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Especially since you didn't search for one of the billion copies of this topic.
Especially since you didn't know you sign up for idiots like me when you use forums for games like Hexcell.
There is clearly not enough information in the starting post to deduce this, so you are just guessing yourself. By your own logic that would make you "not very smart", but I don't know if that is really the case. I have to agree with this though:
To answer the initial question:
All levels in all of the three Hexcells games can be completely deduced, there is never a need to guess. Hexcells Infinite has a random level generator which generates levels in a way that guarantees them to be solvable without guessing.
However, support for user generated levels is coming for Infinite. The editor for these levels (made in part by the arrogant one) has no way of guaranteeing guess-free solving.
I can't in completely good conscience vouch for the generator in Infinite (bugs are always possible), but I didn't come across an unsolvable one while getting the achievement.
Wrong. Many thought that, every single one of them missed something that would allow them to deduce the next step. I solved all of the designed puzzles in all three games and over 200 of the generated ones in Infinite without guessing even once.
Post as many screenshots as you like of situations where you "need to guess". You will be proven wrong in every one of them.
One way to mess yourself up is to prematurely mark a number "done" by right clicking it. I accidentally right clicked a blue number and my brain overlooked it every time I scanned the board for the next move.
Some of them have seen impossible, but after I came back to it the next day, a new move opened up I didn't see before. Let your brainmeats rest a while if you're stuck, it helps.
Good to know they can all be deduced, however im not going to spend 30 minutes staring at a screen to make a move unless there are fleshy bits bouncing around. I'm going to enjoy the ones I can and leave the others. Having gotten each game in this series for a buck, I feel the timewasting-to-money ratio is balanced.