As you are leaving from your previous ordeal, you notice that another convict is being taken to a jail cell. As you watch the guard and the convict go to the cell, they start talking.
"You do realize your rights, right?" says the guard.
The convict replies, "The judge said something strange, but I didn't understand it. What was it?"
"You are free to go anytime you like," declares the guard, "as long as you fulfill the required conditions. In your case, your door is secured with a ten-digit lock. If you can guess the right number, you are free to go."
"That's easy," says the prisoner. " I can just keep guessing numbers until I guess the right one."
"Even so," says the guard, "it would take you a hundred years to find the right number at the rate of one per second. Of course, you can always look for the hints we give you." He then points at you and proceeds to tell the new prisoner about your imprisonment.
"In addition to the normal...amenities, you have a desk and a scientific calculator. Good luck." The guard walks away.
You stand there for a few minutes before you realize that you can go. As you turn to leave, you notice that the new prisoner is walking up behind you.
"Wow, this place is great!" he says. "I only had to input one number!"
What number did he try?
There are 86,400 seconds in a day.
There are 365 days in an ordinary year and 366 in a leap year.
Leap years ordinarily come every fourth year, except that, in the 100 years starting now, the year 2100 will not be leap.
Therefore, starting from now, there are 86,400 * 36,524 seconds in 100 years, or 3155673600. Subtract 1 from this if counting starts with all zeroes. Subtract 999999999 if the assumption was that you'd start with only the first number with no leading zeros.
Therefore there are at most three numbers to try, under the different assumptions. The prisoner made a lucky guess among the three possibilities and got out on his first try. Probably the assumption of starting with all zeroes was correct and he guessed 3155673599.
Posted by Charlie
on 2006-03-31 09:47:29