There appears to be 3 basic principles upon which we disagree:
1) Your color must be within sight.
2) There is no need to prove that your unseen algorithm is unchallengeable.
3) The Master cannot be lying because that is a premise to the puzzle.
You claim that the Master’s assertion that the puzzle is solvable allows you to be certain of whatever pattern and algorithm you envision to be the right one, “else it would not be solvable”.
In the following example (1), the Master has declared that the puzzle is solvable. You can envision a pattern. But you cannot visually see the missing color that completes that pattern:
Remember the Master said that it is solvable.
You seem to deny a “premise” and claim that the Master was lying.
A different example (2), again the Master said that it is solvable. So what is the only possible algorithm and when do they each leave?
And a third example (3), again the Master said that it is solvable, so what is the only possible algorithm and when do they each leave?
The combination of the 3 of those proves that:
1) Your color certainly need not be within sight,
2) You certainly must prove that your chosen algorithm is unchallengeable,
And/Or
3) The Master can be lying.
And of course if the Master can be lying, none of the puzzles are ever solvable.