How to fit 10x10 rectangle, 1x10 rectangle, and 1x1 square into given area

Question

I've been given a 2D rectangle which is 18 wide and 19 long. I've only been given shapes of the size of a 10x10 rectangle (representing 100), a 10x1 rectangle (representing 10), and a 1x1 square (representing one). All of these shapes are 2 dimensional.

Using a total area of 342 (18x19), I am supposed to fit 3 100 blocks, 4 10 blocks, and 2 1 blocks. How can I go about doing this? After drawing the first 100 block, I can't see how I can even fit the other two 100's.

I've attached an image of my drawing so far

I know this should be straightforward, but I can't wrap my head around it ... any help would be greatly appreciated, thank you!

Answer 1

You can not even fit two $10\times10$ squares. If both squares share no rows, then you need $20$ rows, that is, a height of $20$ squares, and if both squares share no columns, you need a width of $20$ squares. If both squares share a row and a column, then they share the square of intersection, so they overlap.