9x9 Queens Puzzle #226
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 21-step reasoning is written out below.
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Step-by-step solution for puzzle #226
What follows is a complete solve of puzzle #226, worked the way a person works it rather than the way a computer does. It runs to 21 deductions — 9 queen placements and 12 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 columns.
Techniques this board needs: region confined to one line, region shadow, pairing argument on columns, pairing argument on rows, last square in a region, last square in a column, last square in a row.
Show the full walkthrough (15 steps) — contains the solution
Step 1. Indigo cannot leave row 1 — every one of its open squares (2 open squares) sits there. That row belongs to indigo, so every square on it owned by another colour is dead: 9 squares in all.
Step 2. Red is down to 8 candidates in rows 4–8, columns 6–8, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about red itself.
Step 3. Orange cannot leave row 9 — every one of its open squares (3 open squares) sits there. That row belongs to orange, so every square on it owned by another colour is dead: 7 squares in all.
Step 4. Wherever khaki ends up among its 4 squares, the same squares fall within reach of it — 2 squares in total, impossible regardless of how the colour resolves.
Step 5. Indigo and khaki are now boxed into columns 8 and 9 and nothing else. That is 2 colours needing 2 columns, so they fill those columns between them — which locks every remaining colour out and removes 6 squares at once.
The board after step 5 — 0 of 9 queens placed. Step 6. The mint region has 4 squares left, spread across rows 2–4, columns 6 and 7. You do not need to know which of them takes the queen: every one of those options attacks the same 2 squares, so they can be crossed out now.
Step 7. Wherever amber ends up among its 4 squares, the same squares fall within reach of it — 1 square in total, impossible regardless of how the colour resolves.
Step 8. Red is down to 4 candidates in rows 5–7, columns 6 and 7, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about red itself.
Step 9. Amber, blue, and mint are now boxed into rows 2–4 and nothing else. That is 3 colours needing 3 rows, so they fill those rows between them — which locks every remaining colour out and removes 4 squares at once.
Step 10. Here is the pairing argument. The mint and red regions have no open squares outside columns 6 and 7 — 2 colours confined to 2 columns. Between them they must take one column each, in some order, so every other colour is shut out of all of them: 3 squares come off in one stroke.
The board after step 10 — 0 of 9 queens placed. Step 11. From here the board cascades. Keep alternating the region sweep and the line sweep and 4 queens fall out in order without any new idea being needed: orange has one square left, so its queen takes row 9, column 5; amber has one square left, so its queen takes row 2, column 4; blue has one square left, so its queen takes row 3, column 1; mint has one square left, so its queen takes row 4, column 6. 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 6.
Step 12. Red cannot leave column 7 — every one of its open squares (2 open squares) sits there. That column belongs to red, so every square in it owned by another colour is dead: 1 square in all.
Step 13. Column 8 now has exactly one open square, row 1, column 8, in the indigo region. Columns must each hold a queen, so that placement is forced. Everything else in row 1, in column 8, in indigo and in the ring around that square is now dead.
Step 14. Pale yellow is down to 3 candidates in rows 6 and 7, columns 2 and 3, and they overlap enough to cover 2 squares elsewhere. Cross those out without deciding anything about pale yellow itself.
Step 15. From here the board cascades. Keep alternating the region sweep and the line sweep and 4 queens fall out in order without any new idea being needed: row 5 is down to one square, putting a queen on row 5, column 3; pale yellow has one square left, so its queen takes row 7, column 2; red has one square left, so its queen takes row 6, column 7; khaki has one square left, so its queen takes row 8, column 9. 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 9.
The board after step 15 — 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 #226
Board #226 of the 9x9 bank carries a hard rating. Its 81 squares are shared between nine colored regions, and the solution places nine 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, #226 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 #226 are: indigo (2 squares), orange (4 squares), khaki (6 squares), red (8 squares), amber (9 squares), blue (9 squares), mint (13 squares), slate (15 squares), pale yellow (15 squares). An even split would hand every color 9 squares, so the indigo region is running 7 squares under that average while the pale yellow region is the roomiest area on the grid with 15 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 15. The spread between them on this board is 13 squares, and the wider that spread runs, the more it pays to solve from the small end inward.
A region's outline can constrain it more than its size does. Here indigo is the most solid, filling 100% of its 1×2 box, and red the most diffuse at 53% of its 5×3 box. Solid blocks give clean eliminations; diffuse ones spread across the board and stay open longer.
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 hard board.
Indigo covers 2 squares, spanning 1 row and 2 columns (rows 1–1, columns 8–9). It never leaves row 1, so its queen is locked to that row.
Orange occupies 4 squares within rows 8–9, columns 5–7.
Khaki: 6 squares across rows 6–9, columns 8–9.
Red covers 8 squares, spanning 5 rows and 3 columns (rows 4–8, columns 6–8).
Amber occupies 9 squares within rows 1–4, columns 3–6.
Blue: 9 squares across rows 1–4, columns 1–4.
Mint covers 13 squares, spanning 5 rows and 4 columns (rows 1–5, columns 6–9).
Slate occupies 15 squares within rows 5–8, columns 2–6.
Pale yellow: 15 squares across rows 3–9, columns 1–4.
Where to start on this board
Open on the tightest color. Here that is indigo, confined to 2 squares between rows 1 and 1 and columns 8 and 9. Its queen has nowhere else to go, which means those 1 row and 2 columns carry more constraint than anywhere else on #226.
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 is no more than two rows tall, so its queen is 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 #226
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 2 and 9 are the narrowest, touched by only 3 colors. Column 1 is the tightest column, with 2 colors.
The fewer colors a line touches, the sooner it surrenders its queen. A row meeting just 3 colors has to be claimed by one of them, which pushes every remaining region into the other 8 rows. Row 8, meeting 5 colors, is the opposite case — the busiest line on #226 and the last one you should expect to crack.
Working through the middle game
Once two or three queens are down, the board changes character. Each queen removes an entire row, an entire column and the ring of up to eight squares around it, so the grid shrinks faster than most people expect. The habit that pays here is marking rather than remembering: after every placement, cross out the full row, the full column and all eight neighbours before hunting for the next move.
Keep alternating between two views of the board. In the region view you ask which of the nine 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 9x9 board unwinds.
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 #226 is rated hard
The hard label comes out of four measurable things about #226: one of its regions is locked to one row or column, its smallest color spans 2 squares, its least crowded row meets 3 colors, and its largest and smallest regions differ by 13. 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.
If #226 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 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.
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 #226 the place to look for one is around column 1.
Here is a shape check that gives nothing away: when #226 is solved, 4 queens sit on the outer edge of the grid and 5 sit inside it, and no queen lands in a corner. A work-in-progress board that clusters its queens in one quadrant while leaving others bare is usually carrying a mistake.
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 #226?
Puzzle #226 is rated hard. Its smallest color region holds 2 squares, its tightest row is touched by 3 colors, and one of its regions is confined to a single row or column, which gives you a forced move early.
Does 9x9 puzzle #226 have only one solution?
Yes. Every puzzle in the 9x9 collection, including #226, 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 #226?
Start with the indigo region — the most constrained color on this board, with 2 squares spanning rows 1–1 and columns 8–9. Narrowing the smallest region first removes the most squares elsewhere on the grid.