9x9 Queens Puzzle #128
Difficulty: hard. Place 9 queens on this 9x9 board so that no two share a row, column or color region and none touch — including diagonally. This puzzle has exactly one solution, and it has been verified solvable by deduction alone: the complete 13-step reasoning is written out below.
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Step-by-step solution for puzzle #128
What follows is a complete solve of puzzle #128, worked the way a person works it rather than the way a computer does. It runs to 13 deductions — 9 queen placements and 4 elimination steps that narrow the board between them. Each step names the rule that forces it, so nothing below is a guess, and the hardest idea required is the region shadow.
Techniques this board needs: last square in a region, region confined to one line, region shadow.
Show the full walkthrough (6 steps) — contains the solution
Step 1. The board opens by cascading. Each of these placements is forced the moment the one before it is marked, so the whole run is really a single sweep repeated: orange has one square left, so its queen takes row 9, column 3; slate has one square left, so its queen takes row 5, column 2; mint has one square left, so its queen takes row 4, column 4; red has one square left, so its queen takes row 6, column 8. After each one, clear that row, that column, the rest of the colour and the ring of neighbours before looking for the next. The last of them seats the queen on row 6, column 8.
Step 2. Blue cannot leave column 1 — every one of its open squares (3 open squares) sits there. That column belongs to blue, so every square in it owned by another colour is dead: 2 squares in all.
Step 3. The amber region has 4 squares left, spread across rows 2 and 3, columns 5–7. You do not need to know which of them takes the queen: every one of those options attacks the same 1 square, so they can be crossed out now.
The board after step 3 — 4 of 9 queens placed. Step 4. Wherever pale yellow ends up among its 3 squares, the same squares fall within reach of it — 1 square in total, impossible regardless of how the colour resolves.
Step 5. All of the khaki region's remaining squares (2 open squares) lie in row 8. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 3 squares come off.
Step 6. From here the board cascades. Keep alternating the region sweep and the line sweep and 5 queens fall out in order without any new idea being needed: pale yellow has one square left, so its queen takes row 7, column 5; blue has one square left, so its queen takes row 3, column 1; amber has one square left, so its queen takes row 2, column 6; indigo has one square left, so its queen takes row 1, column 9; khaki has one square left, so its queen takes row 8, column 7. After each one, clear that row, that column, the rest of the colour and the ring of neighbours before looking for the next. The last of them seats the queen on row 8, column 7.
The board after step 6 — 9 of 9 queens placed.
That completes the board: 9 queens seated, one in every row, one in every column and one in every colour, with no two of them touching. Notice that nothing in the sequence above required a guess — each placement followed from an elimination already on the grid, which is what “single solution, solvable by logic” actually means in practice.
About 9x9 Queens puzzle #128
This is puzzle number 128 in the 9x9 collection, rated hard. The grid holds 81 squares split between nine colored regions, and a finished board carries nine queens — one in every row, one in every column, one in every color, and never two of them touching, diagonals included.
There is exactly one way to finish #128, and it has been verified. More importantly, you can reach it without ever gambling: at every stage some square is provably right or provably wrong. Boards differ only in how deep you must dig before that proof appears, and the geometry of these nine regions is what sets the depth.
How the colors divide this board
From smallest to largest, the regions on puzzle #128 are: orange (1 square), mint (2 squares), slate (4 squares), red (4 squares), blue (11 squares), indigo (12 squares), amber (13 squares), khaki (14 squares), pale yellow (20 squares). An even split would hand every color 9 squares, so the orange region is running 8 squares under that average while the pale yellow region is the roomiest area on the grid with 20 squares.
Every color takes one queen and one only, whatever its size — which is why the 19 square difference between orange and pale yellow is worth noting before you touch the grid. The cramped colors resolve first and hand you information; the roomy ones absorb whatever is left over at the end.
Look at arrangement as well as area. Mint is the densest region on this grid at 100% of a 2×1 frame; pale yellow is the loosest, occupying only 48% of its 6×7 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.
Orange occupies 1 square within rows 9–9, columns 3–3. It never leaves row 9, so its queen is locked to that row.
Mint: 2 squares across rows 4–5, columns 4–4. It sits wholly inside column 4, so its queen must be in that column.
Slate covers 4 squares, spanning 3 rows and 2 columns (rows 3–5, columns 2–3).
Red occupies 4 squares within rows 5–6, columns 6–8.
Blue: 11 squares across rows 2–9, columns 1–2.
Indigo covers 12 squares, spanning 5 rows and 5 columns (rows 1–5, columns 5–9).
Amber occupies 13 squares within rows 1–3, columns 1–7.
Khaki: 14 squares across rows 6–9, columns 6–9.
Pale yellow covers 20 squares, spanning 6 rows and 7 columns (rows 4–9, columns 2–8).
Where to start on this board
Begin where the choices are fewest. On this board that means orange, which owns just 1 square inside a 1×1 window running from row 9 to row 9 and column 3 to column 3. A queen is guaranteed somewhere in there, so every line that window crosses is under pressure from the very first move.
Because orange never leaves row 9, its queen must be in that row — and that instantly settles row 9 for everyone else. Sweep along it and X out every square that is not orange. 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. Mint 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 #128
A quick way to find the next move is to count how many different colors touch each line. On this board, row 1 is the narrowest, touched by only 2 colors. Columns 1 and 9 are the tightest columns, with 2 colors.
Those lines matter because a row touched by few colors gives its queen away sooner. If a row meets only 2 colors, then one of those regions has to own it, and every other region is competing for the remaining 8 rows. By contrast row 5 meets 6 colors — the most crowded line here, and the one least likely to resolve early. Spend your attention accordingly.
Working through the middle game
The middle of #128 is where careless play costs time. Every queen you place kills a row, a column and the eight surrounding squares; if you do not mark all of that immediately, you will later "discover" a move that was available several turns ago. Mark first, then look.
With nine queens to seat and nine regions competing over 81 squares, keep two questions in rotation. Does any region now have exactly one open square left? That queen is forced. Does any row or column now have exactly one open square left? That queen is forced too. Alternating between the region view and the row-and-column view is what keeps a solve moving, and it is the clearest difference between players who finish 9x9 boards quickly and players who stall halfway.
Say the reason out loud: "this region has one square left", "this column has one square left". If no such sentence is available, the eliminating is not finished. One more pass of X marks is almost always quicker than committing to a placement you cannot defend.
Why puzzle #128 is rated hard
Ratings track how generous the opening is. On #128 you get three regions pinned to a single row or column, a smallest color of 1 square, 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.
Rating is a measure of chain length, not of chance. With one guaranteed solution and no guessing required, the only thing that changes across the collection is how many eliminations you must link together before a queen is provably forced.
Stuck on #128 despite the hard rating? The odds strongly favour a bookkeeping error over a hard chain of logic. Re-check each placed queen for its complete set of eliminations, paying particular attention to the four diagonal squares — those are the ones that get overlooked, and one of them is usually sitting on the answer.
Techniques that work well at 9x9
At 9x9 a full re-scan after every move starts to get slow, so work locally instead. Once a queen goes down, check only the regions, rows and columns that placement actually touched — that is where new information appeared. Fall back to a complete sweep only when the local pass turns up nothing, and your solve times will drop noticeably.
There is one technique that repays study at every grid size. Two regions restricted to the same two rows must occupy one row apiece, which excludes all other regions from those rows entirely; the identical logic applies to columns and to larger matched sets. It converts slow boards into fast ones, and the likeliest place to find it on #128 is row 1.
As a sanity check rather than a spoiler: the finished solution to #128 puts 3 queens on the outer border and 6 queens in the interior, 1 of them in an actual corner. If your part-finished grid has queens bunched into one area while whole stretches sit empty, something probably went wrong a few moves back.
How to play Queens
- The board is an N×N grid divided into N colored regions.
- Place exactly one queen (♛) in each row, each column, and each colored region.
- No two queens may touch each other — not horizontally, vertically, or diagonally.
- Tap once to mark a square with an X (where a queen can't go), tap again to place a queen, and once more to clear it.
- There is always exactly one valid solution. Use logic, never guessing, to find it.
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Questions about this puzzle
How hard is 9x9 Queens puzzle #128?
Puzzle #128 is rated hard. Its smallest color region holds 1 square, its tightest row is touched by 2 colors, and three of its regions are confined to a single row or column, which gives you a forced move early.
Does 9x9 puzzle #128 have only one solution?
Yes. Every puzzle in the 9x9 collection, including #128, has been verified to have exactly one valid arrangement of nine queens, and it can always be reached by logic alone — no guessing or backtracking needed.
Where should I place my first queen on puzzle #128?
Start with the orange region — the most constrained color on this board, with 1 square spanning rows 9–9 and columns 3–3. Narrowing the smallest region first removes the most squares elsewhere on the grid.