9x9 Queens Puzzle #229
Difficulty: medium. 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 12-step reasoning is written out below.
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Step-by-step solution for puzzle #229
What follows is a complete solve of puzzle #229, worked the way a person works it rather than the way a computer does. It runs to 12 deductions — 9 queen placements and 3 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 confined to one line.
Techniques this board needs: last square in a region, region confined to one line, last square in a column.
Show the full walkthrough (8 steps) — contains the solution
Step 1. Only row 6, column 8 is still open in red, and since each colour must take a queen, that settles it. That clears row 6, column 8, the rest of the red region and every square adjacent to it — diagonals included.
Step 2. The mint region is down to one open square, at row 4, column 9. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 4 and column 9, the remaining mint squares, and the ring of neighbours around row 4, column 9.
Step 3. Only row 9, column 3 is still open in orange, and since each colour must take a queen, that settles it. Everything else in row 9, in column 3, in orange and in the ring around that square is now dead.
Step 4. All of the indigo region's remaining squares (2 open squares) lie in row 1. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 6 squares come off.
The board after step 4 — 3 of 9 queens placed. Step 5. Pale yellow cannot leave column 1 — every one of its open squares (2 open squares) sits there. That column belongs to pale yellow, so every square in it owned by another colour is dead: 4 squares in all.
Step 6. The amber region is down to one open square, at row 2, column 2. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 2 and column 2, the remaining amber squares, and the ring of neighbours around row 2, column 2.
Step 7. Blue cannot leave row 3 — every one of its open squares (2 open squares) sits there. That row belongs to blue, so every square on it owned by another colour is dead: 2 squares in all.
Step 8. 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: column 7 is down to one square, putting a queen on row 8, column 7; pale yellow has one square left, so its queen takes row 7, column 1; slate has one square left, so its queen takes row 5, column 4; blue has one square left, so its queen takes row 3, column 6; indigo has one square left, so its queen takes row 1, column 5. 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 1, column 5.
The board after step 8 — 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 #229
Puzzle #229 is one of the medium-rated boards in the 9x9 set. Nine colors divide its 81 squares, and you win by placing nine queens so that each row, each column and each color holds exactly one, with no two queens adjacent in any direction.
As with every puzzle in this collection, #229 has a single verified solution and needs no guesswork. Each queen follows from something already visible. What the board controls is tempo — how soon the first forced move shows up and how far apart the rest are spaced — and that is a direct consequence of how these colors are cut.
How the colors divide this board
From smallest to largest, the regions on puzzle #229 are: red (1 square), orange (1 square), indigo (2 squares), mint (4 squares), pale yellow (5 squares), amber (11 squares), blue (13 squares), slate (19 squares), khaki (25 squares). An even split would hand every color 9 squares, so the red region is running 8 squares under that average while the khaki region is the roomiest area on the grid with 25 squares.
Why does the split matter? Because a region's square count has no bearing on how many queens it gets — the answer is always one. So red, with 1 square, is under far more pressure than khaki with 25. A 24-square gap like this one rewards players who start where the choices are fewest.
Look at arrangement as well as area. Indigo is the densest region on this grid at 100% of a 1×2 frame; khaki is the loosest, occupying only 51% of its 7×7 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 medium board.
Red covers 1 square, spanning 1 row and 1 column (rows 6–6, columns 8–8). It never leaves row 6, so its queen is locked to that row.
Orange occupies 1 square within rows 9–9, columns 3–3. It never leaves row 9, so its queen is locked to that row.
Indigo: 2 squares across rows 1–1, columns 5–6. It never leaves row 1, so its queen is locked to that row.
Mint covers 4 squares, spanning 2 rows and 2 columns (rows 4–5, columns 8–9).
Pale yellow occupies 5 squares within rows 6–9, columns 1–2.
Amber: 11 squares across rows 1–5, columns 1–4.
Blue covers 13 squares, spanning 3 rows and 6 columns (rows 1–3, columns 4–9).
Slate occupies 19 squares within rows 3–9, columns 2–6.
Khaki: 25 squares across rows 3–9, columns 3–9.
Where to start on this board
The most constrained color is where a solve should begin, and on #229 that is red with 1 square. It reaches from row 6 to row 6 and from column 8 to column 8 — 1 row by 1 column. One queen has to live inside that footprint no matter what else happens, which makes those lines the busiest real estate on the board.
Because red never leaves row 6, its queen must be in that row — and that instantly settles row 6 for everyone else. Sweep along it and X out every square that is not red. 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. Indigo, orange and mint 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 #229
A quick way to find the next move is to count how many different colors touch each line. On this board, row 2 is the narrowest, touched by only 2 colors. Columns 1 and 7 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 9 meets 4 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.
The whole middle game reduces to two sweeps. Sweep the nine colors looking for one with a single square left; sweep the nine rows and nine columns looking for the same. Each sweep feeds the next, and switching between them deliberately — rather than drifting — is what separates a fast 9x9 solve from a stalled one.
A placement without a reason is a guess. Because this board has exactly one solution, a guess that happens to be wrong will not announce itself for several moves — and unwinding it is slower than simply finishing the eliminations first.
Why puzzle #229 is rated medium
The medium label comes out of four measurable things about #229: five of its regions are locked to one row or column, its smallest color spans 1 square, its least crowded row meets 2 colors, and its largest and smallest regions differ by 24. Boards that score tight on those measures give up their first queen fast.
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.
A board that feels above its rating is nearly always a board with a missing X. Audit every queen on the grid: full row cleared, full column cleared, all eight touching squares cleared. Diagonals are the common omission, and missing one is far more often the cause of a stall than any genuine difficulty in the puzzle.
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.
Learn the pairing argument and you will use it on every board, this one included. If two colors can only sit inside the same two rows, between them they consume both rows and every other color is shut out. It generalises to any matching count — three colors across three rows, four across four. On #229, start hunting for it near row 2.
As a sanity check rather than a spoiler: the finished solution to #229 puts 4 queens on the outer border and 5 queens in the interior, with none in a 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 #229?
Puzzle #229 is rated medium. Its smallest color region holds 1 square, its tightest row is touched by 2 colors, and five of its regions are confined to a single row or column, which gives you a forced move early.
Does 9x9 puzzle #229 have only one solution?
Yes. Every puzzle in the 9x9 collection, including #229, 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 #229?
Start with the red region — the most constrained color on this board, with 1 square spanning rows 6–6 and columns 8–8. Narrowing the smallest region first removes the most squares elsewhere on the grid.