Riddle of Logic: Death by Firing Squad

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Discussion Overview

The discussion revolves around a logic riddle involving four prisoners of war who must deduce the color of their hats to secure their freedom. The scenario presents a challenge of reasoning based on limited visibility and knowledge of their positions and hat colors. Participants explore the implications of the riddle and the reasoning processes involved.

Discussion Character

  • Exploratory
  • Debate/contested
  • Conceptual clarification

Main Points Raised

  • One participant describes the riddle, detailing the arrangement of prisoners and the conditions under which they can deduce their hat colors.
  • Another participant expresses enjoyment of the riddle but admits to seeking a solution from an external source.
  • One participant suggests that the last prisoner, who cannot see the others, might deduce his hat color by observing his shadow on the wall, although this reasoning is not universally accepted.
  • A later reply draws a comparison to a similar riddle, emphasizing the distinction in the conditions for freedom and the implications for the prisoners' reasoning strategies.
  • Another participant notes that if only one prisoner can be set free, there may be no incentive to delay guessing unless it aids another's deduction.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the reasoning behind the hat color deductions. Multiple interpretations and approaches are presented, indicating ongoing debate and uncertainty regarding the solution.

Contextual Notes

Some assumptions about the prisoners' reasoning processes and the implications of their visibility and knowledge are not fully explored, leaving room for further discussion. The distinction between the riddle discussed and similar riddles may affect interpretations of strategy and reasoning.

z3hr
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This is a cool riddle of logic that I heard recently. It is supposed to be drawn out so I'll try to describe it as best as I can.

Four prisoners of war are sentenced to death by firing squad. They line them up from north to south, all of them facing north (so that they are in line facing the person in front of them, Directions are unimportant North South etc..) Each of them is wearing a hat, they are told that there are two black hats and two white hats. If ONE of them can say for sure what color hat they are wearing, they are all set free. The person in front, who cannot see the hat colors of any of his comrades, is wearing a white hat. The man behind him is wearing a black hat, and the man behind him is wearing a white hat. The last man is behind a wall wearing a black hat so he cannot see the hat colors of the men in front of him. All of them are aware of their physical positions; for example, the man in the front knows that there are two men behind him, and another behind a wall etc... The only thing they don't know is their own hat color and the hat colors of those behind them. It looks like this:

Black | White Black White

They can only see the hat colors of the people in --> direction from them, with the exception of the last man behind the wall.

They have exactly ten minutes before they are executed. Which one of them would be able to know their hat color and why?
 
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It is simple:
The second one will know it for sure, his hat is not the same color of the first, cause if it was the same color, the third one would know for sure his hat color. So he just have wait for a moment, and if the third one stays silent, he will know his hat color (different from the first one).
 
I like it! I'm kicking myself for not working it out though (I gave up and looked at Caracrist's spoiler).
 
z3hr said:
This is a cool riddle of logic that I heard recently. It is supposed to be drawn out so I'll try to describe it as best as I can.

Four prisoners of war are sentenced to death by firing squad. They line them up from north to south, all of them facing north (so that they are in line facing the person in front of them, Directions are unimportant North South etc..) Each of them is wearing a hat, they are told that there are two black hats and two white hats. If ONE of them can say for sure what color hat they are wearing, they are all set free. The person in front, who cannot see the hat colors of any of his comrades, is wearing a white hat. The man behind him is wearing a black hat, and the man behind him is wearing a white hat. The last man is behind a wall wearing a black hat so he cannot see the hat colors of the men in front of him. All of them are aware of their physical positions; for example, the man in the front knows that there are two men behind him, and another behind a wall etc... The only thing they don't know is their own hat color and the hat colors of those behind them. It looks like this:

Black | White Black White

They can only see the hat colors of the people in --> direction from them, with the exception of the last man behind the wall.

They have exactly ten minutes before they are executed. Which one of them would be able to know their hat color and why?

The last black knows the colour . i think he looks his shadow in the wall .we all know that shadow will be black but he think his hat is black.
 
The last black knows the colour . i think he looks his shadow in the wall .we all know that shadow will be black but he think his hat is black.
 
Last edited by a moderator:
drizzle said:
it’s almost like https://www.physicsforums.com/showthread.php?t=331079". the only difference is, in my riddle the lame emperor would set free the one who can tell his hat color alone, poor others

Actually, that's a key distinction. If the only way to be set free is to guess the color of your own hat and each prisoner gets an opportunity to guess their own hat color, then there's no benefit to delaying a guess unless someone else's prior guess would help you. If only one prisoner is going to be set free no matter what, then there's definitely no reason for anyone to delay.

The first two will reveal no new info to the 3rd that he doesn't already know and the 4th's guess reveals no info at all. The 3rd doesn't benefit from delaying, even if he doesn't know the color of his own hat.

Prisoners 1, 2, and 4 always benefit from letting the 3rd guess first, even if the 3rd is selfish and willing to guess wrong when he doesn't know. In fact, letting a selfish #3 guess first gives everyone a 67% chance of surviving.

If only one prisoner is going to be set free no matter what, then there's definitely no reason for anyone to delay. In that case, there's about a 54% chance that one of the four prisoners will survive.

I went ahead and put this in a spoiler tag, since it actually gives a really big hint as to the solution of the teaser in the op
 
Last edited by a moderator:

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