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?

A solar year is 365.2425 days (approximately).  Using this approximation, the number of seconds to elapse in 100 years is 3155695200.

Calculating a year as 365.25 days, the number is 3155760000.  This was my initial guess, as it was of others who posted prior to me.

Calculating a year as 365 days, the number is 31536100000.
 
As Charlie pointed out, if leading zeroes are omitted, 999999999 would need to be added.  If all zeroes were permitted, 1 would need to be add.  As 2100 AD is not a leap year, 86400 may need to be subtracted to accomodate this difference. Yet, it is unlikely the Imalasian guard would have considered this, and it may not even be recognized by the Imalasian calendar. 

The slowing down of the Earth's rotation over time may also be a consideration, as is the seconds gained and lost as the earth moves along its orbit, but not likely. These changes pertain more to the sidereal year, not the solar year.  And might be considered unpredictable, even by a Imalsian guard. The sidereal year, by the way, is approximately 365.256363 days in length.

The actual combination number escapes me.  I think I might have had to try more combinations than the other prisoner.  Lucky guess, Imalasian!

Edited on March 31, 2006, 11:39 am

Posted by Dej Mar on 2006-03-31 11:24:40