Interdependent data validation

I’m looking for a way to have drop down list choices automatically filter based on 1) each other, and 2) a field of information.

Example (also attached):

BOX A
BOX B
BOX C

a b c
2 1 3
2 2 3
2 2 3
3 1 4

The numbers under a, b, and c are lists, and the boxes represent drop-down menus with the contents of those lists. If:
1. I set the “a” box to 2 and
2. I set the “b” box to 1, then
3. The only option I want in the drop down menu in box c is 3.

AND, it has to work both ways, e.g. if
1. I set “c” to 4, then
2. The only option that should show up for b is 1, and
3. The only option that should show up for a is 3.

Hope I explained that adequately. Any ideas?