Regarding the zero knowledge proof, there'd be a chance that the two random ones you reveal are the same color, if three weren't enough.
So by doing this over and over again, if the two you choose are always different colors, you approach a 100% certainty that it's legit.
You never really get a 100% proof but the more times you repeat the closer you are to being sure. At 99.999999% after repeating this enough times, you'd most likely be satisfied.
When I read the zero knowledge proof part the first time, my thought was:
The person can just always give two different colors (and never two same colors) when you reveal two post it notes, so you could never proof them false.
Only after re-reading I realized _all_ the colors are to be hidden under the post it notes _beforehand_, not at the time you choose two post it notes.
So by doing this over and over again, if the two you choose are always different colors, you approach a 100% certainty that it's legit.
You never really get a 100% proof but the more times you repeat the closer you are to being sure. At 99.999999% after repeating this enough times, you'd most likely be satisfied.