11x11 Queens Puzzle #286
Difficulty: easy. 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 27-step reasoning is written out below.
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Step-by-step solution for puzzle #286
What follows is a complete solve of puzzle #286, worked the way a person works it rather than the way a computer does. It runs to 27 deductions — 11 queen placements and 16 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: region shadow, pairing argument on rows, line confined to one region, last square in a column, region confined to one line, last square in a region, last square in a row.
Show the full walkthrough (22 steps) — contains the solution
Step 1. Wherever amber ends up among its 5 squares, the same squares fall within reach of it — 2 squares in total, impossible regardless of how the colour resolves.
Step 2. Mint is down to 5 candidates in rows 4–6, columns 5–7, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about mint itself.
Step 3. The sea green region has 3 squares left, spread across rows 10 and 11, columns 10 and 11. 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 4. 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: 13 squares come off in one stroke.
Step 5. Khaki is down to 5 candidates in rows 8 and 9, columns 1, 3, 4, and 5, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about khaki itself.
Step 6. Here is the pairing argument. The red, pale yellow, khaki, and orange regions have no open squares outside rows 6–9 — 4 colours confined to 4 rows. Between them they must take one row each, in some order, so every other colour is shut out of all of them: 15 squares come off in one stroke.
The board after step 6 — 0 of 11 queens placed. Step 7. Wherever mint 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. Slate is down to 3 candidates in rows 4 and 5, columns 1 and 4, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about slate itself.
Step 9. Column 2 has only blue squares left (4 open squares). The column needs a queen and only blue can provide one, which pins that colour to this column and kills its squares elsewhere: 20 squares.
Step 10. Column 3 now has exactly one open square, row 8, column 3, in the khaki region. Columns must each hold a queen, so that placement is forced. That clears row 8, column 3, the rest of the khaki region and every square adjacent to it — diagonals included.
Step 11. Pale yellow is down to 3 candidates in rows 6, 7, and 9, columns 10 and 11, and they overlap enough to cover 3 squares elsewhere. Cross those out without deciding anything about pale yellow itself.
The board after step 11 — 1 of 11 queens placed. Step 12. The red region has 3 squares left, spread across rows 6 and 7, columns 8 and 9. 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 13. Wherever sea green ends up among its 2 squares, the same squares fall within reach of it — 1 square in total, impossible regardless of how the colour resolves.
Step 14. Every open square left in column 1 (2 open squares) belongs to the slate region. Since that column must contain a queen, slate is the colour that supplies it — so slate squares anywhere else on the board are out, 1 square in all.
Step 15. Scan column 4 and only row 2, column 4 remains — a amber square. Every column takes a queen, so it takes this one. Cross out the whole of row 2 and column 4, the remaining amber squares, and the ring of neighbours around row 2, column 4.
Step 16. All of the slate 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: 1 square come off.
Step 17. Column 5 has only mint squares left (2 open squares). The column needs a queen and only mint can provide one, which pins that colour to this column and kills its squares elsewhere: 2 squares.
The board after step 17 — 2 of 11 queens placed. Step 18. Column 6 now has exactly one open square, row 9, column 6, in the orange region. Columns must each hold a queen, so that placement is forced. That clears row 9, column 6, the rest of the orange region and every square adjacent to it — diagonals included.
Step 19. Scan column 7 and only row 11, column 7 remains — a teal square. Every column takes a queen, so it takes this one. Cross out the whole of row 11 and column 7, the remaining teal squares, and the ring of neighbours around row 11, column 7.
Step 20. The sea green region is down to one open square, at row 10, column 10. Every colour holds exactly one queen, so that square is forced. Row 10 and column 10 are now spoken for, along with the squares touching that queen.
Step 21. Pale yellow cannot leave column 11 — every one of its open squares (2 open squares) sits there. That column belongs to pale yellow, so every square in it owned by another colour is dead: 4 squares in all.
Step 22. 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: row 3 is down to one square, putting a queen on row 3, column 2; slate has one square left, so its queen takes row 5, column 1; mint has one square left, so its queen takes row 4, column 5; indigo has one square left, so its queen takes row 1, column 9; red has one square left, so its queen takes row 6, column 8; pale yellow has one square left, so its queen takes row 7, column 11. 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 7, column 11.
The board after step 22 — 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 #286
Board #286 of the 11x11 bank carries a easy 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, #286 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 #286 are: sea green (3 squares), amber (5 squares), mint (5 squares), red (5 squares), teal (6 squares), pale yellow (8 squares), orange (12 squares), indigo (14 squares), khaki (16 squares), slate (18 squares), blue (29 squares). An even split would hand every color 11 squares, so the sea green region is running 8 squares under that average while the blue region is the roomiest area on the grid with 29 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 sea green, with 3 squares, is under far more pressure than blue with 29. A 26-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. Red is the tidiest shape on #286, packing 83% of its 2×3 bounding box, whereas orange straggles across its 5×5 box at just 48%. 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.
Sea green covers 3 squares, spanning 2 rows and 2 columns (rows 10–11, columns 10–11).
Amber occupies 5 squares within rows 1–2, columns 4–7.
Mint: 5 squares across rows 4–6, columns 5–7.
Red covers 5 squares, spanning 2 rows and 3 columns (rows 6–7, columns 8–10).
Teal occupies 6 squares within rows 10–11, columns 7–10.
Pale yellow: 8 squares across rows 6–9, columns 8–11.
Orange covers 12 squares, spanning 5 rows and 5 columns (rows 6–10, columns 5–9).
Indigo occupies 14 squares within rows 1–5, columns 8–11.
Khaki: 16 squares across rows 8–11, columns 1–6.
Slate covers 18 squares, spanning 6 rows and 6 columns (rows 4–9, columns 1–6).
Blue occupies 29 squares within rows 1–6, columns 1–10.
Where to start on this board
Begin where the choices are fewest. On this board that means sea green, which owns just 3 squares inside a 2×2 window running from row 10 to row 11 and column 10 to column 11. A queen is guaranteed somewhere in there, so every line that window crosses is under pressure from the very first move.
With 2 rows and 2 columns of room, sea green needs narrowing rather than solving outright. Test its 3 squares against the neighbours: a candidate that would strand another color is dead, and eliminating even two of them tightens the whole corner of the board around rows 10–11.
Work outward to the other flat regions next. Amber, red and teal 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 #286
A quick way to find the next move is to count how many different colors touch each line. On this board, row 3 is the narrowest, touched by only 2 colors. Columns 1, 2, 3 and 11 are the tightest columns, with 3 colors.
A line with few colors is a line close to resolving. Where only 2 colors appear, one of them owns the row outright and the others must fit into the remaining 10 rows. Row 6 is the crowded extreme at 6 colors — worth revisiting later, not now.
Working through the middle game
After the first few queens the puzzle becomes bookkeeping. A placed queen wipes its row, its column and every square it touches — as many as eight neighbours — so the space collapses quickly. Record those eliminations on the board instead of carrying them in your head, and the next forced move tends to announce itself.
With eleven queens to seat and eleven regions competing over 121 squares, keep two questions in rotation. Does any region now have exactly one open square left? That queen is forced. Does any row or column now have exactly one open square left? That queen is forced too. Alternating between the region view and the row-and-column view is what keeps a solve moving, and it is the clearest difference between players who finish 11x11 boards quickly and players who stall halfway.
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 #286 is rated easy
Ratings track how generous the opening is. On #286 you get no region pinned to a single row or column, a smallest color of 3 squares, a tightest row crossed by 2 colors, and a 26-square gap between the largest and smallest regions. Those four numbers largely explain the easy label.
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 #286, start hunting for it near row 3.
A non-spoiling distribution check: solved, #286 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 #286?
Puzzle #286 is rated easy. Its smallest color region holds 3 squares, its tightest row is touched by 2 colors, and no region is confined to a single row or column, so the opening move takes some hunting.
Does 11x11 puzzle #286 have only one solution?
Yes. Every puzzle in the 11x11 collection, including #286, 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 #286?
Start with the sea green region — the most constrained color on this board, with 3 squares spanning rows 10–11 and columns 10–11. Narrowing the smallest region first removes the most squares elsewhere on the grid.