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Riddle: The Punishment Paradox

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Riddle: The Punishment Paradox
03.09.07 (12:07 pm)   [edit]

Note: People have presented this riddle in various forms throughout the years. I read a version in Labyrinths of Reason, by William Poundstone, that I am using as a template for the current post.

At Amazon: Labyrinths of Reason

Punishment Paradox NooseThe jury found the prisoner guilty of the worst sort of murder, and the judge was well within his rights to sentence the prisoner to death; however, the judge could not indulge himself by condemning the murderer to an excruciating demise. The Law of the State prohibited any death-sentence other than a simple hanging. Nevertheless, the nature of the murderer's remorseless crime filled the judge with outrage, so he struggled within the bounds of his mandate to find a way to make this particular hanging slightly more painful.

The day of the sentencing arrived, and when the prisoner, along with his counselor, appeared before the court, the judge said, "I am tempted to order your immediate execution and wash my hands of this heinous crime once and for all. However, I find you to be a heartless, cold human being, and nothing would please me more than to pierce your hardened caul before you die.

"Therefore, here is your sentence: because an immediate hanging would cut your anxiety short, while an extended wait would only allow you to enjoy your life longer than you deserve, I sentence you to hang at sunrise on one of the seven days next week. I further instruct your executioner to make sure you have no way of knowing in advance what day you shall die.

"Thus, you will approach each night's sleep with the fear that this may be your last night on earth. Then, come sunrise, the executioner will walk you to the gallows, hang the rope about your neck. Perhaps he will then remove the noose and return you to your cell for another day. Or perhaps the door below your feet will vanish, and you will die. However it should happen, it will come as a complete surprise to you, and I guarantee your surprise upon my own honor, and my own life. You will not know the moment of your death until it rises to greet you."

The murderer found himself startled and suddenly afraid, as he had never been throughout the years of his life, of the cruelty of the sentence. But his counselor smiled with relief. The murderer turned then and snarled, "What happiness can you find here?"

"Well, it's just this: the judge cannot hang you now, or ever!

"Consider," the lawyer said, "you are supposed to hang one sunrise in the next seven, but you are not allowed the certainty of knowledge that would confirm for you the day of your death. So they cannot hang you next Saturday morning. It is the last day within the sentencing period, and if you walked to the gallows on that day, you would surely know it was intended to be the day of your hanging. That very knowledge was prohibited by the judge himself, on his honor and his life. Are we agreed? You cannot hang on Saturday."

The murder nodded his head, and said, "So? Who cares? It will not be Saturday; doubtless I will hang on Friday or Monday or any of the other days."

The lawyer shook his head. "Suppose you live to see Thursday afternoon. You will realize that the only remaining mornings are Friday and Saturday. However, you already know it cannot be Saturday. But if it must be Friday, then it cannot be Friday, either! Your knowledge that Friday is the only possible day on which the judge could legitimately carry out his sentence prevents the judge from carrying out his sentence!

"And now," the lawyer said, "you must see that this holds true for any day of the seven. On Wednesday afternoon you will know that Thursday is the only possible day; and then, of course, it cannot possibly be Thursday! So on, so forth. The judge must release you or break his solemn oath as a judge--and lose his own life in the process, as he has staked it to his oath."

At last the murderer began to smile.

That night he slept like a baby, and walked confidently to the gallows on Sunday morning, and just as he suspected, he walked back to his cell. He walked again on Monday morning, felt the rope secured about his neck, but he smiled nonetheless. Sure enough, the rope was removed, and he strolled back to his cell yet again.

And then on Tuesday morning, as well, the executioner led him to the gallows and secured the noose. That morning gave birth to a piercing sunrise. The sun silhouetted the murderer like a frame around a photograph, as he hanged by a stout rope - quite unexpectedly.

Did the judge fulfill his sentence?

At Amazon: Labyrinths of Reason

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posted by: surrogate (reply)
post date: 03.09.07 (6:30 pm)

It would seem that the counselor's reasoning, though sound, was nulified by the very fact it had been explained to the murderer. Had the counselor simply made his point to the judge, then the judge would not have been within his self imposed bounds to carry out the sentence on any of the days during the week, and therefore, ever. By giving the murderer the confindence of knowing he could not be hung, it recereated condition that allowed the sentence to be carried out on ANY of the seven days.

Either that, or the lawyer simply wanted to relieve his client of the worry of not knowing and therefore create a condition where the murderer could relax and sleep soundly till the inevitable occurred.



posted by: tabootenente (reply)
post date: 03.13.07 (8:05 pm)

Reply to: surrogate

i think you're right. it's a knowledge paradox. without the reasoning that allows the murderer to "know" he can't be killed, say, on saturday, and therefore not on friday, the murderer should be surprised on any day that the judge brings down his sentence.

but with the reasoning, he's certain to be surprised on any day, just the same.

there's still a problem, i think; even the least observant murderer would be sure to see the problem come saturday morning. there is no other day he could possibly hang. and what about on friday morning? the murderer would probably be confused as to how the judge planned on carrying out the sentence, but is confusion the same as surprise? also, wouldn't the judge need to be absolutely certain that the murderer WOULD know the day of his death--and therefore that he SHOULDN'T hang? if he could be sure the murderer knew, then he could go ahead and hang him.

this is a real paradox - one without an answer. the problem is that the judge needs to be sure that the murderer does know, and therefore, can't. at the same time, the judge must be sure that the prisoner doesn't know.

my thought is that the murderer will be surprised on any day he hangs; but at the same time the judge can't fulfill his sentence to the letter.



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