11x11 Queens Puzzle #149
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 22-step reasoning is written out below.
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Step-by-step solution for puzzle #149
What follows is a complete solve of puzzle #149, worked the way a person works it rather than the way a computer does. It runs to 22 deductions — 11 queen placements and 11 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, line confined to one region, last square in a column.
Show the full walkthrough (17 steps) — contains the solution
Step 1. Only row 11, column 8 is still open in teal, and since each colour must take a queen, that settles it. That clears row 11, column 8, the rest of the teal region and every square adjacent to it — diagonals included.
Step 2. The sea green region is down to one open square, at row 10, column 2. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 10 and column 2, the remaining sea green squares, and the ring of neighbours around row 10, column 2.
Step 3. Indigo cannot leave row 1 — every one of its open squares (4 open squares) sits there. That row belongs to indigo, so every square on it owned by another colour is dead: 5 squares in all.
Step 4. Wherever amber ends up among its 5 squares, the same squares fall within reach of it — 1 square in total, impossible regardless of how the colour resolves.
The board after step 4 — 2 of 11 queens placed. Step 5. Mint is down to 3 candidates in rows 3 and 4, columns 7 and 9, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about mint itself.
Step 6. All of the amber region's remaining squares (4 open squares) lie in row 2. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 4 squares come off.
Step 7. Blue cannot leave column 1 — 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: 4 squares in all.
Step 8. Orange is down to 4 candidates in rows 8 and 9, columns 5, 7, and 9, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about orange itself.
Step 9. Blue and mint are now boxed into rows 3 and 4 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 12 squares at once.
The board after step 9 — 2 of 11 queens placed. Step 10. The slate region is down to one open square, at row 5, column 3. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 5 and column 3, the remaining slate squares, and the ring of neighbours around row 5, column 3.
Step 11. Only row 6, column 11 is still open in red, and since each colour must take a queen, that settles it. Everything else in row 6, in column 11, in red and in the ring around that square is now dead.
Step 12. The khaki region has 4 squares left, spread across rows 7–9, columns 9 and 10. 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 13. Wherever orange ends up among its 3 squares, the same squares fall within reach of it — 2 squares in total, impossible regardless of how the colour resolves.
The board after step 13 — 4 of 11 queens placed. Step 14. Every open square left in column 4 (2 open squares) belongs to the pale yellow region. Since that column must contain a queen, pale yellow is the colour that supplies it — so pale yellow squares anywhere else on the board are out, 4 squares in all.
Step 15. Scan column 6 and only row 2, column 6 remains — a amber square. Every column takes a queen, so it takes this one. Cross out the whole of row 2 and column 6, the remaining amber squares, and the ring of neighbours around row 2, column 6.
Step 16. All of the pale yellow region's remaining squares (2 open squares) lie in column 4. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 1 square come off.
Step 17. From here the board cascades. Keep alternating the region sweep and the line sweep and 6 queens fall out in order without any new idea being needed: column 5 is down to one square, putting a queen on row 9, column 5; pale yellow has one square left, so its queen takes row 7, column 4; khaki has one square left, so its queen takes row 8, column 10; indigo has one square left, so its queen takes row 1, column 9; mint has one square left, so its queen takes row 4, column 7; blue has one square left, so its queen takes row 3, column 1. 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 3, column 1.
The board after step 17 — 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 #149
Puzzle #149 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 #149, 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 #149 are: teal (1 square), mint (4 squares), sea green (4 squares), indigo (5 squares), amber (8 squares), blue (11 squares), slate (11 squares), red (14 squares), orange (15 squares), khaki (16 squares), pale yellow (32 squares). An even split would hand every color 11 squares, so the teal region is running 10 squares under that average while the pale yellow region is the roomiest area on the grid with 32 squares.
Every color takes one queen and one only, whatever its size — which is why the 31 square difference between teal 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 1×5 box that encloses it, while slate is the most scattered at 44% of its 5×5 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.
Teal occupies 1 square within rows 11–11, columns 8–8. It never leaves row 11, so its queen is locked to that row.
Mint: 4 squares across rows 3–4, columns 7–9.
Sea green covers 4 squares, spanning 2 rows and 3 columns (rows 10–11, columns 1–3).
Indigo occupies 5 squares within rows 1–1, columns 7–11. It never leaves row 1, so its queen is locked to that row.
Amber: 8 squares across rows 1–3, columns 5–10.
Blue covers 11 squares, spanning 4 rows and 4 columns (rows 1–4, columns 1–4).
Slate occupies 11 squares within rows 2–6, columns 1–5.
Red: 14 squares across rows 2–7, columns 8–11.
Orange covers 15 squares, spanning 4 rows and 6 columns (rows 8–11, columns 4–9).
Khaki occupies 16 squares within rows 6–11, columns 9–11.
Pale yellow: 32 squares across rows 4–10, columns 1–7.
Where to start on this board
Teal is the natural opening on #149: it is the smallest region on the grid at 1 square, boxed into rows 11–11 and columns 8–8. 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 teal never leaves row 11, its queen must be in that row — and that instantly settles row 11 for everyone else. Sweep along it and X out every square that is not teal. 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, mint and sea green 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 #149
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 1, 5, 7, 8 and 9 are the narrowest, touched by only 3 colors. Columns 6 and 11 are the tightest columns, with 3 colors.
A line with few colors is a line close to resolving. Where only 3 colors appear, one of them owns the row outright and the others must fit into the remaining 10 rows. Row 4 is the crowded extreme at 5 colors — worth revisiting later, not now.
Working through the middle game
The middle of #149 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.
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 #149 is rated hard
The hard label comes out of four measurable things about #149: three 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 31. Boards that score tight on those measures give up their first queen fast.
Difficulty in Queens is never arithmetic and never luck. Every board has one solution and none require guessing. What varies is the length of the chain you must follow before the next queen becomes certain — one or two steps on an easy board, five or six on a hard one, sometimes with several partial eliminations held in play at once.
Stuck on #149 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.
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 #149 is row 1.
A non-spoiling distribution check: solved, #149 carries 4 queens on the perimeter against 7 queens inside, with the corners empty. Because no two queens may touch, real solutions always look fairly evenly spread — a lopsided board in progress is a warning sign.
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 #149?
Puzzle #149 is rated hard. Its smallest color region holds 1 square, its tightest row is touched by 3 colors, and three of its regions are confined to a single row or column, which gives you a forced move early.
Does 11x11 puzzle #149 have only one solution?
Yes. Every puzzle in the 11x11 collection, including #149, 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 #149?
Start with the teal region — the most constrained color on this board, with 1 square spanning rows 11–11 and columns 8–8. Narrowing the smallest region first removes the most squares elsewhere on the grid.