11x11 Queens Puzzle #92
Difficulty: medium. Place 11 queens on this 11x11 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 20-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 20 deductions — 11 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, pairing argument on rows, last square in a region, region confined to one line, pairing argument on columns, last square in a column.
Show the full walkthrough (12 steps) — contains the solution
Step 1. Wherever khaki ends up among its 6 squares, the same squares fall within reach of it — 1 square in total, impossible regardless of how the colour resolves.
Step 2. Teal is down to 3 candidates in rows 10 and 11, columns 1 and 2, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about teal itself.
Step 3. Sea green and teal are now boxed into rows 10 and 11 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 11 squares at once.
Step 4. The orange region is down to one open square, at row 9, column 10. Every colour holds exactly one queen, so that square is forced. Row 9 and column 10 are now spoken for, along with the squares touching that queen.
The board after step 4 — 1 of 11 queens placed. Step 5. Khaki cannot leave row 8 — every one of its open squares (2 open squares) sits there. That row belongs to khaki, so every square on it owned by another colour is dead: 7 squares in all.
Step 6. The pale yellow region has 5 squares left, spread across rows 6 and 7, columns 1, 2, 4, and 5. 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 7. Indigo and red are now boxed into columns 9 and 11 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 5 squares at once.
Step 8. Here is the pairing argument. The amber and teal regions have no open squares outside columns 1 and 2 — 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: 9 squares come off in one stroke.
The board after step 8 — 1 of 11 queens placed. 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: 5 squares in all.
Step 10. 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 9 is down to one square, putting a queen on row 1, column 9; column 2 is down to one square, putting a queen on row 11, column 2; sea green has one square left, so its queen takes row 10, column 7; khaki has one square left, so its queen takes row 8, column 6; pale yellow has one square left, so its queen takes row 7, column 4. 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 4.
Step 11. The blue region has 3 squares left, spread across rows 3, 5, and 6, columns 5 and 8. 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 12. 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: mint has one square left, so its queen takes row 4, column 8; blue has one square left, so its queen takes row 3, column 5; amber has one square left, so its queen takes row 2, column 1; slate has one square left, so its queen takes row 5, column 3; red has one square left, so its queen takes row 6, column 11. 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 6, column 11.
The board after step 12 — 11 of 11 queens placed.
That completes the board: 11 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 11x11 Queens puzzle #92
This is puzzle number 92 in the 11x11 collection, rated medium. The grid holds 121 squares split between eleven colored regions, and a finished board carries eleven queens — one in every row, one in every column, one in every color, and never two of them touching, diagonals included.
As with every puzzle in this collection, #92 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 #92 are: teal (3 squares), amber (5 squares), khaki (6 squares), indigo (7 squares), orange (7 squares), sea green (7 squares), mint (11 squares), red (14 squares), blue (19 squares), pale yellow (20 squares), slate (22 squares). An even split would hand every color 11 squares, so the teal region is running 8 squares under that average while the slate region is the roomiest area on the grid with 22 squares.
One queen per color, regardless of acreage: that is what turns this uneven split into a solving order. Teal is working with 3 squares while slate has 22 to spare, a gap of 19. Attack the cramped end and the roomy regions tend to resolve themselves.
A region's outline can constrain it more than its size does. Here indigo is the most solid, filling 78% of its 3×3 box, and blue the most diffuse at 45% of its 7×6 box. Solid blocks give clean eliminations; diffuse ones spread across the board and stay open longer.
Region by region
Below is every color on #92 with its exact reach, smallest region first. It is worth a slow read: the spans reveal which rows and columns several regions are fighting over.
Teal occupies 3 squares within rows 10–11, columns 1–2.
Amber: 5 squares across rows 1–4, columns 1–2.
Khaki covers 6 squares, spanning 4 rows and 3 columns (rows 8–11, columns 6–8).
Indigo occupies 7 squares within rows 1–3, columns 9–11.
Orange: 7 squares across rows 9–11, columns 9–11.
Sea green covers 7 squares, spanning 2 rows and 5 columns (rows 10–11, columns 3–7).
Mint occupies 11 squares within rows 1–5, columns 7–10.
Red: 14 squares across rows 4–9, columns 8–11.
Blue covers 19 squares, spanning 7 rows and 6 columns (rows 1–7, columns 4–9).
Pale yellow occupies 20 squares within rows 6–10, columns 1–6.
Slate: 22 squares across rows 1–7, columns 1–6.
Where to start on this board
Open on the tightest color. Here that is teal, confined to 3 squares between rows 10 and 11 and columns 1 and 2. Its queen has nowhere else to go, which means those 2 rows and 2 columns carry more constraint than anywhere else on #92.
Teal does not collapse onto a single line, so it will not hand you a queen on move one. What it does give you is a short list of 3 candidates. Take each one in turn, imagine the queen there, cross out its row, its column and the eight squares around it, and ask whether any other region is left with nowhere to go. One or two candidates usually fail that test immediately.
Work outward to the other flat regions next. Sea green 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 #92
A quick way to find the next move is to count how many different colors touch each line. On this board, row 8 is the narrowest, touched by only 3 colors. Columns 3 and 11 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 3 colors, so one of that handful must take the row and the rest are squeezed into the other 10 rows. Row 10 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.
The whole middle game reduces to two sweeps. Sweep the eleven colors looking for one with a single square left; sweep the eleven rows and eleven columns looking for the same. Each sweep feeds the next, and switching between them deliberately — rather than drifting — is what separates a fast 11x11 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 #92 is rated medium
What earns a board its rating is the shape of its opening. Here that opening offers no single-line region at all, a 3-square smallest color, a tightest row touched by 3 colors, and a region-size spread of 19. Lopsided grids with flat regions fall quickly; balanced ones like this take more patience.
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.
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 11x11
At 11x11 you are managing 121 squares, and holding the whole board in your head will not work. Split it into quadrants and solve locally. Most useful deductions on a grid this large are regional — a color pinched between two placed queens, or a band of rows that two regions must share. Trust the marks on the board over your memory.
Whatever the grid size, the pairing rule is the technique to internalise. When a pair of regions is boxed into the same pair of rows, they split those rows between them and nobody else may enter — and the same holds for columns, or for any n regions confined to n lines. Look for an instance of it around row 8 on this board.
Use this as a rough check on your progress: the completed board has 4 queens around the border and 7 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.
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Questions about this puzzle
How hard is 11x11 Queens puzzle #92?
Puzzle #92 is rated medium. Its smallest color region holds 3 squares, its tightest row is touched by 3 colors, and no region is confined to a single row or column, so the opening move takes some hunting.
Does 11x11 puzzle #92 have only one solution?
Yes. Every puzzle in the 11x11 collection, including #92, has been verified to have exactly one valid arrangement of eleven 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 teal region — the most constrained color on this board, with 3 squares spanning rows 10–11 and columns 1–2. Narrowing the smallest region first removes the most squares elsewhere on the grid.