Three rules, and that is all there is
First: no three identical symbols may sit in a row, in any line, in either direction. Second: every row and every column holds exactly as many suns as moons. Third, where they appear, the small markers between two cells say those cells are equal or that they differ.
There is no arithmetic, no colouring, no adjacency geometry to hold in your head. Two symbols and three constraints. The entire difficulty comes from how those constraints interact along a line, which is why the puzzle stays interesting long after you have understood it completely.
The two moves that solve most of the board
A pair is the first thing to hunt for. Two identical symbols side by side cannot be allowed to become three, so both cells flanking them take the other symbol. On a partly filled board this cascades: the symbol you just placed often creates a new pair, which places another, and a line can resolve in a single sweep.
The gap is the mirror image. Two identical symbols with a single space between them must have the opposite symbol in that space, for exactly the same reason. Between the pair and the gap you will finish most easy boards without ever consciously counting anything.
Counting is the third move and it arrives later: once a line already holds half its cells as suns, every remaining cell in that line is a moon, no further thought required.
When the simple moves run out
Harder boards reach a state where no pair, no gap and no full line is available, and this is where the genre earns its reputation. The move is to look at a line as a whole and ask which completions of it are legal at all. Often several are - but if every one of them puts a sun in the same cell, that cell is a sun, and no simpler rule would ever have told you.
The hardest tier goes one step further: assume a cell is a sun, follow only the simple rules, and if the line becomes impossible then the cell was a moon. You never keep the assumption. You only ever use it to rule one out, which is why this is still deduction rather than guessing.
Why the boards here never need a guess
It is easy to make a binary grid with one answer and no reasonable way to find it. Those are the boards that make people give up on the genre, and they are exactly the ones that do not get published here.
Every board is checked twice: once to confirm the answer is unique, and once by a solver that is only allowed to use the named techniques above. If the second one cannot finish, the board is not used. The tier you see is the hardest technique it actually needed.
Common questions
What makes a binary puzzle different from sudoku?
There are only two symbols instead of nine digits, and no regions. The constraints are that no three identical symbols sit in a line, and that each row and column ends up with equal numbers of both.
What do the small symbols between cells mean?
An equals marker says the two cells it sits between hold the same symbol; a cross says they differ. Knowing one side settles the other, which makes them a good place to start.
Do I ever have to guess?
Not on any board here. The hardest tier can require assuming a cell and showing the assumption breaks a rule - but that rules a possibility out rather than gambling on one, and you never keep the assumption.