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6 generals propose locking a safe with a number of different locks

  1. Nov 30, 2005 #1
    6 generals propose locking a safe with a number of different locks .each general will be given a key to certain of these locks .how many locks and keys are required and how many keys must each general possess such that the lock will be opened only if 4 generals are present?
     
  2. jcsd
  3. Nov 30, 2005 #2
    it may be like this

    we can select 4 generals from 6 in 15 ways.hence 15 locks are required are required & 15 keys are required.each general must possess atleast 3 keys each.
     
  4. Jan 2, 2006 #3
    There are 6 people and you need that only if 4 combines all the locks will be opened
    ie if you take any 3 people there will be 1 lock which needs to be opened and the key to that is available only with any of the other 3 people
    Hence for any 3 people you need to distribute one lock among the other 3 peopl
    This requires a total of 6C3 distinct locks wie 20 distinct locks
    Hence the safe should be locked with 20 locks and te key distribution for each of the general would be
    General 1 :K1, K2, K3, K4, K5, K6, K7, K8, K9, K10,
    General 2 :K1, K2, K3, K4, K11, K12, K13, K14, K15, K16,
    General 3 :K1, K5, K6, K7, K11, K12, K13, K17, K18, K19,
    General 4 :K2, K5, K8, K9, K11, K14, K15, K17, K18, K20,
    General 5 :K3, K6, K8, K10, K12, K14, K16, K17, K19, K20,
    General 6 :K4, K7, K9, K10, K13, K15, K16, K18, K19, K20,
     
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