11x11 Queens Puzzle #61
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 21-step reasoning is written out below.
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Step-by-step solution for puzzle #61
What follows is a complete solve of puzzle #61, worked the way a person works it rather than the way a computer does. It runs to 21 deductions — 11 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 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, line confined to one region, last square in a column.
Show the full walkthrough (14 steps) — contains the solution
Step 1. Wherever amber 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 2. Red is down to 4 candidates in rows 6 and 7, columns 9–11, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about red itself.
Step 3. The pale yellow region has 3 squares left, spread across rows 6 and 7, columns 2 and 3. You do not need to know which of them takes the queen: every one of those options attacks the same 3 squares, so they can be crossed out now.
Step 4. Wherever orange 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 5. Red cannot leave row 6 — every one of its open squares (3 open squares) sits there. That row belongs to red, so every square on it owned by another colour is dead: 7 squares in all.
The board after step 5 — 0 of 11 queens placed. Step 6. The pale yellow region is down to one open square, at row 7, column 3. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 7 and column 3, the remaining pale yellow squares, and the ring of neighbours around row 7, column 3.
Step 7. Slate cannot leave row 5 — every one of its open squares (3 open squares) sits there. That row belongs to slate, so every square on it owned by another colour is dead: 6 squares in all.
Step 8. Here is the pairing argument. The khaki, orange, sea green, and teal regions have no open squares outside rows 8–11 — 4 colours confined to 4 rows. Between them they must take one row each, in some order, so every other colour is shut out of all of them: 1 square come off in one stroke.
Step 9. Red, orange, and teal are now boxed into columns 9–11 and nothing else. That is 3 colours needing 3 columns, so they fill those columns between them — which locks every remaining colour out and removes 13 squares at once.
The board after step 9 — 1 of 11 queens placed. Step 10. The indigo region is down to one open square, at row 1, column 8. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 1 and column 8, the remaining indigo squares, and the ring of neighbours around row 1, column 8.
Step 11. Only row 2, column 2 is still open in amber, and since each colour must take a queen, that settles it. Everything else in row 2, in column 2, in amber and in the ring around that square is now dead.
Step 12. The mint region has 2 squares left, spread across rows 3 and 4, columns 5 and 7. You do not need to know which of them takes the queen: every one of those options attacks the same 5 squares, so they can be crossed out now.
Step 13. Column 6 has only sea green squares left (3 open squares). The column needs a queen and only sea green can provide one, which pins that colour to this column and kills its squares elsewhere: 9 squares.
Step 14. From here the board cascades. Keep alternating the region sweep and the line sweep and 8 queens fall out in order without any new idea being needed: column 7 is down to one square, putting a queen on row 4, column 7; 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 1; khaki has one square left, so its queen takes row 8, column 5; orange has one square left, so its queen takes row 9, column 10; teal has one square left, so its queen takes row 11, column 11; red has one square left, so its queen takes row 6, column 9; sea green has one square left, so its queen takes row 10, 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 10, column 6.
The board after step 14 — 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 #61
Puzzle #61 is one of the medium-rated boards in the 11x11 set. Eleven colors divide its 121 squares, and you win by placing eleven queens so that each row, each column and each color holds exactly one, with no two queens adjacent in any direction.
Like every board on this site, #61 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 #61 are: pale yellow (3 squares), amber (4 squares), red (4 squares), slate (6 squares), orange (6 squares), teal (7 squares), indigo (14 squares), blue (16 squares), khaki (18 squares), sea green (18 squares), mint (25 squares). An even split would hand every color 11 squares, so the pale yellow region is running 8 squares under that average while the mint region is the roomiest area on the grid with 25 squares.
Every color takes one queen and one only, whatever its size — which is why the 22 square difference between pale yellow and mint 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. Teal is the tidiest shape on #61, packing 78% of its 3×3 bounding box, whereas blue straggles across its 4×7 box at just 57%. 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 #61, smallest first. Reading these spans before you place anything is the quickest way to see which parts of the grid are genuinely contested.
Pale yellow covers 3 squares, spanning 2 rows and 2 columns (rows 6–7, columns 2–3).
Amber occupies 4 squares within rows 1–2, columns 1–3.
Red: 4 squares across rows 6–7, columns 9–11.
Slate covers 6 squares, spanning 2 rows and 4 columns (rows 5–6, columns 1–4).
Orange occupies 6 squares within rows 7–9, columns 9–11.
Teal: 7 squares across rows 9–11, columns 9–11.
Indigo covers 14 squares, spanning 5 rows and 4 columns (rows 1–5, columns 8–11).
Blue occupies 16 squares within rows 1–4, columns 1–7.
Khaki: 18 squares across rows 7–11, columns 1–5.
Sea green covers 18 squares, spanning 4 rows and 7 columns (rows 8–11, columns 3–9).
Mint occupies 25 squares within rows 1–8, columns 5–9.
Where to start on this board
Pale yellow is the natural opening on #61: it is the smallest region on the grid at 3 squares, boxed into rows 6–7 and columns 2–3. Since one of those squares must hold a queen, that block of 2 rows and 2 columns is the most contested part of the board.
Pale yellow 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. Amber, slate and red 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 #61
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 3, 4, 5, 10 and 11 are the narrowest, touched by only 3 colors. Columns 6, 7 and 8 are the tightest columns, with 3 colors.
Those lines matter because a row touched by few colors gives its queen away sooner. If a row meets only 3 colors, then one of those regions has to own it, and every other region is competing for the remaining 10 rows. By contrast row 7 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
The middle of #61 is where careless play costs time. Every queen you place kills a row, a column and the eight surrounding squares; if you do not mark all of that immediately, you will later "discover" a move that was available several turns ago. Mark first, then look.
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 #61 is rated medium
The rating reflects how much the board concedes up front. Puzzle #61 has no region confined to a single row or column, its smallest color holds 3 squares, its tightest row meets just 3 colors, and the gap between its largest and smallest regions is 22 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 #61 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 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.
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 #61 is row 3.
As a sanity check rather than a spoiler: the finished solution to #61 puts 3 queens on the outer border and 8 queens in the interior, 1 of them in an actual 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 11x11 Queens puzzle #61?
Puzzle #61 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 #61 have only one solution?
Yes. Every puzzle in the 11x11 collection, including #61, 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 #61?
Start with the pale yellow region — the most constrained color on this board, with 3 squares spanning rows 6–7 and columns 2–3. Narrowing the smallest region first removes the most squares elsewhere on the grid.