Carpet Cutting Puzzle

[GeoffC]

Originally Posted by travger

I must say, there are much more ways to cut a carpet to 4 pieces than I suspected!

something based on 2 "L" shapes ?

[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.

[Mickey330]

Sigh.

I kept looking at the durn thing, almost daily. Your posting has saved me another try 'cause when I saw it - I persuaded myself I was never going to get it.

So I looked at your answer.

Oi!

I really wouldn't have gotten that solution ... not in a bazillion years!

So, now I'm glad I gave up and looked. Now, I can throw away the graph paper (& put away the scissors, pencil and eraser!).

Thanks for the puzzle, pdurrant. Eventually, I will get one without having to peek ... !!!

Marilyn

[clarknova]

Originally Posted by Mickey330

I really wouldn't have gotten that solution ... not in a bazillion years!

Same here. That one was as tough as those "a bunch of really smart guys must infer the solution to some really complex puzzle with a tiny amount of information or they die" puzzles. I had no chance.

[pdurrant]

Originally Posted by clarknova

Same here. That one was as tough as those "a bunch of really smart guys must infer the solution to some really complex puzzle with a tiny amount of information or they die" puzzles. I had no chance.

I apologise a little for this one. I hadn't realised how much harder is was to find the smallest number of pieces possible than to find a solution for a known number of pieces.