Reading a board before your first move

Why the opening is different

On a fresh board every square is open, so neither sweep will produce anything — no colour is down to one square, no line is down to one square. The techniques that carry the middle of the solve have nothing to work with yet. What the opening needs instead is a reading of the board's structure, which determines which colour you attack first and therefore how quickly the first forced move appears.

This is the part of the solve that rewards patience most and gets rushed most. Thirty seconds of looking routinely saves several minutes of grinding, because attacking the right colour first produces a cascade and attacking the wrong one produces nothing.

Four things to read

First, region sizes. Every colour takes exactly one queen regardless of how many squares it owns, so a colour with three squares has three candidate positions and a colour with fourteen has fourteen. Information is concentrated where the options are fewest. Find the smallest colour and note it.

Second, single-line colours. Does any colour lie entirely within one row, or entirely within one column? If so, that line belongs to it and every other colour is locked out immediately — a free elimination sweep before you have placed anything. Boards with two or three of these fall apart quickly. This is the single most valuable thing to check and takes about five seconds.

Third, colour counts per line. Walk the rows counting distinct colours, then the columns. The tightest lines are where the next deduction is most likely to hide, and the most crowded ones are where you should not waste attention.

Fourth, compactness. A colour crammed into a two-by-two block behaves very differently from one straggling across five rows, even at the same square count. Compact colours cast shadows and resolve early; straggling ones reach into many lines and stay open until late. Note which colours are which so you know where to expect resolution and where not to.

Turning the reading into a first move

If the board has a single-line colour, start there — claim the line, cross out everyone else on it, then run both sweeps. That is usually enough to start a chain.

If it does not, take the smallest colour and test its candidates. For each square, imagine the queen there and apply the eliminations that would follow. If any of those trial placements would leave another colour with nowhere to go, the candidate is dead. Killing even two candidates in the smallest colour tightens the entire board around it.

If neither applies — no single-line colour, and the smallest colour is still four or five squares — go to the shadow check. A compact colour with three or four candidates is very likely to be covering a square or two next to it, and one elimination is all you need to get the sweeps moving.

What not to do first

Do not start from the largest colour, however tempting its shape. It has the most candidates and the weakest constraint; it will be the last thing to resolve on almost every board and working it early is wasted effort.

Do not start by placing a queen that looks right. The board offers no forced placements at move one, so any queen you place at that point is a guess by definition, regardless of how strongly the geometry seems to suggest it. On a single-solution puzzle a wrong guess does not announce itself for several moves.

And do not scan from the top-left out of habit. The corner of the board is no more likely to be informative than the middle. Let the structure of the colours decide where to look, not the reading direction you learned for text.