11x11 Queens Puzzle #258
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 17-step reasoning is written out below.
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Step-by-step solution for puzzle #258
What follows is a complete solve of puzzle #258, worked the way a person works it rather than the way a computer does. It runs to 17 deductions — 11 queen placements and 6 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 confined to one line, region shadow, pairing argument on rows.
Show the full walkthrough (10 steps) — contains the solution
Step 1. Only row 6, column 5 is still open in red, and since each colour must take a queen, that settles it. That clears row 6, column 5, the rest of the red region and every square adjacent to it — diagonals included.
Step 2. All of the indigo region's remaining squares (5 open squares) lie in row 1. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 5 squares come off.
Step 3. The mint region has 4 squares left, spread across rows 4 and 5, 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.
The board after step 3 — 1 of 11 queens placed. Step 4. Wherever sea green ends up among its 3 squares, the same squares fall within reach of it — 1 square in total, impossible regardless of how the colour resolves.
Step 5. Teal is down to 3 candidates in rows 10 and 11, columns 8 and 9, and they overlap enough to cover 2 squares elsewhere. Cross those out without deciding anything about teal itself.
Step 6. All of the sea green region's remaining squares (2 open squares) lie in column 11. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 7 squares come off.
Step 7. Only row 5, column 10 is still open in slate, and since each colour must take a queen, that settles it. Everything else in row 5, in column 10, in slate and in the ring around that square is now dead.
The board after step 7 — 2 of 11 queens placed. Step 8. The mint region is down to one open square, at row 4, column 1. Every colour holds exactly one queen, so that square is forced. Row 4 and column 1 are now spoken for, along with the squares touching that queen.
Step 9. Amber and blue are now boxed into rows 2 and 3 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 10. 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 9; teal has one square left, so its queen takes row 11, column 8; sea green has one square left, so its queen takes row 10, column 11; orange has one square left, so its queen takes row 9, column 7; amber has one square left, so its queen takes row 2, column 6; 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 3; khaki has one square left, so its queen takes row 8, 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 8, column 2.
The board after step 10 — 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 #258
Board #258 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.
Like every board on this site, #258 has been verified to have exactly one valid solution, and that solution is reachable by deduction alone. You never have to guess and then unwind; every queen can be justified by something already visible on the grid. What changes from puzzle to puzzle is where the first certainty appears and how long the chain of reasoning runs before the next one — and that is entirely a product of how these particular colors are shaped.
How the colors divide this board
From smallest to largest, the regions on puzzle #258 are: red (1 square), sea green (3 squares), teal (4 squares), indigo (6 squares), slate (6 squares), mint (8 squares), amber (13 squares), blue (14 squares), orange (15 squares), pale yellow (21 squares), khaki (30 squares). An even split would hand every color 11 squares, so the red region is running 10 squares under that average while the khaki region is the roomiest area on the grid with 30 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 red, with 1 square, is under far more pressure than khaki with 30. A 29-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 #258, packing 100% of its 1×6 bounding box, whereas amber straggles across its 5×6 box at just 43%. Tidy blocks are easy to work around; scattered ones touch more lines and resist resolution.
Region by region
Below is every color on #258 with its exact reach, smallest region first. It is worth a slow read: the spans reveal which rows and columns several regions are fighting over.
Red: 1 square across rows 6–6, columns 5–5. It never leaves row 6, so its queen is locked to that row.
Sea green covers 3 squares, spanning 2 rows and 2 columns (rows 10–11, columns 10–11).
Teal occupies 4 squares within rows 10–11, columns 8–10.
Indigo: 6 squares across rows 1–1, columns 4–9. It never leaves row 1, so its queen is locked to that row.
Slate covers 6 squares, spanning 5 rows and 2 columns (rows 1–5, columns 10–11).
Mint occupies 8 squares within rows 4–7, columns 1–4.
Amber: 13 squares across rows 1–5, columns 5–10.
Blue covers 14 squares, spanning 4 rows and 4 columns (rows 1–4, columns 1–4).
Orange occupies 15 squares within rows 6–10, columns 6–11.
Pale yellow: 21 squares across rows 3–8, columns 5–10.
Khaki covers 30 squares, spanning 6 rows and 7 columns (rows 6–11, columns 1–7).
Where to start on this board
Begin where the choices are fewest. On this board that means red, which owns just 1 square inside a 1×1 window running from row 6 to row 6 and column 5 to column 5. A queen is guaranteed somewhere in there, so every line that window crosses is under pressure from the very first move.
Because red never leaves row 6, its queen must be in that row — and that instantly settles row 6 for everyone else. Sweep along it and X out every square that is not red. 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, teal and sea green 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 #258
A quick way to find the next move is to count how many different colors touch each line. On this board, row 9 is the narrowest, touched by only 2 colors. Columns 1, 2, 3 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 2 colors, then one of those regions has to own it, and every other region is competing for the remaining 10 rows. By contrast row 6 meets 5 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.
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 #258 is rated hard
What earns a board its rating is the shape of its opening. Here that opening offers three single-line regions, a 1-square smallest color, a tightest row touched by 2 colors, and a region-size spread of 29. Lopsided grids with flat regions fall quickly; balanced ones like this take more patience.
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.
If #258 feels harder than its rating suggests, the usual culprit is incomplete marking rather than a difficult deduction. Check that every queen already on the grid has its full cross of eliminations recorded — including the diagonal neighbours, which are by far the easiest to miss. More stalled solves come from one forgotten diagonal X than from any genuinely deep chain of logic.
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 #258, start hunting for it near row 9.
As a sanity check rather than a spoiler: the finished solution to #258 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 #258?
Puzzle #258 is rated hard. Its smallest color region holds 1 square, its tightest row is touched by 2 colors, and three of its regions are confined to a single row or column, which gives you a forced move early.
Does 11x11 puzzle #258 have only one solution?
Yes. Every puzzle in the 11x11 collection, including #258, 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 #258?
Start with the red region — the most constrained color on this board, with 1 square spanning rows 6–6 and columns 5–5. Narrowing the smallest region first removes the most squares elsewhere on the grid.