A very easy or very difficult problem

[davemath]

Hi,

Can you tell me following belong to what kind of problem and teach me solve it or point the relevant articles. Thanks a lot for your help.

Without overlapping, put some small rectangles onto a big rectangle. The big rectangle have known width and infinite length, while the small rectangles' shorter edge less or equals to the width of the big rectangle. Find the pattern so that it occupies the smallest length of the big rectangle.

 

[Loren]

I think you are after the word "tessellation".

 

[davemath]

A tessellation is created when a shape is repeated over and over again covering a plane without any gaps or overlaps.
Howeve in my case, gaps will be allowed and shapes may differ from each other!

 

[DrMike]

Are the small rectangles all the same size/shape ?

 

[davemath]

Thank you.
The small rectangles may have different size/shape!!

 

[DrMike]

Can't you just use one infinitesimally thin small rectangle, whose length is the width of the big rectangle? I get the feeling that the problem is still not clearly defined...