11x11 Queens Puzzle #129
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 16-step reasoning is written out below.
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Step-by-step solution for puzzle #129
What follows is a complete solve of puzzle #129, worked the way a person works it rather than the way a computer does. It runs to 16 deductions — 11 queen placements and 5 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: last square in a region, region confined to one line, region shadow, pairing argument on rows.
Show the full walkthrough (10 steps) — contains the solution
Step 1. Only row 6, column 1 is still open in red, and since each colour must take a queen, that settles it. That clears row 6, column 1, the rest of the red region and every square adjacent to it — diagonals included.
Step 2. 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: 10 squares come off.
Step 3. Blue cannot leave column 8 — 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.
The board after step 3 — 1 of 11 queens placed. Step 4. The sea green region is down to one open square, at row 10, column 7. Every colour holds exactly one queen, so that square is forced. Row 10 and column 7 are now spoken for, along with the squares touching that queen.
Step 5. Amber is down to 5 candidates in rows 2–4, columns 4–6, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about amber itself.
Step 6. All of the teal region's remaining squares (3 open squares) lie in row 11. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 4 squares come off.
Step 7. Only row 9, column 2 is still open in orange, and since each colour must take a queen, that settles it. Everything else in row 9, in column 2, in orange and in the ring around that square is now dead.
The board after step 7 — 3 of 11 queens placed. Step 8. The indigo region is down to one open square, at row 1, column 3. Every colour holds exactly one queen, so that square is forced. Row 1 and column 3 are now spoken for, along with the squares touching that queen.
Step 9. Amber, blue, and mint are now boxed into rows 2–4 and nothing else. That is 3 colours needing 3 rows, so they fill those rows between them — which locks every remaining colour out and removes 4 squares at once.
Step 10. 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: slate has one square left, so its queen takes row 5, column 4; khaki has one square left, so its queen takes row 8, column 6; amber has one square left, so its queen takes row 2, column 5; blue has one square left, so its queen takes row 3, column 8; mint has one square left, so its queen takes row 4, column 10; teal has one square left, so its queen takes row 11, column 9; pale yellow has one square left, so its queen takes row 7, 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 7, column 11.
The board after step 10 — 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 #129
Puzzle #129 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, #129 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 #129 are: red (1 square), sea green (2 squares), indigo (3 squares), blue (6 squares), mint (9 squares), teal (9 squares), orange (10 squares), amber (14 squares), khaki (14 squares), slate (22 squares), pale yellow (31 squares). An even split would hand every color 11 squares, so the red region is running 10 squares under that average while the pale yellow region is the roomiest area on the grid with 31 squares.
Every color takes one queen and one only, whatever its size — which is why the 30 square difference between red and pale yellow 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.
Shape matters as much as size. The indigo region is the most compact color here, filling 100% of the 1×3 box that encloses it, while blue is the most scattered at 50% of its 3×4 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
Below is every color on #129 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.
Red: 1 square across rows 6–6, columns 1–1. It never leaves row 6, so its queen is locked to that row.
Sea green covers 2 squares, spanning 1 row and 2 columns (rows 10–10, columns 7–8). It never leaves row 10, so its queen is locked to that row.
Indigo occupies 3 squares within rows 1–1, columns 1–3. It never leaves row 1, so its queen is locked to that row.
Blue: 6 squares across rows 1–3, columns 8–11.
Mint covers 9 squares, spanning 3 rows and 4 columns (rows 2–4, columns 8–11).
Teal occupies 9 squares within rows 10–11, columns 4–9.
Orange: 10 squares across rows 7–11, columns 1–3.
Amber covers 14 squares, spanning 5 rows and 5 columns (rows 1–5, columns 4–8).
Khaki occupies 14 squares within rows 5–10, columns 3–6.
Slate: 22 squares across rows 2–8, columns 1–5.
Pale yellow covers 31 squares, spanning 8 rows and 7 columns (rows 4–11, columns 5–11).
Where to start on this board
Red is the natural opening on #129: it is the smallest region on the grid at 1 square, boxed into rows 6–6 and columns 1–1. Since one of those squares must hold a queen, that block of 1 row and 1 column is the most contested part of the board.
Because red never leaves row 6, its queen must be in that row — and that instantly settles row 6 for everyone else. Sweep along it and X out every square that is not red. Then look at which colors just lost ground: on a grid this size that one observation usually forces a second region within a move or two.
Work outward to the other flat regions next. Indigo, sea green and teal 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 #129
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 1, 9 and 11 are the narrowest, touched by only 3 colors. Columns 2, 10 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
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 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.
The trap on a board like this is placing a queen that is merely plausible. Every placement should be traceable to an elimination you can point at. If you cannot name the rule that forced it, you are guessing — and on a single-solution grid a guess costs more to unwind than the deduction would have taken to find.
Why puzzle #129 is rated medium
What earns a board its rating is the shape of its opening. Here that opening offers four single-line regions, a 1-square smallest color, a tightest row touched by 3 colors, and a region-size spread of 30. 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.
If #129 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 #129 is row 1.
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 #129?
Puzzle #129 is rated medium. Its smallest color region holds 1 square, its tightest row is touched by 3 colors, and four of its regions are confined to a single row or column, which gives you a forced move early.
Does 11x11 puzzle #129 have only one solution?
Yes. Every puzzle in the 11x11 collection, including #129, 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 #129?
Start with the red region — the most constrained color on this board, with 1 square spanning rows 6–6 and columns 1–1. Narrowing the smallest region first removes the most squares elsewhere on the grid.