Solving 11x11 and 12x12

What actually changes

The rules are identical and so are the techniques. What changes is the cost of a full scan. On a 7x7 grid there are 49 squares and seven colours; re-reading the entire board after every placement takes a few seconds and the simplicity is worth it. On a 12x12 grid there are 144 squares and twelve colours, and a full scan after every one of twelve placements will dominate your solve time while producing new information on only a fraction of the board.

The second thing that changes is memory load. Holding partial eliminations in your head works at 49 squares and does not work at 144. The most common cause of a failed large-board solve is not a missed technique but a player who remembered a square was eliminated, never marked it, and later treated it as open.

Working locally

A newly placed queen creates new information only where it reaches: its row, its column, its colour, and the colours that own squares in those lines. Nowhere else on the board has changed. So the sweep after a placement should start local — check the colours the queen actually touched, and the rows and columns it cleared — and expand to a full pass only when the local check yields nothing.

In practice this cuts the work by more than half on a 12x12 board and costs nothing in completeness, because a deduction that was available before the placement and is still available after it will be found on the next full pass anyway.

The same applies to the narrowing techniques. Re-check for locks in the lines you just crossed squares out of. Re-check for shadows on the colours that just lost candidates. Both are triggered by your own eliminations, so the moment after you make them is when they are easiest to spot.

Quadrants

On 11x11 and 12x12 it helps to divide the board into four rough quadrants and treat them semi-independently. Most useful deductions at that scale are regional rather than global: a colour pinched between two placed queens, a pair of colours sharing two rows in the same part of the board, a compact colour casting shadows on its neighbours. Very few deductions span the whole grid.

Work one quadrant until it stops producing, then move to the next, then return. The rotation matters because eliminations in one quadrant propagate into the others through shared rows and columns, so a quadrant that was silent ten moves ago may have become the most productive one.

The obvious exception is the pairing argument, which genuinely is global: two colours sharing two rows may sit at opposite ends of the board. Run that check across the full grid, but run it only when the local work has stalled — it is the expensive search, and on a large board the expensive searches need to be earned.

Marking discipline

Mark everything, immediately, including the marks you are certain you will remember. This is boring advice and it is the difference between finishing a 12x12 board and abandoning it.

The specific failure to guard against is the partial sweep: you place a queen, clear its row and column, get distracted by an interesting deduction three rows away, and never finish the colour and the diagonals. The deduction you chased was real, but the board now carries a lie, and everything you derive from that point is suspect. Finish the marking before you follow the idea. The idea will still be there.

If a large board does go wrong — you reach a position with a colour that has no legal square — do not try to repair it by adjusting the last placement. Work backwards through the queens auditing each one's full ring of eliminations. The error is almost always a missing mark rather than a wrong queen, and finding it is faster than re-solving.