Time for another fun filled brain teaser! Enjoy!
Note: If you could all please input your answers using the previously noted html code it will allow others to answer without having a spoiler. Also, two things, in your answer, do not include any ' or " and html is case sensitive, so don't add any capital letters outside of your answer or it will not work properly. Lastly, don't answer first if you can't use the button and if your button doesn't work, check your code because there's something wrong (read: it's not me, it's you).
Question
10 straight-jacketed prisoners are on death row. Tomorrow they will be arranged in single file, all facing one direction. The guy in the front of the line (he can't see anything in front of him) will be called the 1st guy, and the guy in the back of the line (he can see the heads of the other nine people) will be called the 10th guy. An executioner will then put a hat on everyone's head; the hat will either be black or white, totally random. Prisoners cannot see the color of their own hat. The executioner then goes to the 10th guy and asks him what color hat he is wearing; the prisoner can respond with either "black" or "white". If what he says matches the color of the hat he's wearing, he will live. Else, he dies. The executioner then proceeds to the 9th guy, and asks the same question, then asks the 8th guy ... this continues until all of the prisoners have been queried.
This is the night before the execution. The prisoners are allowed to get together to discuss a plan for maximizing the number of lives saved tomorrow. What is the optimal plan?
Good Luck!
I guess that was assuming their are 5 white and 5 black hats. Even if their are more of one color than the other, I believe this would still be an optimal strategy because they have to assume their are 5 white and 5 black hats.
I'm not going to assume that are 5 of each color; if there were, the tenth guy in line could just look at the hats of the others and realize what color hat is missing, knowing that missing hat is his. This could continue down the line until everyone has it. 5 of each color seems too obvious, so I am going to assume they could be completely random.
I'm sure there is a trickier answer than this one that saves all of them except the first one, but I figured it wasn't a poor attempt.
The prisoners would agree the night before to say the color of the hat of the person in front of them if they were not already told by the person behind them; the last person in line would have no idea, so he would just say the color hat of the 9th prisoner. The 9th prisoner obviously knows this, so he says his own color and saves his own life. The 8th person would have no idea, so he would just say the 7th persons color. This would continue and would allow every odd numbered prisoner to live every time, while the even numbered inmates would have a 50/50 chance of surviving, as their own hat may be the same color as the person in front of them. The odds live every time and the evens live half the time, making an expected value of 7.5, but I will round that up to 8.
Provided the first guy to say a color is not a total douche, I'm pretty sure he can save everyone except himself. All he needs to do is say: or vice versa. Then as each person says their hat color, the next person simply looks at all the ones in front of him and does the math.
I hope I did the html right
Okay, I used an apostrophe, even after mikesswimn specifically said not to. Let's try this again:
The tenth would say the color of the ninth's hood, so the ninth would live. The eight would say the color of the seventh's, so that the seventh would live. This would guarantee that 50% lived, and the others would each have a 50% chance of guessing correctly. This would make approximately 75% live.
The HTML didn't work for anyone
I don't know why but I thought the prisoners had to respond immediately. Anyways yeah yours makes complete sense and just adds time to what RealMax and I said, saving more lives. Nicely done.
The html should be {input type='button' value='Answer' onClick="alert('YOUR ANSWER HERE')"} surrounded with "
I tried to fix mine, answers don't pop up when I click the button. Anyway, I think you can get 9 to live, 50/50 on the first guy
rule: high pitch voice for black, low pitch for white 10th guy yells out 9th guy's color, 9th guy yells out own color in a specific pitch according to the color of the person in front of him and so on and so forth. Only 10th guy is in jeopardy making it 9.5 prisoners alive on average.
Aut inventore porro libero vel. Aut qui minus vero eos facere alias sequi. Explicabo aut dolor similique molestiae.
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