You have an 8 by 8 carpet and another 6 by 1 strip of carpet.
                                                 
You are required to cut the 8 by 8 carpet into exactly two pieces, using only one cut, so that these two pieces and the 6 by 1 strip can be used to form a 10 by 7 carpet.

Solution: Before looking at the solution, give this a good good try. It is actually a very interesting problem.

The solution is as follows. This is how we cut the carpet:

Now we translate the two parts 1 unit each in opposite directions, so that the situation looks something like this:

Finally, we translate the part at the right 1 unit upwards, so that we have:

A 6 by 1 area forms in the middle. Now we just fit our 6 by 1 strip of carpet here, and the 10 by 7 carpet gets completed!