11x11 Queens Puzzle #246
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 21-step reasoning is written out below.
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Step-by-step solution for puzzle #246
What follows is a complete solve of puzzle #246, worked the way a person works it rather than the way a computer does. It runs to 21 deductions — 11 queen placements and 10 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 shadow, region confined to one line, line confined to one region, pairing argument on rows.
Show the full walkthrough (14 steps) — contains the solution
Step 1. Only row 11, column 9 is still open in teal, and since each colour must take a queen, that settles it. That clears row 11, column 9, the rest of the teal region and every square adjacent to it — diagonals included.
Step 2. Amber is down to 3 candidates in rows 2 and 3, columns 3 and 4, and they overlap enough to cover 3 squares elsewhere. Cross those out without deciding anything about amber itself.
Step 3. Slate cannot leave column 11 — every one of its open squares (5 open squares) sits there. That column belongs to slate, so every square in it owned by another colour is dead: 5 squares in all.
Step 4. All of the orange 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: 10 squares come off.
Step 5. Only row 1, column 2 is still open in indigo, and since each colour must take a queen, that settles it. That clears row 1, column 2, the rest of the indigo region and every square adjacent to it — diagonals included.
The board after step 5 — 2 of 11 queens placed. Step 6. The amber region has 2 squares left, spread across rows 2 and 3, columns 3 and 4. You do not need to know which of them takes the queen: every one of those options attacks the same 2 squares, so they can be crossed out now.
Step 7. Red cannot leave column 3 — every one of its open squares (4 open squares) sits there. That column belongs to red, so every square in it owned by another colour is dead: 4 squares in all.
Step 8. The amber region is down to one open square, at row 2, column 4. Every colour holds exactly one queen, so that square is forced. Row 2 and column 4 are now spoken for, along with the squares touching that queen.
Step 9. Slate cannot leave column 11 — every one of its open squares (3 open squares) sits there. That column belongs to slate, so every square in it owned by another colour is dead: 1 square in all.
The board after step 9 — 3 of 11 queens placed. Step 10. All of the pale yellow region's remaining squares (2 open squares) lie in column 5. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 5 squares come off.
Step 11. Sea green is down to 4 candidates in rows 9 and 10, columns 6–8, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about sea green itself.
Step 12. Every open square left in row 8 (4 open squares) belongs to the khaki region. Since that row must contain a queen, khaki is the colour that supplies it — so khaki squares anywhere else on the board are out, 8 squares in all.
Step 13. Orange and sea green are now boxed into rows 9 and 10 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 3 squares at once.
Step 14. From here the board cascades. Keep alternating the region sweep and the line sweep and 8 queens fall out in order without any new idea being needed: pale yellow has one square left, so its queen takes row 7, column 5; red has one square left, so its queen takes row 6, column 3; blue has one square left, so its queen takes row 3, column 6; mint has one square left, so its queen takes row 4, column 8; slate has one square left, so its queen takes row 5, column 11; sea green has one square left, so its queen takes row 10, column 7; khaki has one square left, so its queen takes row 8, column 10; orange has one square left, so its queen takes row 9, 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 9, column 1.
The board after step 14 — 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 #246
Board #246 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, #246 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 #246 are: teal (1 square), amber (3 squares), indigo (5 squares), slate (5 squares), orange (6 squares), sea green (9 squares), red (15 squares), blue (16 squares), pale yellow (16 squares), mint (17 squares), khaki (28 squares). An even split would hand every color 11 squares, so the teal region is running 10 squares under that average while the khaki region is the roomiest area on the grid with 28 squares.
That imbalance is the first thing to read, because every region takes exactly one queen regardless of how much space it owns. Teal has only 1 place to put its queen; khaki has 28. The spread between them on this board is 27 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. Slate is the tidiest shape on #246, packing 100% of its 5×1 bounding box, whereas pale yellow straggles across its 9×4 box at just 44%. Tidy blocks are easy to work around; scattered ones touch more lines and resist resolution.
Region by region
The complete breakdown of each region on this board follows, ordered from tightest to roomiest. Skimming the spans first tells you where the board is crowded and where it has slack.
Teal: 1 square across rows 11–11, columns 9–9. It never leaves row 11, so its queen is locked to that row.
Amber covers 3 squares, spanning 2 rows and 2 columns (rows 2–3, columns 3–4).
Indigo occupies 5 squares within rows 1–2, columns 1–3.
Slate: 5 squares across rows 1–5, columns 11–11. It sits wholly inside column 11, so its queen must be in that column.
Orange covers 6 squares, spanning 3 rows and 4 columns (rows 9–11, columns 1–4).
Sea green occupies 9 squares within rows 9–11, columns 5–8.
Red: 15 squares across rows 3–10, columns 1–3.
Blue covers 16 squares, spanning 7 rows and 4 columns (rows 1–7, columns 4–7).
Pale yellow occupies 16 squares within rows 3–11, columns 2–5.
Mint: 17 squares across rows 1–5, columns 6–10.
Khaki covers 28 squares, spanning 8 rows and 7 columns (rows 4–11, columns 5–11).
Where to start on this board
Begin where the choices are fewest. On this board that means teal, which owns just 1 square inside a 1×1 window running from row 11 to row 11 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 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 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 #246
A quick way to find the next move is to count how many different colors touch each line. On this board, row 8 is the narrowest, touched by only 3 colors. Columns 10 and 11 are the tightest columns, 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 5 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.
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 #246 is rated hard
Ratings track how generous the opening is. On #246 you get three regions pinned to a single row or column, a smallest color of 1 square, a tightest row crossed by 3 colors, and a 27-square gap between the largest and smallest regions. Those four numbers largely explain the hard label.
Nothing about the rating involves computation or chance. Each grid has a single solution reachable by pure logic; the rating simply measures how far ahead you have to reason. Easy boards resolve a queen every step or two, while hard ones can ask you to carry three unfinished lines of thought before any of them pays off.
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 #246 the place to look for one is around column 10.
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 #246?
Puzzle #246 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 #246 have only one solution?
Yes. Every puzzle in the 11x11 collection, including #246, 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 #246?
Start with the teal region — the most constrained color on this board, with 1 square spanning rows 11–11 and columns 9–9. Narrowing the smallest region first removes the most squares elsewhere on the grid.