Quote Originally Posted by Lindsay View Post
Then I remembered that genitive plural is used for 0 and 5+, but genitive singular is used for quantities 1-4. I thought perhaps I had to use the genitive singular adjective for "3 plates", but according to my chart that would be белего!
There is one mistake in your explanation. If a numeral ends in "один", the noun takes nominative singular, not genitive.
The genitive singular only works for 2-4, not for 1-4 (more exactly, for any numeral which ends in два/три/четыре, since 12, 13, 14 do not belong to this group: двенадцать, тринадцать, четырнадцать).

Quote Originally Posted by Lindsay View Post
So please - can someone explain the logic of when to use белые and when to use белых - and perhaps also why it's not белего?
Although it is not related to your original question, but the form "белего" does not exist.
The genitive singular masculine of "белый" is "белого" (I've underlined the stressed vowel). However, it does not work with numerals for the reasons I explained above.
This adjective has a hard stem in -ый. So, all its ending should belong to the hard group. Actually, all the adjectival endings come in pairs for the hard stem and soft stem:
-ой(-ый) / -ий
-ая / -яя
-ое / -ее
- ого / -его
etc. etc.