Programmatic analysis of geometric shapes

Question

I’m trying to work out a math / geometry problem in a Java project I’m working.

Here is the scenario:

There are two sets of blocks, each with a different number of blocks and different dimensions. In this example Set A has 5 blocks, each is 20x20 pixels; Set B has 6 blocks, and each is 25x50 pixels:

I’m trying to come up with a way to mathematically or logically determine how those sets would line up to maximize the contact between them. If you were to line these set up end-to-end it would look like this:

In this image, 4 of the blocks in set B are in contact with the blocks in set A. However, if you shift set A to the right a bit, you can get 5 of the blocks in set B to touch:

The problem is that the formula / algorithm / logic needs to be flexible enough to handle different combinations. In this example, set C has only 3 blocks, and each block is 40x40:

Any ideas?

Answer 1

Center the two sets of blocks and shift one of them by a small amount.