Iron Doughnut
A piece of solid iron in the shape of a doughnut (with a hole in the middle, of course) is heated over a fire. As the iron expands, does the hole become larger or smaller or does it remain the same size?
Leaning Tower of Dominoes
Stack Dominoes on top of each other so that each domino projects as far as possible over the domino below without falling. If you stack two dominoes, the top one can overhang by as much as 50% of its own length. If you stack three dominoes, the greatest offset is obtained when the center of gravity of the top domino is directly above the end of the domino below and the combined center of gravity of these two dominoes is directly above the edge of the third domino. The top domino now overhangs the bottom one by 75% of its length.
By continuing this pattern, is it possible to build a tower in which the top domino projects more than a full domino length beyond the bottom domino? If so, approximately how many dominoes do you think will be required to achieve this?
Rotation counter
If a bike with equal wheels has a rotation counter on each, which wheel would register a higher reading?
Hat Logic, #3
Tim, John, Sarah and Mary each wear a hat. Tim’s hat is blue; John’s is red, Sarah’s is blue and Mary’s is red. Nobody knows what the color of the hat he/she is wearing however, they know there are 2 reds and 2 blues. Tim is in a room by himself who cannot see anyone. John, Sarah and Mary are in the same room with John facing a corner, not able to see anyone else; Sarah is behind John so she can see the John is wearing a red hat. Mary is behind Sarah so she can see both John and Sarah’s hat. They are instructed to speak up if anyone who can figure out what color of hat himself/herself is wearing. Can anyone?
Hat Logic, #2
While a red hat was placed on the head of each of three blindfolded women seated facing each other in a circle, they were told that the hat might be either red or white. Upon removal of the blindfolds, each was to raise her hand if she saw at least one red hat, and then to take it down if she could logically deduce the color of her own hat. All three hands were quickly raised, but then one of them lowered her hand. How did she know?
Hat Logic #1
Three men were standing in a row, all facing the same direction, so that there was one in back who could see the two in front of him, one in the middle, and one in front who could not see either of the other two. There were three blue and two red hats. One hat was placed on each man, without them seeing which two were left over. Each man was told the total number of each color of hat. First the man in the back was asked if he could deduce what color hat he had on, but he said he couldn’t. Neither could the man in the middle, when he was next asked. But then man in the front, who could see neither of those behind him but could hear their answers, correctly deduced by logic what color hat he was wearing. What color was it and why?
