Neon strategy guide
Connecting pairs on a grid that must end up completely full is a routing problem, and routing problems reward structure over trial and error. Here is how strong solvers read a Neon board before the first drag.
Read the border first
The edge of the board is where Neon puzzles give the most away. A symbol on the border has only three neighbors, and a symbol in a corner has two, so a line leaving it has almost no choice about its first step. When both symbols of a pair sit on the same wall, the line between them almost always runs straight along that wall: any detour inward would have to come back out and would cut off the cells it looped around.
Strong solvers trace the perimeter mentally before touching the screen. Which pairs own the edges? Where does an edge line have to turn inward because another pair's symbol sits in its way? Those forced border segments are free information, and they shrink the interior problem dramatically.
Think in full coverage, not shortest paths
The rule that every cell must be lit changes the puzzle completely. If you draw the shortest line between every pair, you will almost always leave dark cells behind, and there is no line left to fill them. So the real question for each pair is not "how do I connect these?" but "which cells is this line responsible for?"
Look for regions that only one line can plausibly reach — a pocket beside one pair's symbol, or a strip between two lines that are already fixed. The line that can reach that region must bend to fill it. Filling pockets deliberately, rather than discovering them at the end, is the single biggest jump in solving speed.
Count dead ends
A dark cell needs two free neighbors to be passed through, or one free neighbor plus a symbol on itself to be an endpoint. As lines fill the board, keep an eye on any dark cell that is down to a single open side. If it holds no symbol, a line must enter and leave it, which is impossible — so whichever line just sealed it off is wrong and must be pulled back.
The same reasoning works in advance. Before drawing a segment, glance at the cells alongside it: would any of them be left with one exit? If so, the segment needs to swing through them instead. This local check catches most mistakes before they cost a full reroute.
Every line is a wall
Because lines cannot cross, each finished line divides the board into two sides. Two symbols of the same pair must always be on the same side of every other line. A long line that separates a pair from its twin is illegal no matter how neatly it fills its own cells, so check the pairs that are still open before committing to a route that spans the board.
Turn this into a habit: after each line, ask which pairs remain and whether each still has a connected path of dark cells between its two symbols. If one does not, undo immediately. On the 7×7 and 8×8 boards this check is what separates a steady solve from a tangle of restarts.
Use the parity of the grid
Color the cells like a checkerboard in your mind. Every step of a line moves from one color to the other, so a line with an odd number of cells starts and ends on the same color and a line with an even number of cells starts and ends on opposite colors. That fixes the parity of every pair's line length before you draw a thing.
When two candidate routes both seem to fill a region, count the cells: if one route would leave an odd-sized region for a pair whose symbols sit on opposite colors, that route is impossible. Parity rarely solves a board alone, but it settles the last ambiguous corner far faster than trial and error.