9x9 Queens Puzzle #92
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 18-step reasoning is written out below.
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Step-by-step solution for puzzle #92
What follows is a complete solve of puzzle #92, worked the way a person works it rather than the way a computer does. It runs to 18 deductions — 9 queen placements and 9 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 shadow, region confined to one line, last square in a region, pairing argument on rows, pairing argument on columns.
Show the full walkthrough (12 steps) — contains the solution
Step 1. Wherever indigo ends up among its 3 squares, the same squares fall within reach of it — 1 square in total, impossible regardless of how the colour resolves.
Step 2. Mint is down to 9 candidates in rows 2–6, columns 6–8, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about mint itself.
Step 3. Red cannot leave column 1 — 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: 9 squares in all.
Step 4. The indigo region is down to one open square, at row 1, column 2. Every colour holds exactly one queen, so that square is forced. Row 1 and column 2 are now spoken for, along with the squares touching that queen.
The board after step 4 — 1 of 9 queens placed. Step 5. Amber is down to 4 candidates in rows 2 and 3, columns 6 and 8, and they overlap enough to cover 2 squares elsewhere. Cross those out without deciding anything about amber itself.
Step 6. All of the pale yellow region's remaining squares (2 open squares) lie in row 7. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 10 squares come off.
Step 7. Only row 6, column 1 is still open in red, and since each colour must take a queen, that settles it. Everything else in row 6, in column 1, in red and in the ring around that square is now dead.
Step 8. Mint is down to 4 candidates in rows 4 and 5, columns 6–8, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about mint itself.
The board after step 8 — 2 of 9 queens placed. Step 9. Amber, blue, mint, and slate are now boxed into rows 2–5 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 2 squares at once.
Step 10. Here is the pairing argument. The slate and pale yellow regions have no open squares outside columns 8 and 9 — 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: 5 squares come off in one stroke.
Step 11. 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: 6 squares in all.
Step 12. From here the board cascades. Keep alternating the region sweep and the line sweep and 7 queens fall out in order without any new idea being needed: mint has one square left, so its queen takes row 4, column 7; amber has one square left, so its queen takes row 2, column 6; orange has one square left, so its queen takes row 9, column 5; khaki has one square left, so its queen takes row 8, column 3; blue has one square left, so its queen takes row 3, column 4; slate has one square left, so its queen takes row 5, column 9; pale yellow has one square left, so its queen takes row 7, column 8. 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 7, column 8.
The board after step 12 — 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 #92
This is puzzle number 92 in the 9x9 collection, rated hard. 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.
There is exactly one way to finish #92, and it has been verified. More importantly, you can reach it without ever gambling: at every stage some square is provably right or provably wrong. Boards differ only in how deep you must dig before that proof appears, and the geometry of these nine regions is what sets the depth.
How the colors divide this board
From smallest to largest, the regions on puzzle #92 are: red (2 squares), pale yellow (2 squares), indigo (3 squares), slate (7 squares), amber (9 squares), mint (9 squares), orange (11 squares), blue (18 squares), khaki (20 squares). An even split would hand every color 9 squares, so the red region is running 7 squares under that average while the khaki 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 18 square difference between red and khaki 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.
Square count is only half the story — how a color is arranged counts too. Red is the tidiest shape on #92, packing 100% of its 2×1 bounding box, whereas slate straggles across its 5×3 box at just 47%. Tidy blocks are easy to work around; scattered ones touch more lines and resist resolution.
Region by region
Here is the full footprint of every color on puzzle #92, smallest first. Reading these spans before you place anything is the quickest way to see which parts of the grid are genuinely contested.
Red occupies 2 squares within rows 6–7, columns 1–1. It sits wholly inside column 1, so its queen must be in that column.
Pale yellow: 2 squares across rows 7–7, columns 8–9. It never leaves row 7, so its queen is locked to that row.
Indigo covers 3 squares, spanning 2 rows and 2 columns (rows 1–2, columns 1–2).
Slate occupies 7 squares within rows 2–6, columns 7–9.
Amber: 9 squares across rows 1–3, columns 5–9.
Mint covers 9 squares, spanning 5 rows and 3 columns (rows 2–6, columns 6–8).
Orange occupies 11 squares within rows 7–9, columns 5–9.
Blue: 18 squares across rows 1–5, columns 1–5.
Khaki covers 20 squares, spanning 5 rows and 5 columns (rows 5–9, columns 1–5).
Where to start on this board
Begin where the choices are fewest. On this board that means red, which owns just 2 squares inside a 2×1 window running from row 6 to row 7 and column 1 to column 1. A queen is guaranteed somewhere in there, so every line that window crosses is under pressure from the very first move.
Because red stays inside column 1, its queen belongs to that column and no other region may use it. Cross out the rest of column 1 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. Pale yellow and indigo 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 #92
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 8 and 9 are the narrowest, touched by only 2 colors. Columns 3 and 4 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 2 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
After the first few queens the puzzle becomes bookkeeping. A placed queen wipes its row, its column and every square it touches — as many as eight neighbours — so the space collapses quickly. Record those eliminations on the board instead of carrying them in your head, and the next forced move tends to announce itself.
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.
Resist the plausible-looking queen. On #92 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 #92 is rated hard
The rating reflects how much the board concedes up front. Puzzle #92 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 18 squares. Flat, lopsided boards open quickly; even, sprawling ones make you earn the first placement.
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.
Stuck on #92 despite the hard rating? The odds strongly favour a bookkeeping error over a hard chain of logic. Re-check each placed queen for its complete set of eliminations, paying particular attention to the four diagonal squares — those are the ones that get overlooked, and one of them is usually sitting on the answer.
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 #92 is row 8.
As a sanity check rather than a spoiler: the finished solution to #92 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 #92?
Puzzle #92 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 #92 have only one solution?
Yes. Every puzzle in the 9x9 collection, including #92, 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 #92?
Start with the red region — the most constrained color on this board, with 2 squares spanning rows 6–7 and columns 1–1. Narrowing the smallest region first removes the most squares elsewhere on the grid.