11x11 Queens Puzzle #50
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 16-step reasoning is written out below.
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Step-by-step solution for puzzle #50
What follows is a complete solve of puzzle #50, 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 region shadow.
Techniques this board needs: last square in a region, region shadow, region confined to one line.
Show the full walkthrough (8 steps) — contains the solution
Step 1. Only row 5, column 6 is still open in slate, and since each colour must take a queen, that settles it. That clears row 5, column 6, the rest of the slate region and every square adjacent to it — diagonals included.
Step 2. The teal region is down to one open square, at row 11, column 10. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 11 and column 10, the remaining teal squares, and the ring of neighbours around row 11, column 10.
Step 3. The amber region has 4 squares left, spread across rows 1 and 2, columns 1–3. 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 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 — 2 of 11 queens placed. Step 5. Pale yellow is down to 5 candidates in rows 6–8, columns 7–9, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about pale yellow itself.
Step 6. All of the sea green region's remaining squares (2 open squares) lie in column 1. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 9 squares come off.
Step 7. Wherever indigo ends up among its 4 squares, the same squares fall within reach of it — 1 square in total, impossible regardless of how the colour resolves.
Step 8. 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 2; indigo has one square left, so its queen takes row 1, column 4; blue has one square left, so its queen takes row 3, column 5; mint has one square left, so its queen takes row 4, column 8; red has one square left, so its queen takes row 6, column 11; orange has one square left, so its queen takes row 9, column 9; pale yellow has one square left, so its queen takes row 7, column 7; sea green has one square left, so its queen takes row 10, column 1; khaki has one square left, so its queen takes row 8, column 3. 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 8, column 3.
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 #50
Board #50 of the 11x11 bank carries a hard 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, #50 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 #50 are: slate (1 square), teal (1 square), amber (4 squares), sea green (5 squares), blue (7 squares), red (8 squares), indigo (10 squares), pale yellow (10 squares), orange (15 squares), mint (22 squares), khaki (38 squares). An even split would hand every color 11 squares, so the slate region is running 10 squares under that average while the khaki region is the roomiest area on the grid with 38 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 slate, with 1 square, is under far more pressure than khaki with 38. A 37-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. Slate is the tidiest shape on #50, packing 100% of its 1×1 bounding box, whereas indigo straggles across its 5×4 box at just 50%. 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 hard board.
Slate occupies 1 square within rows 5–5, columns 6–6. It never leaves row 5, so its queen is locked to that row.
Teal: 1 square across rows 11–11, columns 10–10. It never leaves row 11, so its queen is locked to that row.
Amber covers 4 squares, spanning 2 rows and 3 columns (rows 1–2, columns 1–3).
Sea green occupies 5 squares within rows 9–11, columns 1–3.
Blue: 7 squares across rows 2–5, columns 4–6.
Red covers 8 squares, spanning 3 rows and 3 columns (rows 4–6, columns 9–11).
Indigo occupies 10 squares within rows 1–5, columns 1–4.
Pale yellow: 10 squares across rows 6–8, columns 5–10.
Orange covers 15 squares, spanning 5 rows and 4 columns (rows 7–11, columns 8–11).
Mint occupies 22 squares within rows 1–5, columns 5–11.
Khaki: 38 squares across rows 4–11, columns 1–8.
Where to start on this board
Begin where the choices are fewest. On this board that means slate, which owns just 1 square inside a 1×1 window running from row 5 to row 5 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 slate never leaves row 5, its queen must be in that row — and that instantly settles row 5 for everyone else. Sweep along it and X out every square that is not slate. 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 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 #50
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 1, 3, 6, 7, 8, 9 and 10 are the narrowest, touched by only 3 colors. Columns 4, 7 and 11 are the tightest columns, with 3 colors.
Those lines matter because a row touched by few colors gives its queen away sooner. If a row meets only 3 colors, then one of those regions has to own it, and every other region is competing for the remaining 10 rows. By contrast row 5 meets 6 colors — the most crowded line here, and the one least likely to resolve early. Spend your attention accordingly.
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 #50 is rated hard
The hard label comes out of four measurable things about #50: four 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 37. 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.
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 #50, start hunting for it near row 1.
As a sanity check rather than a spoiler: the finished solution to #50 puts 4 queens on the outer border and 7 queens in the interior, with none in a corner. If your part-finished grid has queens bunched into one area while whole stretches sit empty, something probably went wrong a few moves back.
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 #50?
Puzzle #50 is rated hard. 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 #50 have only one solution?
Yes. Every puzzle in the 11x11 collection, including #50, 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 #50?
Start with the slate region — the most constrained color on this board, with 1 square spanning rows 5–5 and columns 6–6. Narrowing the smallest region first removes the most squares elsewhere on the grid.