- 14 Apr '08 15:45

Lets see...*Originally posted by FabianFnas***Can you cut a chess board into four rectangles so they have the ratios 1:1, 1:2, 1:3 and 1:4 respectively?**

You cannot cut squares in parts.

To cut the board into 4 rectangles, we must make 3 paralle cuts or 2 perpendicular cuts.

The first option is impossible since the 1:1 rectangle is a square.

The second option is impossible since the rectangle having no common edge with the 1:1 rectangle is a square, but 1:2, 1:3, 1:4 are not squares.

So there is no solution, even if cutting squares in parts is allowed. - 14 Apr '08 20:08

Shame:'(*Originally posted by David113***Lets see...**

To cut the board into 4 rectangles, we must make 3 paralle cuts or 2 perpendicular cuts.

The first option is impossible since the 1:1 rectangle is a square.

The second option is impossible since the rectangle having no common edge with the 1:1 rectangle is a square, but 1:2, 1:3, 1:4 are not squares.

So there is no solution, even if cutting squares in parts is allowed.

I forgot the third way, which gives a solution - 18 Apr '08 05:01

You're calculating areas. The problem is about ratios.*Originally posted by Guych***I think you cannot do that. Maybe my calculations are wrong:**

I suggest letting x be the largest part of the board. Then we can rite the following equasion:

x + 1/2x + 1/3x + 1/4x = 64

Multiply the equasion by 12:

12x + 6x + 4x + 3x = 768

x = 30.72