# The Man and the Judge

sloppyb
Posers and Puzzles 18 Mar '10 13:10
1. 18 Mar '10 13:10
A man was to be sentenced, and the judge told him, "You may make a statement. If it is true, I'll sentence you to four years in prison. If it is false, I'll sentence you to six years in prison." After the man made his statement, the judge decided to let him go free. What did the man say?

2. 18 Mar '10 13:30
should we move my riddles to the general forum for more responses?
3. 18 Mar '10 14:02
"You will sentence me to six years in prison"
4. 18 Mar '10 14:12
Originally posted by luskin
"You will sentence me to six years in prison"
5. PBE6
Bananarama
18 Mar '10 14:391 edit
Originally posted by sloppyb
If we assume that the statement "you will sentence me to 6 years in prison" is true, then the judge is obliged to sentence the man to 4 years in prison. However, this contradicts the original assumption that the statement is true. If, on the other hand, we assume that the statement is false, then the judge is obliged to sentence the man to 6 years in prison. However, this contradicts the original assumption that the statement is false. Therefore, the truth or falsehood of the statement "you will sentence me to 6 years in prison" is indeterminable, and hence the judge let the man go free.

Kurt Godel would be shocked to see his Incompleteness Theorem abused in such a manner. ðŸ˜‰
6. 18 Mar '10 14:40
Originally posted by sloppyb
well, lets see here.

the prisoner asks for 6 years.
If the judge gives him 6 years, this will mean that the statement is true. But if its true then he should get four year.
Similarly, if he gets four years, the statement is false, meanig he should get 6 years.

Logically, the judge cannot give the prisoner either of the sentences and instead of doing something sensible like hitting the prisoner with the little judges hammer, the judge lets the prisoner go.

Phil.
7. 18 Mar '10 15:00
Originally posted by PBE6
Kurt Godel would be shocked to see his Incompleteness Theorem abused in such a manner. ðŸ˜‰
It's more of an Epimenides paradox - goes back much further than Gödel.
8. 18 Mar '10 15:03
Originally posted by MrPhil
Logically, the judge cannot give the prisoner either of the sentences and instead of doing something sensible like hitting the prisoner with the little judges hammer, the judge lets the prisoner go.
Of course, letting him go isn't any more logical than any other action - e.g. life imprisonment. Or, as you suggest, a good working over with a heavy object.
9. 18 Mar '10 17:41
are the riddles too easy or something?
10. AThousandYoung
18 Mar '10 18:30
Originally posted by sloppyb
are the riddles too easy or something?
This is an old riddle. I've seen it before.

Not only that, but this riddle pattern is old and common. Similar is the one that goes:

Lacey is trying to get to Freaktown. She comes to a fork in the road. There are two men standing there.

There is a sign - "you may ask one question. One of these man always lies; the other always tells the truth".

How can Lacy figure out how to get to Freaktown with certainty? Which road must she take?
11. AThousandYoung
18 Mar '10 18:32
Originally posted by AThousandYoung
This is an old riddle. I've seen it before.

Not only that, but this riddle pattern is old and common. Similar is the one that goes:

Lacey is trying to get to Freaktown. She comes to a fork in the road. There are two men standing there.

There is a sign - "you may ask one question. One of these man always lies; the other always tells the t ...[text shortened]...

How can Lacy figure out how to get to Freaktown with certainty? Which road must she take?
Actually I don't know if that's the same riddle pattern, but it's also an old riddle in which the person must play language games in order to solve the problem.
12. 18 Mar '10 20:562 edits
Originally posted by AThousandYoung
Actually I don't know if that's the same riddle pattern, but it's also an old riddle in which the person must play language games in order to solve the problem.
How about when there is only one man standing at the fork who either lies or tells the truth randomly, and only one question allowed....
13. 19 Mar '10 22:25
Originally posted by iamatiger
How about when there is only one man standing at the fork who either lies or tells the truth randomly, and only one question allowed....
I don't know that this one has an answer.

If it did, it would be something like "If I were to ask you if that way is the way to Freaktown, would you say yes?"

The problem is, he answers randomly, his next statement might have the opposite truth value, rendering the standard analysis inapplicable.

Now if we knew all his statements had the same truth value, then we could determine which way...
14. 19 Mar '10 22:29
The necessary question is "do you know that they are giving away free beer in Freaktown?". Whatever his response, you leave and hide behind a bush. You follow him when he goes to get his beer.

Phil.
15. AThousandYoung