8x8 Queens Puzzle #22

About 8x8 Queens puzzle #22

Board #22 of the 8x8 bank carries a hard rating. Its 64 squares are shared between eight colored regions, and the solution places eight queens: one per row, one per column, one per region, none of them side by side or corner to corner.

Like every board on this site, #22 has been verified to have exactly one valid solution, and that solution is reachable by deduction alone. You never have to guess and then unwind; every queen can be justified by something already visible on the grid. What changes from puzzle to puzzle is where the first certainty appears and how long the chain of reasoning runs before the next one — and that is entirely a product of how these particular colors are shaped.

How the colors divide this board

From smallest to largest, the regions on puzzle #22 are: indigo (2 squares), blue (3 squares), red (3 squares), slate (6 squares), amber (7 squares), khaki (8 squares), mint (14 squares), pale yellow (21 squares). An even split would hand every color 8 squares, so the indigo region is running 6 squares under that average while the pale yellow region is the roomiest area on the grid with 21 squares.

That imbalance is the first thing to read, because every region takes exactly one queen regardless of how much space it owns. Indigo has only 2 places to put its queen; pale yellow has 21. The spread between them on this board is 19 squares, and the wider that spread runs, the more it pays to solve from the small end inward.

Look at arrangement as well as area. Indigo is the densest region on this grid at 100% of a 1×2 frame; amber is the loosest, occupying only 47% of its 3×5 frame. The loose one reaches into more rows and columns, which is exactly why it usually settles last.

Region by region

The complete breakdown of each region on this board follows, ordered from tightest to roomiest. Skimming the spans first tells you where the board is crowded and where it has slack.

Indigo covers 2 squares, spanning 1 row and 2 columns (rows 1–1, columns 7–8). It never leaves row 1, so its queen is locked to that row.

Blue occupies 3 squares within rows 2–3, columns 7–8.

Red: 3 squares across rows 6–7, columns 3–4.

Slate covers 6 squares, spanning 4 rows and 2 columns (rows 2–5, columns 1–2).

Amber occupies 7 squares within rows 1–3, columns 1–5.

Khaki: 8 squares across rows 6–8, columns 1–3.

Mint covers 14 squares, spanning 5 rows and 4 columns (rows 1–5, columns 3–6).

Pale yellow occupies 21 squares within rows 3–8, columns 4–8.

Where to start on this board

Indigo is the natural opening on #22: it is the smallest region on the grid at 2 squares, boxed into rows 1–1 and columns 7–8. Since one of those squares must hold a queen, that block of 1 row and 2 columns is the most contested part of the board.

Because indigo never leaves row 1, its queen must be in that row — and that instantly settles row 1 for everyone else. Sweep along it and X out every square that is not indigo. Then look at which colors just lost ground: on a grid this size that one observation usually forces a second region within a move or two.

Work outward to the other flat regions next. Blue and red are no more than two rows tall, so their queens are confined to a narrow band. When two flat regions overlap the same pair of rows, those rows are spoken for and every other color is locked out of both — the single most productive pattern in the game, and it is live on this board.

The tightest lines on puzzle #22

A quick way to find the next move is to count how many different colors touch each line. On this board, row 8 is the narrowest, touched by only 2 colors. Column 6 is the tightest column, with 2 colors.

A line with few colors is a line close to resolving. Where only 2 colors appear, one of them owns the row outright and the others must fit into the remaining 7 rows. Row 3 is the crowded extreme at 5 colors — worth revisiting later, not now.

Working through the middle game

After the first few queens the puzzle becomes bookkeeping. A placed queen wipes its row, its column and every square it touches — as many as eight neighbours — so the space collapses quickly. Record those eliminations on the board instead of carrying them in your head, and the next forced move tends to announce itself.

Keep alternating between two views of the board. In the region view you ask which of the eight colors is down to one open square. In the line view you ask the same of each row and column. Both produce forced queens, and each placement refreshes the other view, so cycling between them deliberately is how a 8x8 board unwinds.

The trap on a board like this is placing a queen that is merely plausible. Every placement should be traceable to an elimination you can point at. If you cannot name the rule that forced it, you are guessing — and on a single-solution grid a guess costs more to unwind than the deduction would have taken to find.

Why puzzle #22 is rated hard

Ratings track how generous the opening is. On #22 you get one region pinned to a single row or column, a smallest color of 2 squares, a tightest row crossed by 2 colors, and a 19-square gap between the largest and smallest regions. Those four numbers largely explain the hard label.

Nothing about the rating involves computation or chance. Each grid has a single solution reachable by pure logic; the rating simply measures how far ahead you have to reason. Easy boards resolve a queen every step or two, while hard ones can ask you to carry three unfinished lines of thought before any of them pays off.

If #22 feels harder than its rating suggests, the usual culprit is incomplete marking rather than a difficult deduction. Check that every queen already on the grid has its full cross of eliminations recorded — including the diagonal neighbours, which are by far the easiest to miss. More stalled solves come from one forgotten diagonal X than from any genuinely deep chain of logic.

Techniques that work well at 8x8

At 8x8 the whole grid stays within a single glance, which makes systematic scanning practical. Read the rows in order and count the colors in each — a row touched by two colors is far more constrained than one touched by five, and that is usually where the next forced move hides. The board is small enough that re-scanning from the top after each placement costs almost nothing.

One pattern is worth learning at every size, and it is available here. When two regions can only fit inside the same two rows, they must take one row each — which locks every other region out of both. The same argument works for columns, and for any matching count: three regions sharing three rows, four sharing four. Spotting these pairings turns a slow grind into a quick cascade, and on #22 the place to look for one is around row 8.

A non-spoiling distribution check: solved, #22 carries 4 queens on the perimeter against 4 queens inside, with the corners empty. Because no two queens may touch, real solutions always look fairly evenly spread — a lopsided board in progress is a warning sign.