11x11 Queens Puzzle #46
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 #46
What follows is a complete solve of puzzle #46, 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 region shadow.
Techniques this board needs: last square in a region, region confined to one line, region shadow, last square in a column.
Show the full walkthrough (9 steps) — contains the solution
Step 1. The board opens by cascading. Each of these placements is forced the moment the one before it is marked, so the whole run is really a single sweep repeated: indigo has one square left, so its queen takes row 1, column 9; amber has one square left, so its queen takes row 2, column 11; blue has one square left, so its queen takes row 3, column 1; sea green has one square left, so its queen takes row 10, 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 10, column 2.
Step 2. Mint cannot leave row 4 — every one of its open squares (2 open squares) sits there. That row belongs to mint, so every square on it owned by another colour is dead: 5 squares in all.
Step 3. All of the pale yellow region's remaining squares (2 open squares) lie in column 3. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 5 squares come off.
The board after step 3 — 4 of 11 queens placed. Step 4. Only row 4, column 7 is still open in mint, and since each colour must take a queen, that settles it. Everything else in row 4, in column 7, in mint and in the ring around that square is now dead.
Step 5. The orange region is down to one open square, at row 9, column 4. Every colour holds exactly one queen, so that square is forced. Row 9 and column 4 are now spoken for, along with the squares touching that queen.
Step 6. Only row 7, column 3 is still open in pale yellow, and since each colour must take a queen, that settles it. That clears row 7, column 3, the rest of the pale yellow region and every square adjacent to it — diagonals included.
The board after step 6 — 7 of 11 queens placed. Step 7. Wherever slate ends up among its 2 squares, the same squares fall within reach of it — 2 squares in total, impossible regardless of how the colour resolves.
Step 8. Khaki is down to 2 candidates in rows 8 and 11, columns 5 and 6, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about khaki itself.
Step 9. 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: column 6 is down to one square, putting a queen on row 8, column 6; column 5 is down to one square, putting a queen on row 5, column 5; red has one square left, so its queen takes row 6, column 10; teal has one square left, so its queen takes row 11, 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 11, column 8.
The board after step 9 — 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 #46
Board #46 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, #46 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 #46 are: indigo (1 square), amber (4 squares), sea green (5 squares), orange (6 squares), blue (7 squares), pale yellow (8 squares), teal (10 squares), slate (12 squares), khaki (15 squares), mint (26 squares), red (27 squares). An even split would hand every color 11 squares, so the indigo region is running 10 squares under that average while the red region is the roomiest area on the grid with 27 squares.
That imbalance is the first thing to read, because every region takes exactly one queen regardless of how much space it owns. Indigo has only 1 place to put its queen; red has 27. The spread between them on this board is 26 squares, and the wider that spread runs, the more it pays to solve from the small end inward.
Square count is only half the story — how a color is arranged counts too. Indigo is the tidiest shape on #46, packing 100% of its 1×1 bounding box, whereas orange straggles across its 4×3 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 medium board.
Indigo covers 1 square, spanning 1 row and 1 column (rows 1–1, columns 9–9). It never leaves row 1, so its queen is locked to that row.
Amber occupies 4 squares within rows 1–2, columns 10–11.
Sea green: 5 squares across rows 8–11, columns 1–2.
Orange covers 6 squares, spanning 4 rows and 3 columns (rows 8–11, columns 2–4).
Blue occupies 7 squares within rows 1–3, columns 1–4.
Pale yellow: 8 squares across rows 6–9, columns 1–3.
Teal covers 10 squares, spanning 3 rows and 5 columns (rows 9–11, columns 6–10).
Slate occupies 12 squares within rows 4–6, columns 3–8.
Khaki: 15 squares across rows 6–11, columns 4–7.
Mint covers 26 squares, spanning 5 rows and 10 columns (rows 1–5, columns 1–10).
Red occupies 27 squares within rows 3–11, columns 7–11.
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 9 to column 9. 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. Amber is no more than two rows tall, so its queen is 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 #46
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 2, 3, 4, 5 and 7 are the narrowest, touched by only 3 colors. Column 11 is the tightest column, with 2 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 #46 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 #46 is rated medium
The medium label comes out of four measurable things about #46: 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 26. 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.
One pattern is worth learning at every size, and it is available here. When two regions can only fit inside the same two rows, they must take one row each — which locks every other region out of both. The same argument works for columns, and for any matching count: three regions sharing three rows, four sharing four. Spotting these pairings turns a slow grind into a quick cascade, and on #46 the place to look for one is around column 11.
Here is a shape check that gives nothing away: when #46 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 #46?
Puzzle #46 is rated medium. 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 #46 have only one solution?
Yes. Every puzzle in the 11x11 collection, including #46, 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 #46?
Start with the indigo region — the most constrained color on this board, with 1 square spanning rows 1–1 and columns 9–9. Narrowing the smallest region first removes the most squares elsewhere on the grid.