if any three slaves unlock their respective locks, the chain is broken.

Can't fully visualize this but think it would work

[Avileet]

what if the vizer was also a slave. that why he/she would have a key for being the slave and also a key for being a slave. So if the Vizer has 2 keys he/she only needed one more slave to help open the slave room. otherwise the 3 remaining slaves can open the room by themselves. so to answer the question as to how many locks there are, i think the answer is 3.

[Arjit Saraswat]

Spoiler for an alternative, perhaps?

Instead of a series of hasps with a lock and key for each, what if the treasure chest is locked with a chain-like configuration? Within the links of the chain are nine larger rings (1-9). Each of the four slaves (A,B,C,D) and the vizier (V) have their own lock and key. Lock A goes through rings 1,2,3,4,7,8. Lock B goes through rings 1,2,3,5,6,8,9. Lock C goes through rings 1,2,4,5,7,8,9. Lock D goes through rings 2,3,6,7,8,9. Lock V goes through rings 3,4,5,6,7.

1-ABC-2-ABD-3-AV-4-CV-5-BV-6-DV-7-ACD-8-BCD-9

So if the vizier and any one slave or if any three slaves unlock their respective locks, the chain is broken.

Can't fully visualize this but think it would work

in this way, 2 slaves can break the chain together... but the question states that it is opened when 3 of them worked together.....
but gud try

[Arjit Saraswat]

I interpreted the question the same way, that ANY combination of 3 slaves should be able to open the door.
If this were the problem, then I wonder what the answer would be?

Spoiler for The first step

Find a combination which allows any 3 of 6 slaves to unlock the chest, (if this is possible), then, stitch two slaves together (like a human centipede) and give them the job of vazir. Then you have a vazir who can open the chest with 1 more of 4 slaves.

sorry but your step is wrong
what you have to do is give every key to a different pair of salves e.g. give key 1 to slaves A and B... keep diving the keys until no more pair of slaves is left... now say you have divided n keys to the slaves.... now give (n+1)th key to every slave and give n keys to the vizier

[plainglazed]

in this way, 2 slaves can break the chain together... but the question states that it is opened when 3 of them worked together.....
but gud try

Spoiler for some thoughts

Don't think two slaves can unlock the chain. With my solution the vizier's lock goes through rings 3,4,5,6,7 so effectively the links between those rings cannot be broken by two slaves.

So if two slaves were to break the chain, it would have to be between rings 1 and 2, 2 and 3, 7 and 8, or 8 and 9.

If slaves A & B work together; lock C secures rings 1 and 2, lock D secures rings 2 and 3, and locks C and D secure rings 7 and 8 and rings 8 and 9.

If slaves A & C work together; lock B secures rings 1 and 2, locks B and D secure rings 2 and 3, lock D secures rings 7 and 8, and locks B and D secure rings 8 and 9.

If slaves A & D work together; locks B and C secure rings 1 and 2, lock B secures rings 2 and 3, lock C secures rings 7 and 8, and locks B & C secure rings 8 and 9.

If slaves B & C work together; lock A secures rings 1 and 2, locks A and D secure rings 2 and 3 and rings 7 and 8, and lock D secures rings 8 and 9.

If slaves B & D work together; locks A and C secure rings 1 and 2, lock A secures rings 2 and 3, locks A and C secure rings 7 and 8, and lock C secures rings 8 and 9.

If slaves C & D work together; locks A and B secure rings 1 and 2 and rings 2 and 3, lock A secures rings 7 and 8 and lock B secures rings 8 and 9.
A third slaves cooperation is needed in every case.

To break the chain between rings 1 and 2, slaves A,B,C must work together
To break the chain between rings 2 and 3, slaves A,B,D must work together
To break the chain between rings 7 and 8, slaves A,C,D must work together
To break the chain between rings 8 and 9, slaves B,C,D must work together