11x11 Queens Puzzle #150
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 18-step reasoning is written out below.
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Step-by-step solution for puzzle #150
What follows is a complete solve of puzzle #150, 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 shadow, pairing argument on rows, pairing argument on columns.
Show the full walkthrough (12 steps) — contains the solution
Step 1. Only row 1, column 6 is still open in indigo, and since each colour must take a queen, that settles it. That clears row 1, column 6, the rest of the indigo region and every square adjacent to it — diagonals included.
Step 2. The amber region is down to one open square, at row 2, column 10. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 2 and column 10, the remaining amber squares, and the ring of neighbours around row 2, column 10.
Step 3. Only row 9, column 11 is still open in orange, and since each colour must take a queen, that settles it. Everything else in row 9, in column 11, in orange and in the ring around that square is now dead.
Step 4. Wherever blue 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 4 — 3 of 11 queens placed. Step 5. Mint is down to 3 candidates in rows 3 and 4, columns 8 and 9, and they overlap enough to cover 2 squares elsewhere. Cross those out without deciding anything about mint itself.
Step 6. The sea green region has 5 squares left, spread across rows 10 and 11, columns 1–4. 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. 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 6 squares at once.
Step 8. Here is the pairing argument. The sea green and teal regions have no open squares outside rows 10 and 11 — 2 colours confined to 2 rows. Between them they must take one row each, in some order, so every other colour is shut out of all of them: 5 squares come off in one stroke.
The board after step 8 — 3 of 11 queens placed. Step 9. Mint and pale yellow are now boxed into columns 8 and 9 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 5 squares at once.
Step 10. From here the board cascades. Keep alternating the region sweep and the line sweep and 4 queens fall out in order without any new idea being needed: teal has one square left, so its queen takes row 11, column 7; sea green has one square left, so its queen takes row 10, column 4; blue has one square left, so its queen takes row 3, column 3; slate has one square left, so its queen takes row 5, column 5. 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 5, column 5.
Step 11. Red is down to 4 candidates in rows 6–8, columns 1 and 2, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about red itself.
Step 12. From here the board cascades. Keep alternating the region sweep and the line sweep and 4 queens fall out in order without any new idea being needed: khaki has one square left, so its queen takes row 8, column 2; red has one square left, so its queen takes row 6, column 1; pale yellow has one square left, so its queen takes row 7, column 9; mint has one square left, so its queen takes row 4, column 8. 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 4, column 8.
The board after step 12 — 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 #150
Board #150 of the 11x11 bank carries a medium rating. Its 121 squares are shared between eleven colored regions, and the solution places eleven queens: one per row, one per column, one per region, none of them side by side or corner to corner.
As with every puzzle in this collection, #150 has a single verified solution and needs no guesswork. Each queen follows from something already visible. What the board controls is tempo — how soon the first forced move shows up and how far apart the rest are spaced — and that is a direct consequence of how these colors are cut.
How the colors divide this board
From smallest to largest, the regions on puzzle #150 are: indigo (1 square), orange (2 squares), amber (3 squares), sea green (6 squares), teal (13 squares), blue (14 squares), slate (14 squares), pale yellow (15 squares), mint (16 squares), red (18 squares), khaki (19 squares). An even split would hand every color 11 squares, so the indigo region is running 10 squares under that average while the khaki region is the roomiest area on the grid with 19 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 khaki with 19. A 18-square gap like this one rewards players who start where the choices are fewest.
Square count is only half the story — how a color is arranged counts too. Indigo is the tidiest shape on #150, packing 100% of its 1×1 bounding box, whereas red straggles across its 8×5 box at just 45%. Tidy blocks are easy to work around; scattered ones touch more lines and resist resolution.
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 medium board.
Indigo: 1 square across rows 1–1, columns 6–6. It never leaves row 1, so its queen is locked to that row.
Orange covers 2 squares, spanning 1 row and 2 columns (rows 9–9, columns 10–11). It never leaves row 9, so its queen is locked to that row.
Amber occupies 3 squares within rows 1–2, columns 10–11.
Sea green: 6 squares across rows 9–11, columns 1–4.
Teal covers 13 squares, spanning 3 rows and 6 columns (rows 9–11, columns 6–11).
Blue occupies 14 squares within rows 1–4, columns 1–6.
Slate: 14 squares across rows 3–7, columns 3–7.
Pale yellow covers 15 squares, spanning 5 rows and 4 columns (rows 5–9, columns 8–11).
Mint occupies 16 squares within rows 1–5, columns 7–11.
Red: 18 squares across rows 3–10, columns 1–5.
Khaki covers 19 squares, spanning 5 rows and 7 columns (rows 7–11, columns 2–8).
Where to start on this board
Begin where the choices are fewest. On this board that means indigo, which owns just 1 square inside a 1×1 window running from row 1 to row 1 and column 6 to column 6. A queen is guaranteed somewhere in there, so every line that window crosses is under pressure from the very first move.
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.
Work outward to the other flat regions next. Orange and amber 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 #150
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 2, 6, 8 and 11 are the narrowest, touched by only 3 colors. Columns 1 and 9 are the tightest columns, with 3 colors.
The fewer colors a line touches, the sooner it surrenders its queen. A row meeting just 3 colors has to be claimed by one of them, which pushes every remaining region into the other 10 rows. Row 9, meeting 6 colors, is the opposite case — the busiest line on #150 and the last one you should expect to crack.
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.
Keep alternating between two views of the board. In the region view you ask which of the eleven colors is down to one open square. In the line view you ask the same of each row and column. Both produce forced queens, and each placement refreshes the other view, so cycling between them deliberately is how a 11x11 board unwinds.
Say the reason out loud: "this region has one square left", "this column has one square left". If no such sentence is available, the eliminating is not finished. One more pass of X marks is almost always quicker than committing to a placement you cannot defend.
Why puzzle #150 is rated medium
The medium label comes out of four measurable things about #150: 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 18. 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.
A board that feels above its rating is nearly always a board with a missing X. Audit every queen on the grid: full row cleared, full column cleared, all eight touching squares cleared. Diagonals are the common omission, and missing one is far more often the cause of a stall than any genuine difficulty in the puzzle.
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 #150, start hunting for it near row 2.
Here is a shape check that gives nothing away: when #150 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 #150?
Puzzle #150 is rated medium. 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 #150 have only one solution?
Yes. Every puzzle in the 11x11 collection, including #150, 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 #150?
Start with the indigo region — the most constrained color on this board, with 1 square spanning rows 1–1 and columns 6–6. Narrowing the smallest region first removes the most squares elsewhere on the grid.