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

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.

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 think I used a simlar method, the areas of the simpler ratios were 1,2,3 and 4. I then multiplied these by 4 to make a total of 64 (doubling the sizes). This was a slight hunch because 64=2^6 so I assumed trebling would not help.

Originally posted by Jirakon Can you cut the chessboard into four congruent shapes, each of which contains exactly one of the following squares: a1, b2, c3, d4?

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

You're calculating areas. The problem is about ratios.