Squaring the Square
The problem of dividing a square into a number of smaller squares, all of different sizes, was not solved until the late 1930s. The smallest possible solution was found by A. J. W. Duijvestijn in 1978. It has 21 smaller squares ranging in size from 50 units down to 2.
For more history of this, see the Wikipedia Page. For many more details and examples, see: Squaring.net which has more on the subject than you would ever want to know!
My wooden cabinet follows Duijvestijn's solution (although upside down from the diagram above).