9x9 Queens Puzzle #293
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 19-step reasoning is written out below.
Previous puzzle · All 9x9 puzzles · Next puzzle
Step-by-step solution for puzzle #293
What follows is a complete solve of puzzle #293, worked the way a person works it rather than the way a computer does. It runs to 19 deductions — 9 queen placements and 10 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: region confined to one line, region shadow, pairing argument on rows, last square in a region.
Show the full walkthrough (11 steps) — contains the solution
Step 1. Blue cannot leave column 4 — 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: 11 squares in all.
Step 2. Mint is down to 4 candidates in rows 4 and 5, columns 2, 3, 5, and 6, and they overlap enough to cover 4 squares elsewhere. Cross those out without deciding anything about mint itself.
Step 3. The indigo region has 4 squares left, spread across rows 1 and 2, columns 1–3. 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 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 — 0 of 9 queens placed. Step 5. Indigo cannot leave row 1 — every one of its open squares (3 open squares) sits there. That row belongs to indigo, so every square on it owned by another colour is dead: 5 squares in all.
Step 6. The pale yellow region has 4 squares left, spread across rows 7–9, columns 1 and 2. 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. Khaki cannot leave column 9 — every one of its open squares (4 open squares) sits there. That column belongs to khaki, so every square in it owned by another colour is dead: 4 squares in all.
The board after step 7 — 0 of 9 queens placed. Step 8. Amber is down to 5 candidates in rows 2 and 3, columns 6–8, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about amber itself.
Step 9. Amber and blue are now boxed into rows 2 and 3 and nothing else. That is 2 colours needing 2 rows, so they fill those rows between them — which locks every remaining colour out and removes 2 squares at once.
Step 10. All of the slate region's remaining squares (2 open squares) lie in column 1. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 5 squares come off.
Step 11. From here the board cascades. Keep alternating the region sweep and the line sweep and 9 queens fall out in order without any new idea being needed: pale yellow has one square left, so its queen takes row 7, column 2; indigo has one square left, so its queen takes row 1, column 3; blue has one square left, so its queen takes row 3, column 4; mint has one square left, so its queen takes row 4, column 6; slate has one square left, so its queen takes row 5, column 1; red has one square left, so its queen takes row 6, column 8; amber has one square left, so its queen takes row 2, column 7; khaki has one square left, so its queen takes row 8, column 9; orange has one square left, so its queen takes row 9, 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 9, column 5.
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 #293
Puzzle #293 is one of the hard-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, #293 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 #293 are: blue (2 squares), pale yellow (4 squares), khaki (4 squares), mint (7 squares), slate (7 squares), indigo (8 squares), red (11 squares), amber (15 squares), orange (23 squares). An even split would hand every color 9 squares, so the blue region is running 7 squares under that average while the orange region is the roomiest area on the grid with 23 squares.
Every color takes one queen and one only, whatever its size — which is why the 21 square difference between blue and orange 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. Blue is the densest region on this grid at 100% of a 2×1 frame; mint is the loosest, occupying only 47% of its 3×5 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.
Blue occupies 2 squares within rows 2–3, columns 4–4. It sits wholly inside column 4, so its queen must be in that column.
Pale yellow: 4 squares across rows 7–9, columns 1–2.
Khaki covers 4 squares, spanning 4 rows and 1 column (rows 5–8, columns 9–9). It sits wholly inside column 9, so its queen must be in that column.
Mint occupies 7 squares within rows 4–6, columns 2–6.
Slate: 7 squares across rows 2–6, columns 1–2.
Indigo covers 8 squares, spanning 4 rows and 4 columns (rows 1–4, columns 1–4).
Red occupies 11 squares within rows 3–7, columns 5–8.
Amber: 15 squares across rows 1–4, columns 5–9.
Orange covers 23 squares, spanning 4 rows and 8 columns (rows 6–9, columns 2–9).
Where to start on this board
The most constrained color is where a solve should begin, and on #293 that is blue with 2 squares. It reaches from row 2 to row 3 and from column 4 to column 4 — 2 rows 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 blue stays inside column 4, its queen belongs to that column and no other region may use it. Cross out the rest of column 4 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.
No region here is pinned to a shallow band of rows, so turn the same idea sideways: slate and pale yellow span only two columns. Two narrow regions sharing the same two columns take one column each and lock everyone else out of both, which is usually enough to crack a board that offers no free opening.
The tightest lines on puzzle #293
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 1 and 9 are the narrowest, touched by only 2 colors. Columns 1, 3, 7, 8 and 9 are the tightest columns, with 3 colors.
Count colors per line and you have a ranking of where to look. The narrowest rows here see only 2 colors, so one of that handful must take the row and the rest are squeezed into the other 8 rows. Row 6 sits at the far end with 5 colors crossing it; it will almost certainly be among the last to settle.
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.
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 #293 is rated hard
Ratings track how generous the opening is. On #293 you get two regions pinned to a single row or column, a smallest color of 2 squares, a tightest row crossed by 2 colors, and a 21-square gap between the largest and smallest regions. Those four numbers largely explain the hard label.
The scale has nothing to do with maths or luck — every puzzle here is solvable by deduction and has exactly one answer. It measures reasoning depth: how many eliminations must stack up before a placement becomes provable. That depth is what separates a hard board from the rest.
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.
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 #293 is row 1.
Use this as a rough check on your progress: the completed board has 4 queens around the border and 5 queens in the middle, and nothing in the corners. Solutions spread out; if yours is bunching up in one region of the grid, retrace a few moves.
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 #293?
Puzzle #293 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 #293 have only one solution?
Yes. Every puzzle in the 9x9 collection, including #293, 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 #293?
Start with the blue region — the most constrained color on this board, with 2 squares spanning rows 2–3 and columns 4–4. Narrowing the smallest region first removes the most squares elsewhere on the grid.