9x9 Queens Puzzle #224
Difficulty: easy. 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 16-step reasoning is written out below.
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Step-by-step solution for puzzle #224
What follows is a complete solve of puzzle #224, worked the way a person works it rather than the way a computer does. It runs to 16 deductions — 9 queen placements and 7 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 pairing argument on rows.
Techniques this board needs: last square in a region, region confined to one line, region shadow, pairing argument on rows, last square in a column.
Show the full walkthrough (11 steps) — contains the solution
Step 1. Only row 1, column 9 is still open in indigo, and since each colour must take a queen, that settles it. That clears row 1, column 9, the rest of the indigo region and every square adjacent to it — diagonals included.
Step 2. The orange region is down to one open square, at row 9, column 3. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 9 and column 3, the remaining orange squares, and the ring of neighbours around row 9, column 3.
Step 3. Blue cannot leave column 8 — every one of its open squares (2 open squares) sits there. That column belongs to blue, so every square in it owned by another colour is dead: 5 squares in all.
Step 4. Wherever slate ends up among its 5 squares, the same squares fall within reach of it — 1 square in total, impossible regardless of how the colour resolves.
The board after step 4 — 2 of 9 queens placed. Step 5. Pale yellow is down to 7 candidates in rows 5–8, columns 2, 4, 5, and 6, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about pale yellow itself.
Step 6. The khaki region has 3 squares left, spread across rows 7 and 8, columns 6 and 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.
Step 7. Slate, red, pale yellow, and khaki are now boxed into rows 5–8 and nothing else. That is 4 colours needing 4 rows, so they fill those rows between them — which locks every remaining colour out and removes 3 squares at once.
The board after step 7 — 2 of 9 queens placed. Step 8. The blue region is down to one open square, at row 3, column 8. Every colour holds exactly one queen, so that square is forced. Row 3 and column 8 are now spoken for, along with the squares touching that queen.
Step 9. Amber cannot leave column 6 — every one of its open squares (2 open squares) sits there. That column belongs to amber, so every square in it owned by another colour is dead: 2 squares in all.
Step 10. All of the khaki region's remaining squares (2 open squares) lie in column 7. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 2 squares come off.
Step 11. From here the board cascades. Keep alternating the region sweep and the line sweep and 6 queens fall out in order without any new idea being needed: slate has one square left, so its queen takes row 5, column 5; amber has one square left, so its queen takes row 2, column 6; column 4 is down to one square, putting a queen on row 7, column 4; khaki has one square left, so its queen takes row 8, column 7; red has one square left, so its queen takes row 6, column 1; mint has one square left, so its queen takes row 4, column 2. 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 4, column 2.
The board after step 11 — 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 #224
This is puzzle number 224 in the 9x9 collection, rated easy. 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.
Puzzle #224 has been checked to admit exactly one arrangement of queens, and every step toward it is deducible from what is already on the board. There is no point at which you are expected to pick a square and hope. The only thing that differs between boards is how quickly the first certainty surfaces, and that depends entirely on the shapes the colors happen to take here.
How the colors divide this board
From smallest to largest, the regions on puzzle #224 are: indigo (1 square), orange (1 square), slate (5 squares), blue (6 squares), red (9 squares), pale yellow (10 squares), khaki (14 squares), amber (15 squares), mint (20 squares). An even split would hand every color 9 squares, so the indigo region is running 8 squares under that average while the mint 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 indigo and mint 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. Indigo is the densest region on this grid at 100% of a 1×1 frame; pale yellow is the loosest, occupying only 40% of its 5×5 frame. The loose one reaches into more rows and columns, which is exactly why it usually settles last.
Region by region
Each region's exact extent on this grid is listed below, starting with the most constrained. Knowing which lines a color can and cannot reach is most of the work on a easy board.
Indigo occupies 1 square within rows 1–1, columns 9–9. It never leaves row 1, so its queen is locked to that row.
Orange: 1 square across rows 9–9, columns 3–3. It never leaves row 9, so its queen is locked to that row.
Slate covers 5 squares, spanning 2 rows and 3 columns (rows 5–6, columns 5–7).
Blue occupies 6 squares within rows 2–5, columns 8–9.
Red: 9 squares across rows 6–9, columns 1–3.
Pale yellow covers 10 squares, spanning 5 rows and 5 columns (rows 5–9, columns 2–6).
Khaki occupies 14 squares within rows 6–9, columns 5–9.
Amber: 15 squares across rows 1–5, columns 3–8.
Mint covers 20 squares, spanning 5 rows and 5 columns (rows 1–5, columns 1–5).
Where to start on this board
Begin where the choices are fewest. On this board that means indigo, which owns just 1 square inside a 1×1 window running from row 1 to row 1 and column 9 to column 9. A queen is guaranteed somewhere in there, so every line that window crosses is under pressure from the very first move.
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. Orange and slate 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 #224
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 1, 2, 3, 4, 7 and 8 are the narrowest, touched by only 3 colors. Column 1 is the tightest column, with 2 colors.
Those lines matter because a row touched by few colors gives its queen away sooner. If a row meets only 3 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 5 colors — the most crowded line here, and the one least likely to resolve early. Spend your attention accordingly.
Working through the middle game
Past the opening, treat this as an elimination exercise rather than a placement exercise. Each queen takes out a row, a column and its eight neighbours, and the value of a move is measured by how much it removes. Cross everything out as you go and let the board do the remembering.
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.
Resist the plausible-looking queen. On #224 every correct placement has a stated reason behind it, and any move you cannot justify is a guess wearing a disguise. Backing out of a wrong guess on a single-solution board takes far longer than finding the real deduction would have.
Why puzzle #224 is rated easy
The easy label comes out of four measurable things about #224: four of its regions are locked to one row or column, its smallest color spans 1 square, its least crowded row meets 3 colors, and its largest and smallest regions differ by 19. Boards that score tight on those measures give up their first queen fast.
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.
When a board plays tougher than its label, look for a missed mark before you look for a clever deduction. Walk back over every queen you have placed and confirm the full row, the full column and all eight surrounding squares are crossed out. The diagonal neighbours are the ones players skip, and a single skipped diagonal will hide the next forced move indefinitely.
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 #224 is column 1.
As a sanity check rather than a spoiler: the finished solution to #224 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 #224?
Puzzle #224 is rated easy. Its smallest color region holds 1 square, its tightest row is touched by 3 colors, and four of its regions are confined to a single row or column, which gives you a forced move early.
Does 9x9 puzzle #224 have only one solution?
Yes. Every puzzle in the 9x9 collection, including #224, 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 #224?
Start with the indigo region — the most constrained color on this board, with 1 square spanning rows 1–1 and columns 9–9. Narrowing the smallest region first removes the most squares elsewhere on the grid.