Doors and Keys
Probability
Level
pending
You are in a hallway with 6 doors in it. You also have 6 keys and each key opens only one door. You don't know which key opens which door. In maximum, how many tries you will have to do to know which key opens which door?
The answer is 15.
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1 solution
Let's say that you tested 5 keys in the first door, and none of these keys worked. Then, the sixth key left must open this door, because one key opens only one door.
Now you have 5 keys to five doors. You tested 4 keys in the second door and none of these keys worked. Then, the fifth key left must open this door.
Repeating this process until the fifth door, the number os tries you did will be 5 + 4 + 3 + 2 + 1 = 1 5 .