7 thieves wanted to lock the treasure looted from a ship. They wanted to put locks to the treasure where each lock had multiple keys. Find the minimum number of locks N and minimum no. of keys K with every thief subject to the following conditions:-
All the locks should open each time a majority of thieves(4 or more) try to open the locks.
At least one lock remains unopened if less than 4 thieves try opening them.
All locks should have same no. of keys.
All thieves must have same no. of keys with them.
Shamir's paper on Secret Sharing Scheme states this problem and gives the answer with the explanation that its written in standard Combinatorics books
Update (11/12/09) Solution: Provided by Jaadu in comments!!