Can the key that opens all doors

http://jackchen2012.blogetery.com/2012/08/31/clever-boy/

One of my friends in a university dormitory administrator, have a chat, she told me a funny thing.
She managed the house lives a group of boys, each dormitory four people, each person a key. These students have love to sleep late, always love until the time for class to hurry up and wash, then went to the classroom. Wait until the school back, feel a pocket, broken, left the key in the dorm, so can only wait for others to come back. In four a total of one or two individuals with key. But there are a few times, all four of us forget take the key, so the whole blocked in the dormitory. No way, only to find the dormitory administrator, who was my friend, she keeps the house all quarters backup key.
Many times, a friend will feel trouble. She made it a rule, each dormitory each semester to find her keys to the more than three, more than three times, to find their own tools to the lock, and then buy the new.
At the end of the semester, friends all dormitory condition made a statistic, she found an interesting phenomenon: 5 floor several together dormitory, 501 to 506, he never once to ask her to open the door! A record is also no dormitory is not, but now has six dormitories, and still be together. This caused a friend's interest.
In order to understand the mystery friend specially happy, open 504 doors, finally know their secret. Originally, they each dormitory are also equipped with a new key, deposited into a dormitory. So to speak, put in six quarters and six keys are numbered, their approach is: keys to a deposited into the dormitory two, key two deposited into three quarters, and so on, finally the key six deposited into the dormitory. In this way, twenty-four personal medium as long as there is one to have the key, that all are not blocked in the dormitory, as long as there is a key to open a door, first, and then made second keys to open second doors, and so, to open all the doors.
Hearing this, I could not help but took the pen to forget about. Assuming that each students forget the key risk is 50% ( in fact should be less than this figure ), then there will be twenty-four students do not take the key? It is theoretically possible, can be calculated by probability theory, the probability is 1 / 16777216 -- -- almost zero!
I couldn't help but admire the clever boys. They trust each other, cooperate with each other. Lacking spirit of cooperation, fight the enemy separately, everyone has to act with confusion when; while only stand together, face the common problem, to dig out the maximum potential, at this time, often become cannot withstand a single blow, because at that time, everyone is a key, turn to the key that opens all doors.
http://www.blogujem.cz/blog.php?user=wodekao&note=257205