11x11 Queens Puzzle #141
Difficulty: hard. 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 18-step reasoning is written out below.
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Step-by-step solution for puzzle #141
What follows is a complete solve of puzzle #141, worked the way a person works it rather than the way a computer does. It runs to 18 deductions — 11 queen placements and 7 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: last square in a region, region confined to one line, region shadow, pairing argument on columns.
Show the full walkthrough (10 steps) — contains the solution
Step 1. Only row 1, column 10 is still open in indigo, and since each colour must take a queen, that settles it. That clears row 1, column 10, the rest of the indigo region and every square adjacent to it — diagonals included.
Step 2. The blue region is down to one open square, at row 3, column 9. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 3 and column 9, the remaining blue squares, and the ring of neighbours around row 3, column 9.
Step 3. Amber cannot leave row 2 — every one of its open squares (2 open squares) sits there. That row belongs to amber, so every square on it owned by another colour is dead: 5 squares in all.
The board after step 3 — 2 of 11 queens placed. Step 4. All of the slate region's remaining squares (2 open squares) lie in column 11. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 6 squares come off.
Step 5. Orange is down to 3 candidates in rows 9 and 10, columns 7 and 8, and they overlap enough to cover 3 squares elsewhere. Cross those out without deciding anything about orange itself.
Step 6. The sea green region has 4 squares left, spread across rows 9–11, columns 5, 6, 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 7. Wherever orange ends up among its 2 squares, the same squares fall within reach of it — 1 square in total, impossible regardless of how the colour resolves.
The board after step 7 — 2 of 11 queens placed. Step 8. Red is down to 3 candidates in rows 5 and 6, columns 7 and 8, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about red itself.
Step 9. Red and orange are now boxed into columns 7 and 8 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 6 squares at once.
Step 10. From here the board cascades. Keep alternating the region sweep and the line sweep and 9 queens fall out in order without any new idea being needed: amber has one square left, so its queen takes row 2, column 6; sea green has one square left, so its queen takes row 10, column 5; mint has one square left, so its queen takes row 4, column 4; slate has one square left, so its queen takes row 5, column 11; red has one square left, so its queen takes row 6, column 8; pale yellow has one square left, so its queen takes row 7, column 3; orange has one square left, so its queen takes row 9, column 7; khaki has one square left, so its queen takes row 8, column 1; teal has one square left, so its queen takes row 11, column 2. 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 11, column 2.
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 #141
Puzzle #141 is one of the hard-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 #141, 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 #141 are: indigo (1 square), blue (7 squares), sea green (7 squares), slate (8 squares), pale yellow (10 squares), amber (11 squares), teal (12 squares), red (13 squares), khaki (14 squares), orange (15 squares), mint (23 squares). An even split would hand every color 11 squares, so the indigo region is running 10 squares under that average while the mint region is the roomiest area on the grid with 23 squares.
Why does the split matter? Because a region's square count has no bearing on how many queens it gets — the answer is always one. So indigo, with 1 square, is under far more pressure than mint with 23. A 22-square gap like this one rewards players who start where the choices are fewest.
Shape matters as much as size. The indigo region is the most compact color here, filling 100% of the 1×1 box that encloses it, while sea green is the most scattered at 47% of its 3×5 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
Each region's exact extent on this grid is listed below, starting with the most constrained. Knowing which lines a color can and cannot reach is most of the work on a hard board.
Indigo: 1 square across rows 1–1, columns 10–10. It never leaves row 1, so its queen is locked to that row.
Blue covers 7 squares, spanning 4 rows and 3 columns (rows 1–4, columns 8–10).
Sea green occupies 7 squares within rows 9–11, columns 5–9.
Slate: 8 squares across rows 1–7, columns 10–11.
Pale yellow covers 10 squares, spanning 4 rows and 5 columns (rows 5–8, columns 3–7).
Amber occupies 11 squares within rows 1–3, columns 1–7.
Teal: 12 squares across rows 8–11, columns 1–5.
Red covers 13 squares, spanning 8 rows and 3 columns (rows 2–9, columns 7–9).
Khaki occupies 14 squares within rows 4–10, columns 1–3.
Orange: 15 squares across rows 6–11, columns 7–11.
Mint covers 23 squares, spanning 6 rows and 8 columns (rows 2–7, columns 1–8).
Where to start on this board
Indigo is the natural opening on #141: it is the smallest region on the grid at 1 square, boxed into rows 1–1 and columns 10–10. 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 indigo never leaves row 1, its queen must be in that row — and that instantly settles row 1 for everyone else. Sweep along it and X out every square that is not indigo. 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.
No region here is pinned to a shallow band of rows, so turn the same idea sideways: slate spans only two columns. Two narrow regions sharing the same two columns take one column each and lock everyone else out of both, which is usually enough to crack a board that offers no free opening.
The tightest lines on puzzle #141
A quick way to find the next move is to count how many different colors touch each line. On this board, row 11 is the narrowest, touched by only 3 colors. Column 11 is the tightest column, with 2 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 7 sits at the far end with 6 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.
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 #141 is rated hard
The hard label comes out of four measurable things about #141: two of its regions are locked to one row or column, its smallest color spans 1 square, its least crowded row meets 3 colors, and its largest and smallest regions differ by 22. Boards that score tight on those measures give up their first queen fast.
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.
Stuck on #141 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 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.
Learn the pairing argument and you will use it on every board, this one included. If two colors can only sit inside the same two rows, between them they consume both rows and every other color is shut out. It generalises to any matching count — three colors across three rows, four across four. On #141, start hunting for it near column 11.
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 #141?
Puzzle #141 is rated hard. Its smallest color region holds 1 square, its tightest row is touched by 3 colors, and two of its regions are confined to a single row or column, which gives you a forced move early.
Does 11x11 puzzle #141 have only one solution?
Yes. Every puzzle in the 11x11 collection, including #141, 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 #141?
Start with the indigo region — the most constrained color on this board, with 1 square spanning rows 1–1 and columns 10–10. Narrowing the smallest region first removes the most squares elsewhere on the grid.