## Tuesday, September 08, 2009

### The Great and Powerful Sultan

The harem of a great and powerful sultan was protected by a door with many locks.  The sultan had distributed keys to a vizier and four slaves for safe keeping.

The sultan, knowing well how men can be tempted, had distributed the keys so that the vizier could only open the door if he was with one of the slaves, while the slaves could only open the door if three of them worked together.

How many locks were there on the door?

Hint: Although there are many possible answers, I'm looking for the minimum number of locks.

Hint 2: Each person can hold more than one key.

1. I would say there are three locks
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2. One? Only one of the keys works and it's being held by one of the slaves. The slaves don't know which key is the right one but the vizier does.

That's my guess anyway.

3. three, the vizier had two keys and the slaves each had one. Though the vizier would have to have the same two keys as two slaves unless all the locks had the same key, but then he wouldn't need a slave with him. Unless the sultan deceived the vizier into thinking they were different locks but really they could use the same key. Or there was only one key needed but the reason the vizier needed a slave is because he is short and the lock is high up, then the slaves are really short because they need three of them to reach the lock.

4. 7 Locks.
Lets say the Locks are A,B,C,D,E,F and G
Keys with:
Vizier - A,B,C,D,E,F
Slave 1- A,D,F,G
Slave 2- B,C,F,G
Slave 3- C,B,E,G
Slave 4- D,A,E,G

5. I believe seven locks is the answer. I don't believe any of the explanations given cover all the rules otherwise.

Anonymous explained how seven locks (and keys) works, so I won't re-explain it.

6. 1
4 different modules that are the same, the vizier has 2 and each slave has 1 each therefore if the lock requires 3, three slaves or 1 slave with 1 vizier

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