Carpets

There are two carpets with measure 10 x 10 and 8 x 1. You have to cut one of them so that you get totally three parts now. With these three parts you have to cover a surface of 12 x 9.

Originally posted by crazyblue
There are two carpets with measure 10 x 10 and 8 x 1. You have to cut one of them so that you get totally three parts now. With these three parts you have to cover a surface of 12 x 9.

Cut them anywhere you like, they already cover 12x9.

Originally posted by Tactics
Cut them anywhere you like, they already cover 12x9.

try again

Originally posted by crazyblue
There are two carpets with measure 10 x 10 and 8 x 1. You have to cut one of them so that you get totally three parts now. With these three parts you have to cover a surface of 12 x 9.

I think he means 1 cut (only) and no layover.

The simple solution would be to make 2 cuts:

cut the 10x10 into 10x8 + 10x2
then cut 10x2 into 9x2 + 1x2

Then the four pieces drop easily in a 12x9 area.
1x2 + 1x8 = 1x10
1x10 + 8x10 = 9x10
9x10 + 9x2 = 9x12

But this requires two cuts.

To make this work with one cut -- I don't want to give the solution away -- prepare to cut an odd shape out.

Originally posted by sdrawkcab
I think he means 1 cut (only) and no layover.

The simple solution would be to make 2 cuts:

cut the 10x10 into 10x8 + 10x2
then cut 10x2 into 9x2 + 1x2

Then the four pieces drop easily in a 12x9 area.
1x2 + 1x8 = 1x10
1x10 + 8x10 = 9x10
9x10 + 9x2 = 9x12

But this requires two cuts.

To make this work with one cut -- I don't want to give the solution away -- prepare to cut an odd shape out.

You propsed the followong two cuts:
cut the 10x10 into 10x8 + 10x2
then cut 10x2 into 9x2 + 1x2

Can't you put the carpets on top of eachother so the same cut cuts both of them?

Originally posted by sdrawkcab
I think he means 1 cut (only) and no layover.

The simple solution would be to make 2 cuts:

cut the 10x10 into 10x8 + 10x2
then cut 10x2 into 9x2 + 1x2

Then the four pieces drop easily in a 12x9 area.
1x2 + 1x8 = 1x10
1x10 + 8x10 = 9x10
9x10 + 9x2 = 9x12

But this requires two cuts.

To make this work with one cut -- I don't want to give the solution away -- prepare to cut an odd shape out.

"totally three pieces" means you can't use four pieces.

This reminds me of my next door neighbour.

He came round one day and said.

"You have the same size of living room as me, how many rolls
of wall paper did you buy to decorate it?"

"Six." I replied.

He came back a few days later and said he has one roll left.

I said, "So have I."

Originally posted by FabianFnas
Can't you put the carpets on top of eachother so the same cut cuts both of them?

You can only cut one of them.

Solution sent. I am not sure if it is the only one, but I am fairly certain it is the solution crazyblue had in mind.

Originally posted by geepamoogle
Solution sent. I am not sure if it is the only one, but I am fairly certain it is the solution crazyblue had in mind.

yep correct

i hav a prob..lets say for example, we take 4 squares say a1,a2,b1,b2.. if we take away a2 and b1 squares, wud it imply that a1 and b2 has also separated or not?? and again, can I use both sides of the carpet??

The problem as stated can be solved under the following parameters.

1) The 10x10 carpet is laid perfectly flat on a flat surface before cutting.
2) The single cut made only touches the edge of the 10x10 square at the start and the end of the cut.
3) The single cut does not intersect itself at any point.

In short, there is no "trick" answer required, but rather there is a solution consists of cutting the 10x10 square into two distinct and whole parts, and no more.

I will note here one hint to help you a little (but not much).

If you were to drawn a 10x10 grid on the carpet, there is at least one solution where you only cut along the grid lines only.

I may give a much bigger hint later which is much more spoilerish, provided there is need for it.

By 'one cut' does that mean you have only one straight line cut or can you say, turn right 90 degrees some way down the cut? Does that still qualify as 'one cut'?

Originally posted by sonhouse
By 'one cut' does that mean you have only one straight line cut or can you say, turn right 90 degrees some way down the cut? Does that still qualify as 'one cut'?

yes definitely it must be.. otherwise it seems impossible..

Originally posted by blacknight1985
yes definitely it must be.. otherwise it seems impossible..

In that case the problem is almost trivial.
Seems like cheating though, in the real world you have to stop cutting in one direction to start cutting in another. I guess you could do it by approaching a smaller and smaller circular cut, small radius so you don't stop cutting