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Seems more a game of trial-and-error than actual logic. Still, it's a novel idea, so definitely points deserved there.
You generally can use some logic to winnow the possibilities down to something managable. Experimentation is certainly an option, but if you think you need to brute-force the solution then there's probably a better way.
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This was very fun until I started getting to levels where two different blocks are the same color. At this point I no longer feel I'm able to properly strategize, and my attempts are reduced to a brute force approach. I really enjoy that.
Haha - they're pretty evil arn't they? Sorry about that. Fortunately there arn't very many of those. I don't recommend you try to brute-force them. The trick is to figure out which blocks are which type by running experiments over them. Yes this needs great recall or documentation of your progress. Props for getting so far.
I think in-game achievements are worthless in most casual games. They don't have the bragging potential of account-based achievements. Would having an additional icon for each bunch of levels give any additional incentive over the pride of turning all the level buttons yellow? Not in my eyes.
This game is set up with stats, so it's "achievement ready" for Kongregate badges. However to get those a game essentially needs an average player rating of over 4/5. So if you do want them, voting anything less than five is counterproductive.
Obviously I'd like this game to get a high rating, but that's true in general, for Kongregate at least.