Okay I have two logic puzzles. Both of them there are 3 prisoners who are shown 3 black hats and 2 white hats. In both scenarios a hat is placed on each man's head in such a way that they cannot see the hat on their head and the other hats are hidden. #1) The prisoners are lined up in order of height with the shortest at the front. The man at the back can see both of the other hats. The man in the middle can see the front hat only. The man at the front cannot see anybody's hat. The men are told that if any one of them can guess the color hat he is wearing all of them can go free. If someone guesses but is wrong all of them will be executed. They are only allowed to speak to the warden. The warden walks to the man at the back and asks him what color hat he is wearing. The man replied "I cannot guess because I don't know". The warden walks to the man in the middle and asks him what color hat he is wearing. The man replied "I cannot guess because I don't know". The warden walks to the man at the front and asks him. The man replied correctly and all were set free. What color was his hat and how did he know? Spoiler His hat was black. He knew because. If the man at the back had seen two white hats he would have know his hat was black and would have responded. Because he didn't see two white he didn't know. The man in the middle knew that the guy at the back didn't see two white hats. Had he seen the guy at the front wearing a white hat he would have known his was black. Because he responded that he didn't know the guy at the front knew his hat had to be black. #2) This time the men are allowed to see each of the other two hats but not their own. They are told that the first one to correctly get his hat right and tell how he knew would be set free and the other two executed. If he was wrong or couldn't come up with how he knew all would be executed. The three men were all turned so that they could see at the same time. After about 10 minutes one of them walked to the guard, answered, and was freed. Again what color and how did he know? Spoiler Again it was black. Had any of the men seen two white hats he would have immediately known his was black and raced off. Since nobody raced off it meant there were not two white hats and that he could see at least one black hat. If someone else had seen one black and one white he would have paused to look at the man in the black hat. If the man in black didn't run away immediately it would have meant that he didn't see two white hats and since the second man could see one that would have meant his was black. Because it took 10 minutes and neither guy moved the third guy knew everyone was wearing a black hat. Anybody else got one?
