[pdurrant]

Originally Posted by pdurrant

What's the smallest number of pieces I must cut the 10x10 metre carpet into, to make it fit the 12x9 space, with the 8x1 hole in the middle? Hint: It's less than four.

Answer:

Spoiler:

Only one cut giving two pieces of carpet is required.

The way to do it is to cut on a zig-zag diagonal, so that one piece can be moved two across and one down, giving the 12x9 outer dimensions from the 10x10 original carpet. Of course, this zig-zag from the bottom left won't meet up with a similar zig-zag from the top right. But by cutting along the horizontal line in the middle that they both reach, interesting shapes are created that give the required 1x8 hole in the middle of the finished carpet. when moved as described.

I attach a zipped gif. Download and decompress to see a picture of the solution.