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 Lesson: Why Does the Euclidean Algorithm Work & Lock Riddle Solution

Thanks for reading!

Follow Math Memoirs for fresh perspectives on math and more challenges!