You can easily "tile" an 8x8 chessboard with 32 2x1 tiles, meaning that you can place these 32 tiles on the board and cover every square.
But if you take away two opposite corners from the chessboard, it becomes impossible to tile this new 62-square board.
Can you explain why tiling this board isn't possible?
Color in the chessboard, alternating with red and blue tiles. Then color all of your tiles half red and half blue. Whenever you place a tile down, you can always make it so that the red part of the tile is on a red square and the blue part of the tile is on the blue square.
Since you'll need to place 31 tiles on the board (to cover the 62 squares), you would have to be able to cover 31 red squares and 31 blue squares. But when you took away the two corners, you can see that you are taking away two red spaces, leaving 30 red squares and 32 blue squares. There is no way to cover 30 red squares and 32 blue squares with the 31 tiles, since these tiles can only cover 31 red squares and 31 blue squares, and thus, tiling this board is not possible.shortwhat am I
I’m tall when I’m young, I’m short when I’m old, and every Halloween I stand up inside Jack O Lanterns. What am I?
It was a man's birthday. He lay dead in the lounge room of his house. Next to his body was a note, written in pencil. The note read 'Happy Birthday, Friend'. The victim had a girlfriend and the police suspected her ex-boyfriend. They could find no obvious evidence. While searching the ex-boyfriend's car, the police saw an envelope with the girlfriend's address written on it. They thought they would get the handwriting checked against the note. The scientist in charge came in early to work the next day; it was 7am. He looked out his window which faced east and stared at the rising sun and it was then that he realised how to prove the ex-boyfriend killed the man, even though the girlfriend's address was not written in the same handwriting. How did he do it?
The scientist's office faced east, and the sun was coming in through the window at a very low angle. He saw some very faint shadows on the surface of the envelope. He looked closer. There were the words embossed on the paper. They read "Happy Birthday, Friend". The ex-boyfriend had forgotten that a pencil leaves an impression on paper beneath the page written on.logicshort
Swaff was traveling in an elevator, being cool, when he suddenly heard the cord supporting the elevator snap. Being the cool guy that he is, he knew of a myth where if you could jump at the right time, you could possibly be able to survive a plunge in an elevator.
Now, when Swaff was a boy, he spent all of his math classes making fun of his female teacher's moustache. He never paid attention, so he was a tad bit slow in his mathematical calculations. He did, however, have a very bizarre talent, in which he could tell the exact speed he was traveling. That came in pretty lucky today.
Swaff knew he was falling at an even rate of 50 miles per hour. When the cord snapped, he was exactly 110 feet above the ground. He knew that he must jump at the right time to have any hopes of surviving.
Now, after doing the math, please tell me when Swaff jumped.
He never did. By the time Swaff figured out that he would have to jump in 1.5 seconds, he would already be dead. Not even the best of mathematicians could do all the math needed in 1 and half seconds. Swaff fell to his death.funnyshort
What has five eyes, but cannot see?
The Mississippi River.