*vizier and 4 slaves*in such a way that vizier could open the treasure if he was with any of the slaves , and the slaves could open the treasure if 3 of them worked together.

**How many locks do the treasure have?**

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Guest Message by DevFuse

Started by Arjit Saraswat, Nov 28 2011 06:54 AM

40 replies to this topic

Posted 28 November 2011 - 06:54 AM

A very intelligent king protected his treasure by giving the keys to the locks of the treasure to his *vizier and 4 slaves* in such a way that vizier could open the treasure if he was with any of the slaves , and the slaves could open the treasure if 3 of them worked together.

**How many locks do the treasure have?**

Posted 28 November 2011 - 07:07 AM

i myself have found the answer..... but i would like someone giving a general solution

Posted 28 November 2011 - 08:00 AM

This is my solution...

Spoiler for The impossible riddle!!!

**Edited by Silas Nunnery, 28 November 2011 - 08:04 AM.**

Posted 28 November 2011 - 10:48 AM

Spoiler for solution

Posted 28 November 2011 - 10:55 AM

Hmm well I'm not sure how general this is, but this is how I found it.. (maybe the same way as you?)i myself have found the answer..... but i would like someone giving a general solution

Spoiler for method

Posted 28 November 2011 - 10:56 AM

Hmm well I'm not sure how general this is, but this is how I found it.. (maybe the same way as you?)

Spoiler for method

Spoiler for correction

Posted 28 November 2011 - 02:13 PM

4 locks.. the vazir has 3 keys.. the forth key is common to all the slaves.. the 3 keys which are with vazir has its copy distributed among the 4 slaves.. so 3 slaves can open it and vazir can open it with any of the slave..

Posted 28 November 2011 - 03:29 PM

You have the right idea but one flaw.Spoiler for solution

Spoiler for error is

Posted 28 November 2011 - 03:43 PM

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.4 locks.. the vazir has 3 keys.. the forth key is common to all the slaves.. the 3 keys which are with vazir has its copy distributed among the 4 slaves.. so 3 slaves can open it and vazir can open it with any of the slave..

Posted 28 November 2011 - 04:04 PM

you are completely right..... in fact you stole my words....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'ld like to hear the answer from you......

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