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.funnylogic
Why is 6 afraid of 7?
Because seven was hungry and 'seven ate nine' (7, 8, 9).cleanfunnyshort
Why is a river rich?
It has two banks.logic
Pete is a worker on a large ship with hundreds of other men. He is constantly making mistakes, tying ropes the wrong way, steering the ship the wrong way, and making other blunders. One time he accidentally caused the ship to get stuck in a shallow shore, causing thousands of dollars in damage.
However, when Steve, the captain of the ship, is asked about Pete, Steve says "I wish we had five men like Pete on this ship."
Why would he say this?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?
Paul is 20 years old in 1980, but only 15 years old in 1985. How is this possible?
The years are in B.C., not A.D. as you probably assumed. Based on the system we use to number the years, the years counted down in B.C. (but they weren't counting backwards back then).cleanlogicmathshort
How do you make the number one disappear by adding to it?
Add the letter 'G' and it becomes Gone.cleanshort
We travelled the sea far and wide. At one time, two of my sailors were standing on opposite sides of the ship. One was looking west and the other one east. And at the same time, they could see each other clearly. How can that be possible?
The sailors had their backs against either ends of the ship.cleanshort
What kind of cup doesn't hold water?
Cupcake.cleanshortwhat am I
I am a nut with a whole. What am I?