# The Lock Riddle

## Could you get out?

*“I believe you are unfamiliar with the penal system in our country,” said the warden, as he led the new prisoner to his cell.*

*“We find that it improves prison morale for each prisoner to have a chance to end his sentence at any time. In your case, we have set up a combination lock on your cell door. There are ten dials on which you can set up any ten-digit number. If you set up the right one, the cell door will unlock and you will be free to leave.”*

*“I see,” said the prisoner. “Then if I try every possible number, I’m sure to hit the right one.”*

*“True,” said the warden, “but even if you were able to change the numbers at the rate of one per second without rest, it would still take you a hundred years to hit the right combination. However, you could try numbers at random and have a chance at choosing the right one. Or, you could search for a clue which we always provide.”*

*“What sort of clue?”*

*“Well it might be almost anything. For example, one of our prisoners was put in an escape-proof cell and told that he would be pardoned if he could break out. He was given permission to keep any plants he wished in his cell.”*

*“What became of him?”*

*The warden chuckled, “After more than two years, he suddenly realized that some words may have more than one meaning. He requested a poison ivy plant. Soon after receiving it, he broke out — in a rash. Naturally, he received his pardon.”*

*The warden unlocked the cell and ushered the prisoner in. “Your cell contains a desk, calculator and writing implements. Good luck.”*

*The prisoner was left alone. He tried a few combinations on the lock without success. What could the clue be? A thought struck him. It seemed worth a try. He made a few calculations, and then set up a number on the lock. The cell door opened and the prisoner strolled out, after serving less than an hour of his sentence.*

*What number did he try?*

— From “*Puzzles in Math & Logic*” by Aaron J. Friedland

Next Les*son: **Why Does the Euclidean Algorithm Work & Lock Riddle Solution*

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