One more fairly easy one: Spoiler your answer! A man is the owner of a winery who recently passed away. In his will, he left 21 barrels (seven of which are filled with wine, seven of which are half full, and seven of which are empty) to his three sons. However, the wine and barrels must be split so that each son has the same number of full barrels, the same number of half-full barrels, and the same number of empty barrels. Note that there are no measuring devices handy. How can the barrels and wine be evenly divided? Edit: evenly divided means that each son gets the same quantity
Just thought I could guess this way: Spoiler SEVEN EMPTY = 0x7 = 0 wine SEVEN HALF = .5x7 = 3.5 wine SEVEN FULL = 1x7 = 7 wine 0 + 3.5 + 7 = 10.5 10.5 / 3 = 3.5 wine barrels each son Each gets 4 barrels: 3 full, one .5 full, three empty? Is that right?
Can you explain it to me a little bit more? Let's say that the first person is indeed wearing a black hat. Starting from the middle man's perspective... <br> So from what he knows, one or both of him and the first person are wearing black hats. Because like you said, if they were wearing white the third person would know and say something. So, the middle person does not know whether his hat is black or white. But he sees that the front person is wearing a black hat. He obviously cannot say anything either. how does the third person's answer factor into the second person's decision to not say anything? That's my main question.
Spoiler 1st son: 3 full, 1 half, 3 empty 2nd son: 2 full, 3 half, 2 empty 3rd son: 2 full, 3 half, 2 empty
Spoiler Yep... but the crux of the question is how to manipulate the barrels to even it out, without a measuring device. But yes, you pretty much have it.
Spoiler If the front person was wearing a white hat, and the guy in the back didn't answer, then the middle man could have deduced fairly quickly that he must be wearing a black hat. The front person, assuming the two men behind him are rational, would give them sufficient time to answer. After that time has elapsed without an answer, he can only assume that he must be wearing a black hat rather than a white hat.
Spoiler The order of answering matters. The back person didn't say anything, then the middle person didn't say anything, then the front person didn't say anything. - The back person would have answered if the front two people were wearing white hats. The fact that he didn't answer means that at least one of the front two people are wearing a black hat. This is what the middle person infers from the back person's lack of response. - The middle person: if the front person is wearing a white hat, the middle person could definitively say that he was wearing a black hat (due to the back person's lack of response). If the front person is wearing a black hat, the middle person cannot answer because he could be wearing a white hat. Hope that helps
Spoiler 4 half-barrels are converted to 2 full barrels and 2 empty barrels. So, we're left with: 9 full barrels, 3 half barrels, and 9 empty barrels. All are multiples of 3, and can be distributed evenly among the 3 sons.
http://bbs.clutchfans.net/showthread.php?p=7565041#post7565041 <br> I actually just want through that step by step from each person's perspective. I see it now. Thanks
Cool. I figured a bit of math did help, but... Spoiler OK, so bring the seven full barrels together. Give each son two. Now they each have 2 FULL barrels. We have 1 full barrel left and seven halves, and seven empties. Empty two halves into two halves, you now have two more full for a total of three, give each son one of those, now you have three halves and three empty.
<br> Spoiler I don't think it's necessary that the back person not answering means that one of the first two are wearing a white hat. For example: If both of them were wearing black, the back person still could not answer because he does not have enough info to know if his hat is the 3rd black one or a white one <br> Spoiler The middle person is where it gets tricky. He cannot answer no matter what, unless the first person is wearing a white hat. He knows that either one of, or both he and the first person are wearing black. He sees the first person wearing black, but he cannot answer because this does not help him know his color <br> This is where the first person comes in. Immediately when the second person does not answer, the first person knows he is wearing black. It does not matter at this point whether the second person was wearing white or black. The first person has to be wearing black.
<br> You can't empty barrels though since you have no measuring device. I gave the correct number of barrels for each without changing the contents of any of the barrels in post #185
Spoiler A measuring device isn't needed. As long as you can identify the "half barrels", just pour the entire contents of one into the other.
Yep, that's all true - I had a mistake in my reply to you, which I edited correct at 5:00pm. The fix is below. I think we all have the logic down Spoiler - The back person would have answered if the front two people were wearing white hats. The fact that he didn't answer means that at most one of the front two people are wearing a white hat. This is what the middle person infers from the back person's lack of response.
