Question: There are three men and a judge. The judge has 5 hats. Three of them are red and two of them are white. The judge says "Close your eyes, I am going to place a hat on each of your heads, who ever can guess what color hat they are wearing can go free." Facts: 1. The three men are standing in a line facing the judge. Where person three can see person two, one and the judge. Person two can see person one and the judge, person one can see the judge. Person three opens his eyes first, then person two, then person one goes last. 2. Each person can hear the others response. 3. The additional 2 hats are not visible 4. Person one guesses correctly. Question: What color hat is person one wearing and how do you know?
Answer: Person 1 is wearing a red hat. He knows his hat is red because: 1. If person three does not know, it means that when he opened his eyes, he didn't see two white hats in front of him. 2. Person two knows that person three did not see two white hats. The only way he could know what color hat he was wearing is if he opened his eyes and saw a white hat. (which means he saw a red hat) 3. Person one knows he is wearing a red hat because if person three doesn't know, then both him and person two don't have white hats. Person would only know what color his hat was if person one was wearing white. Person one knows all of this and concludes his hat is red.
Question: You have a glass of water that looks about half full. How can you tell, only using the glass of water itself, if the glass is half full or not?
The glass is a right cylinder.
Answer: Tip the glass of water until the water reaches the rim of the glass and if the water lines up perfectly with the bottom rim of the glass, it is half full.