Stump the Person Below You! (Game)

Quote:

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Originally Posted by Rota

Ten men are about to be executed. They don't like the idea, but they are willing to sacrifice themselves so that others may live. The execution is explained to them. They will be lined up single file, facing the same direction. Each man will be looking at the back of the person in front of him, except for the man in the front of the line. He has noone's back to look at. Each of them will be given a black or white hat on their head. Starting at the back of the line (the man who can see everyone else) they will ask him to state his hat color. If he guesses right, he will be allowed to live. This process continues up the line until each man has been executed or released. The execution is scheduled tomorrow morning. Tonight they must come up with a strategy. How many men can they guarantee will live, and what strategy will ensure this?

There are NOT necessarily five black and five white hats.

Addendum for all of those thinking the first guy can just shout out the hat order and sacrifice himself:
If the men say any word other than "black" or "white," then they are all executed. If the men speak a word at any time other than when they are asked for their own hat color, then all will be executed. If the men say more than that single word in response to the question, then all are executed.

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You didn't say anything about their voice pitch when they answer the question, right? Assuming the executioners are only concerned about what they're going to say (one word/answer, either black or white), and all of the men have no hearing/seeing disabilities ... they can use this strategy:

Last person [in the line] will have to risk it and sacrifice himself. Whatever his guess (black/white), he should say it in a loud voice if the hat on top of the person's head in front of him is black, and in his normal voice pitch if it's white. The other eight men are to follow this pattern. The last man (the one with no one else in front of him) can say his answer in any voice. lol

Nine (9) people are 100% guaranteed to live. (If the first person got his guess right, then so much the better ... that's 10 out of 10! :D)

;) ... that's my try. lol

That works.

The way I heard the riddle is more math oriented.
The first guy can see all the hats.
His guess is 50/50 no matter what.
He sees nine hats in front of him, so there will be an odd number of ONE color, and an even number (or zero) of the other color.
He says the color he sees an odd number of.
The next person sees 8 hats.
If he sees an odd number of the color said by the first guy, then he has the other color.

Let's say the first person said black.
The next person sees an odd number of black hats, so he says white and lives.
The next person sees an even number of black hats, so he says black and lives.
Now everyone knows a black hat has been removed, so there are now an even number of black hats.

Every time someone hears a black hat removed from the line, then the number remaining goes back and forth between odd/even.
They know if there is an odd/even number of black hats left at any given time, and they know how many black hats they see in front of them.
Using this info, all nine will live.
Only the first person is a 50/50 shot.

Agreed. I guess I took another approach in solving it. ROFL.

Well, now they have two strategies they can use to survive being shot! :D

Classic prisoner dilemma:

You and a friend are caught in a crime. They have enough evidence on both of you to convict you of minor version of the offense. The police can just send you both to jail for 1 year, right now. But, you are being offered a deal.

You can rat on your friend and disclose the details that would allow them to convict a more serious version of the crime. He will go to jail for 10 years, and you walk out the door today as a free man.

Your friend is being offered the exact same deal.

1) If both prisoners stay silent, it's one year in prison for both.
2) If one prisoner rats, then it's 10 years for the other, and freedom for him.
3) If both spill the beans about the dirty details, then both share the 10 years, serving 5 each.


What do you do, and why? Are you silent, or do you tell them everything?

There is no wrong answer, by the way. It's a classic situation I've studied in Psychology, Sociology, and Philosophy classes in college. It can probably be applied to quite a few subjects.

Hmm... I suppose the only logical response to the Prisoner's Dilemma is to know and trust absolutely any person that you're going to commit a crime alongside.

Of course, this would never apply to me; I'm pure and innocent as the driven snow. ;o)

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Brisingr: Inventive, but incorrect; the Dog Watch has nothing whatever to do with the position of any transient star, which even in home waters for a northern navy would be below the horizon much of the time. Moreover, the first dog watch is usually in daylight.

ok I got another, a man sees a apple tree with 2 apples on it, then he leaves, he didn't pick apples, but apples didn't remain, what has happened?

Quote:

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Originally Posted by Rota

You and a friend are caught in a crime.... But, you are being offered a deal.
....
What do you do, and why? ....

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don't do the crime if you can't do the time (baby)

no deals, no way, don't rat

you did what could get you 10 years and you can do only 1??? count your blessings

btw, i have 3 cents left from my nickel

wigibob:
Several possibilities occur to me:
- He's a woodcutter and he needs apple wood for a particular project.
- Someone else picked the apples while he was there, perhaps the small boy that was with him.
- He shook the tree, which dislodged the apples.
- He ate the apples while they were still hanging there.

Of course, there are other possibilities...

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Speaking of other possibilities:
"Dog-watches", according to several contemporary sources, were so named in English from a misinterpretation of a Dutch phrase referring to the end of the day. They exist at dinnertime, and the purpose is to permit both watches to have time to eat the evening meal. The HMS Victory website, among others, erroneously clings to the "dog-star" theory, so if you're wrong, you're wrong in good company.

Patrick O'Brian, in "Post Captain", advances the theory that they are so called because they are "cur-tailed". I happen to like that one.

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While I was going to St. Ives,
I met a man with seven wives.
Each wife had seven sacks;
Each sack had seven cats;
Each cat had seven kits.

Kits, cats, sacks, and wives:
How many were going to St.Ives?