there are 6 keys and 6 locks. then number of combinations to be
tried out to get the actual solution is

• 20 only.
  as it's a lock and key question, there must be exactly one key belonging to one lock.
  so first we try all keys for first lock. one key is bound to open it. after that it is worthless to try that key to other locks or other keys to that lock.
  so our problem converges to 5 keys and 5 locks after trying only 6 combinations.
  then it will converge to 5, then 4, then 3, then 2, then 1.
  so solution will be 6+5+4+3+2+1 = (6*7)/2 = 21.
  but in last step we don't have to check the combination as only 1 lock and 1 key are remaining.
  so we reduce that step.
  and we can solve this problem using
• 13 years agoHelpfull: Yes(59) No(8)
• 6!
  6*5*4*3*2*1
• 13 years agoHelpfull: Yes(20) No(6)
• formula is n(n+1)/2
  Here n=6
  So, 6x7/2=42/2=21
  at last we don't have to check the last combination so no of valid combination is 21-1=20
  
  Answer is 20 combinations
• 12 years agoHelpfull: Yes(7) No(2)
• the question is based on combination....so we have to use all the keys at the same time..not like using one key at one time...it must be 6 keys at one time....so 20 is wrong....it must be 6!=720 combinations......any one disagree this....
• 12 years agoHelpfull: Yes(5) No(6)
• 6^6(power) solution
• 13 years agoHelpfull: Yes(3) No(12)
• coz 1st lock has 6 ways to unlock . then 2nd lock has 5 ways to unlock and so on.... so answer is 6*5*4*3*2*1=720 ans
• 13 years agoHelpfull: Yes(3) No(10)
• 20--(6+5+4+3+2+1)
  but at last step no need to check
  
• 12 years agoHelpfull: Yes(3) No(5)
• 6^6 combinations should be tried to get actual solution.
• 13 years agoHelpfull: Yes(2) No(9)
• Try 5 different keys in the first lock and all fail. (so you know the 6th key is the right one)
  Of those 5, try 4 in the second lock and all fail (so you know the 5th key is the right one)
  Of those 4, try 3 in the third lock and all fail (so you know the 4th key is the right one)
  Of those 3, try 2 in the fourth lock and both fail (so you know the 3rd key is the right one)
  Of those 2, try 1 in the fifth lock and fail (so you know the 2nd key goes here)
  With only 1 key and 1 lock left, there's only one solution, so you don't even have to try it.
  Total number of attempts: 5+4+3+2+1=15
• 5 years agoHelpfull: Yes(0) No(0)