On the right, you see a paper with a chessboard print on it. We want to cut the chessboard paper into pieces (over the lines!) such that each piece has twice as much squares of one color than of the other color (i.e. twice as much black squares as white squares or twice as much white squares as black squares).
Is it possible to do this? Give a proof!
No, it is not possible to cut the chessboard paper into pieces such that each piece has twice as much squares of one color than of the other color.
If it would be possible, then every piece would have a number of squares divisible by 3 (because if a piece has n squares of one color and 2×n squares of the other color, it has 3×n squares in total).
The total number of squares of all pieces would then also be divisible by 3.
This is, however, impossible since the total number of squares on the chessboard is 64, which is not divisible by 3.
More puzzles to try-
- 3 + 3 = 3 5 + 4 = 4 1 + 0 = 3 2 + 3 = 4 ...Read More »
- Five puzzleFry ship’s pirates have obtained 100 gold coins and have to divide up the loot. The pirates are all ...Read More »
- There are 10 stacks of 10 coins each. Each coin weights 10 gms. However, one stack of coins is defective ...Read More »
- Dr.Willam wants to operate for three different persons who were wounded. But he had only two surgical gloves. There is ...Read More »
- Which clock works best? The one that loses a minute a day or the one that doesn’t work at all?Read More »
- In the gear arrangement, To which one will the needle touch, 1 OR 2Read More »
- A man leaves his house in the morning to go to office and kisses his wife. In the evening on ...Read More »
- Which letter replaces the question markRead More »
- Some numbers are very mysterious. They are all integers. They have more than one digit. If you multiply them with ...Read More »
- A bridge will collapse in 17 minutes. 4 people want to cross it before it will collapse. It is a ...Read More »
- In a country where everyone wants a boy, each family continues having babies till they have a boy. After some ...Read More »
- A devotee goes to three temples, temple1, temple2 and temple3 one after the other. In front of each temple, there ...Read More »
- There is a perfectly accurate analog watch with hour, minute, and second hands. How many times a day do all three ...Read More »
- Four days are there which start with the letter ‘T‘. I can remember only two of them as “Tuesday , Thursday”. ...Read More »
- Two fathers took their sons to a fruit stall. Each man and son bought an apple, But when they returned ...Read More »
- A farmer is taking her eggs to the market in a cart, but she hits a pothole, which knocks over ...Read More »
- In the middle of the confounded desert, there is the lost city of “Ash”. To reach it, you will have ...Read More »
- Solve this logic sequence puzzle by the correct digit- 8080 = 6 1357 = 0 2022 = 1 1999 = ...Read More »
- Jasmine, Thibault, and Noah were having a night out and decided to order a pizza for $10. It turned out ...Read More »
- A murderer is condemned to death. He has to choose between three rooms. The first is full of raging fires, ...Read More »