9x9 Queens Puzzle #26
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.
Previous puzzle · All 9x9 puzzles · Next puzzle
Step-by-step solution for puzzle #26
What follows is a complete solve of puzzle #26, 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 confined to one line.
Techniques this board needs: region confined to one line, last square in a region.
Show the full walkthrough (10 steps) — contains the solution
Step 1. Amber cannot leave column 9 — 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: 9 squares in all.
Step 2. The mint region is down to one open square, at row 4, column 8. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 4 and column 8, the remaining mint squares, and the ring of neighbours around row 4, column 8.
Step 3. Only row 2, column 9 is still open in amber, and since each colour must take a queen, that settles it. Everything else in row 2, in column 9, in amber and in the ring around that square is now dead.
The board after step 3 — 2 of 9 queens placed. 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: 5 squares come off.
Step 5. Blue cannot leave row 3 — every one of its open squares (4 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 6. The red region is down to one open square, at row 6, column 7. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 6 and column 7, the remaining red squares, and the ring of neighbours around row 6, column 7.
Step 7. Only row 1, column 6 is still open in indigo, and since each colour must take a queen, that settles it. Everything else in row 1, in column 6, in indigo and in the ring around that square is now dead.
The board after step 7 — 4 of 9 queens placed. Step 8. The slate region is down to one open square, at row 5, column 5. Every colour holds exactly one queen, so that square is forced. Row 5 and column 5 are now spoken for, along with the squares touching that queen.
Step 9. Pale yellow cannot leave row 7 — every one of its open squares (2 open squares) sits there. That row belongs to pale yellow, so every square on it owned by another colour is dead: 4 squares in all.
Step 10. 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 1; pale yellow has one square left, so its queen takes row 7, column 2; khaki has one square left, so its queen takes row 8, column 4; blue has one square left, so its queen takes row 3, column 3. 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 3, column 3.
The board after step 10 — 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 #26
Board #26 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, #26 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 #26 are: amber (2 squares), mint (2 squares), orange (3 squares), indigo (8 squares), slate (9 squares), pale yellow (9 squares), red (10 squares), blue (15 squares), khaki (23 squares). An even split would hand every color 9 squares, so the amber region is running 7 squares under that average while the khaki region is the roomiest area on the grid with 23 squares.
That imbalance is the first thing to read, because every region takes exactly one queen regardless of how much space it owns. Amber has only 2 places to put its queen; khaki has 23. The spread between them on this board is 21 squares, and the wider that spread runs, the more it pays to solve from the small end inward.
Shape matters as much as size. The amber region is the most compact color here, filling 100% of the 2×1 box that encloses it, while slate is the most scattered at 50% of its 6×3 box. Compact regions are easy to eliminate around; straggling ones reach into more rows and columns and tend to stay unresolved until late.
Region by region
Here is the full footprint of every color on puzzle #26, smallest first. Reading these spans before you place anything is the quickest way to see which parts of the grid are genuinely contested.
Amber occupies 2 squares within rows 2–3, columns 9–9. It sits wholly inside column 9, so its queen must be in that column.
Mint: 2 squares across rows 3–4, columns 8–8. It sits wholly inside column 8, so its queen must be in that column.
Orange covers 3 squares, spanning 2 rows and 2 columns (rows 8–9, columns 1–2).
Indigo occupies 8 squares within rows 1–3, columns 6–9.
Slate: 9 squares across rows 1–6, columns 4–6.
Pale yellow covers 9 squares, spanning 3 rows and 4 columns (rows 5–7, columns 1–4).
Red occupies 10 squares within rows 3–6, columns 6–9.
Blue: 15 squares across rows 1–4, columns 1–4.
Khaki covers 23 squares, spanning 4 rows and 8 columns (rows 6–9, columns 2–9).
Where to start on this board
Open on the tightest color. Here that is amber, confined to 2 squares between rows 2 and 3 and columns 9 and 9. Its queen has nowhere else to go, which means those 2 rows and 1 column carry more constraint than anywhere else on #26.
Because amber stays inside column 9, its queen belongs to that column and no other region may use it. Cross out the rest of column 9 straight away. Any color that was relying on those squares now has a visibly smaller footprint, and that shrinkage is where your second deduction comes from.
Work outward to the other flat regions next. Mint and orange 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 #26
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 7, 8 and 9 are the narrowest, touched by only 2 colors. Column 5 is the tightest column, with 2 colors.
The fewer colors a line touches, the sooner it surrenders its queen. A row meeting just 2 colors has to be claimed by one of them, which pushes every remaining region into the other 8 rows. Row 3, meeting 6 colors, is the opposite case — the busiest line on #26 and the last one you should expect to crack.
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.
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.
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 #26 is rated hard
The rating reflects how much the board concedes up front. Puzzle #26 has two regions confined to a single row or column, its smallest color holds 2 squares, its tightest row meets just 2 colors, and the gap between its largest and smallest regions is 21 squares. Flat, lopsided boards open quickly; even, sprawling ones make you earn the first placement.
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 #26 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 #26 the place to look for one is around row 7.
Here is a shape check that gives nothing away: when #26 is solved, 3 queens sit on the outer edge of the grid and 6 sit inside it, with 1 queen 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.
Full rules · Strategy library · Puzzle statistics
Questions about this puzzle
How hard is 9x9 Queens puzzle #26?
Puzzle #26 is rated hard. Its smallest color region holds 2 squares, its tightest row is touched by 2 colors, and two of its regions are confined to a single row or column, which gives you a forced move early.
Does 9x9 puzzle #26 have only one solution?
Yes. Every puzzle in the 9x9 collection, including #26, 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 #26?
Start with the amber region — the most constrained color on this board, with 2 squares spanning rows 2–3 and columns 9–9. Narrowing the smallest region first removes the most squares elsewhere on the grid.