11x11 Queens Puzzle #125
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 15-step reasoning is written out below.
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Step-by-step solution for puzzle #125
What follows is a complete solve of puzzle #125, worked the way a person works it rather than the way a computer does. It runs to 15 deductions — 11 queen placements and 4 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 shadow, region confined to one line, pairing argument on rows.
Show the full walkthrough (8 steps) — contains the solution
Step 1. Only row 6, column 11 is still open in red, and since each colour must take a queen, that settles it. That clears row 6, column 11, the rest of the red region and every square adjacent to it — diagonals included.
Step 2. The pale yellow region is down to one open square, at row 7, column 9. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 7 and column 9, the remaining pale yellow squares, and the ring of neighbours around row 7, column 9.
Step 3. The mint region has 3 squares left, spread across rows 4 and 5, columns 7, 8, and 10. 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 4. All of the khaki region's remaining squares (3 open squares) lie in column 1. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 7 squares come off.
The board after step 4 — 2 of 11 queens placed. Step 5. Only row 11, column 2 is still open in teal, and since each colour must take a queen, that settles it. That clears row 11, column 2, the rest of the teal region and every square adjacent to it — diagonals included.
Step 6. The indigo region has 3 squares left, spread across rows 1 and 2, columns 3 and 4. 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. Orange and sea green are now boxed into rows 9 and 10 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 8. 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: khaki has one square left, so its queen takes row 8, column 1; slate has one square left, so its queen takes row 5, column 4; indigo has one square left, so its queen takes row 1, column 3; mint has one square left, so its queen takes row 4, column 10; blue has one square left, so its queen takes row 3, column 5; sea green has one square left, so its queen takes row 10, column 8; amber has one square left, so its queen takes row 2, column 7; orange has one square left, so its queen takes row 9, 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 9, column 6.
The board after step 8 — 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 #125
Puzzle #125 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.
There is exactly one way to finish #125, 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 eleven regions is what sets the depth.
How the colors divide this board
From smallest to largest, the regions on puzzle #125 are: red (1 square), teal (2 squares), khaki (4 squares), indigo (7 squares), pale yellow (7 squares), orange (9 squares), mint (10 squares), amber (19 squares), blue (19 squares), slate (21 squares), sea green (22 squares). An even split would hand every color 11 squares, so the red region is running 10 squares under that average while the sea green 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. Red is working with 1 square while sea green has 22 to spare, a gap of 21. Attack the cramped end and the roomy regions tend to resolve themselves.
Shape matters as much as size. The red region is the most compact color here, filling 100% of the 1×1 box that encloses it, while slate is the most scattered at 50% of its 6×7 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
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.
Red occupies 1 square within rows 6–6, columns 11–11. It never leaves row 6, so its queen is locked to that row.
Teal: 2 squares across rows 11–11, columns 1–2. It never leaves row 11, so its queen is locked to that row.
Khaki covers 4 squares, spanning 4 rows and 1 column (rows 7–10, columns 1–1). It sits wholly inside column 1, so its queen must be in that column.
Indigo occupies 7 squares within rows 1–2, columns 1–4.
Pale yellow: 7 squares across rows 6–8, columns 8–11.
Orange covers 9 squares, spanning 4 rows and 3 columns (rows 7–10, columns 6–8).
Mint occupies 10 squares within rows 3–5, columns 7–11.
Amber: 19 squares across rows 1–4, columns 5–11.
Blue covers 19 squares, spanning 5 rows and 7 columns (rows 2–6, columns 1–7).
Slate occupies 21 squares within rows 5–10, columns 1–7.
Sea green: 22 squares across rows 8–11, columns 3–11.
Where to start on this board
Red is the natural opening on #125: it is the smallest region on the grid at 1 square, boxed into rows 6–6 and columns 11–11. 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. Teal 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 #125
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 1 and 11 are the narrowest, touched by only 2 colors. Columns 2, 3, 4, 5, 9 and 10 are the tightest columns, with 4 colors.
The fewer colors a line touches, the sooner it surrenders its queen. A row meeting just 2 colors has to be claimed by one of them, which pushes every remaining region into the other 10 rows. Row 8, meeting 5 colors, is the opposite case — the busiest line on #125 and the last one you should expect to crack.
Working through the middle game
Past the opening, treat this as an elimination exercise rather than a placement exercise. Each queen takes out a row, a column and its eight neighbours, and the value of a move is measured by how much it removes. Cross everything out as you go and let the board do the remembering.
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 #125 is rated medium
Ratings track how generous the opening is. On #125 you get four regions pinned to a single row or column, a smallest color of 1 square, a tightest row crossed by 2 colors, and a 21-square gap between the largest and smallest regions. Those four numbers largely explain the medium 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 medium board from the rest.
Stuck on #125 despite the medium 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 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 1 on this board.
Here is a shape check that gives nothing away: when #125 is solved, 4 queens sit on the outer edge of the grid and 7 sit inside it, and no queen lands in a corner. A work-in-progress board that clusters its queens in one quadrant while leaving others bare is usually carrying a mistake.
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 #125?
Puzzle #125 is rated medium. Its smallest color region holds 1 square, its tightest row is touched by 2 colors, and four of its regions are confined to a single row or column, which gives you a forced move early.
Does 11x11 puzzle #125 have only one solution?
Yes. Every puzzle in the 11x11 collection, including #125, 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 #125?
Start with the red region — the most constrained color on this board, with 1 square spanning rows 6–6 and columns 11–11. Narrowing the smallest region first removes the most squares elsewhere on the grid.