Your friend pulls out a perfectly circular table and a sack of quarters, and proposes a game.
"We'll take turns putting a quarter on the table," he says. "Each quarter must lay flat on the table, and cannot sit on top of any other quarters. The last person to successfully put a quarter on the table wins."
He gives you the choice to go first or second. What should you do, and what should your strategy be to win?
You should go first, and put a quarter at the exact center of the table.
Then, each time your opponent places a quarter down, you should place your next quarter in the symmetric position on the opposite side of the table.
This will ensure that you always have a place to set down our quarter, and eventually your oppponent will run out of space.
Allan, Bertrand, and Cecil were caught stealing so the king sent them to the dungeon.
But the king decided to give them a chance.
He mad them stand in a line and put hats on their heads.
He told them that if they answer a riddle, they could go free.
Here is the riddle: "Each of you has a hat on your head. You do not know the color of the hat on your own head. If one of you can guess the color of the hat on your head, I will let you free. But before you answer you must keep standing in this line. You cannot turn around. Here are my only hints: there are only black and white hats. At least one hat is black. At least one hat is white."
Allan couldn't see any hats.
Bertrand could see Allan's hat but not his own.
Cecil could see Bertrand's hat and Allan's hat, but not his own.
After a minute nobody had solved the riddle. But then a short while later, one of them solved the riddle. Who was is and how did he know?
Bertrand knew the answer because Cecil didn't say anything after one minute. If Bertrand and Allan's hats were both the same color, then Cecil would know what color his hat was. But Cecil didn't know. So Bertrand knew that Allan's hat was a different color than his. Since Allan's hat was black, Betrand knew his hat was white.
A farmer challenges an engineer, a physicist, and a mathematician to fence off the largest amount of area using the least amount of fence. The engineer made his fence in a circle and said it was the most efficient. The physicist made a long line and said that the length was infinite. Then he said that fencing half of the Earth was the best. The mathematician laughed at the others and with his design, beat the others. What did he do?
The mathematician made a small circular fence around himself and declared himself to be on the outside.
Why are manhole covers round? Do manhole covers really need to be circular?
Manhole covers are round so that they won't fall through the hole into the sewer below them. No matter how you turn the cover, you won't be able to push the cover through the hole.
However, if you were to have square manhole covers, you would be able to rotate the cover such that one of the edges of the square cover is lined up with the diagonal line of the square hole, which would allow the cover to fall through, causing countless problems that the general public would rather avoid.
