11x11 Queens Puzzle #254
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 22-step reasoning is written out below.
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Step-by-step solution for puzzle #254
What follows is a complete solve of puzzle #254, worked the way a person works it rather than the way a computer does. It runs to 22 deductions — 11 queen placements and 11 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 columns.
Techniques this board needs: region shadow, region confined to one line, pairing argument on rows, pairing argument on columns, last square in a region, last square in a row.
Show the full walkthrough (17 steps) — contains the solution
Step 1. Wherever amber ends up among its 6 squares, the same squares fall within reach of it — 1 square in total, impossible regardless of how the colour resolves.
Step 2. All of the blue region's remaining squares (2 open squares) lie in row 3. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 13 squares come off.
Step 3. The indigo region has 3 squares left, spread across rows 1 and 2, columns 10 and 11. 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 slate ends up among its 6 squares, the same squares fall within reach of it — 1 square in total, impossible regardless of how the colour resolves.
The board after step 4 — 0 of 11 queens placed. Step 5. Khaki cannot leave row 8 — every one of its open squares (3 open squares) sits there. That row belongs to khaki, so every square on it owned by another colour is dead: 10 squares in all.
Step 6. The pale yellow region has 3 squares left, spread across rows 6 and 7, columns 1 and 2. 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 7. Wherever teal ends up among its 7 squares, the same squares fall within reach of it — 1 square in total, impossible regardless of how the colour resolves.
Step 8. Here is the pairing argument. The indigo, amber, mint, and slate regions have no open squares outside rows 1, 2, 4, and 5 — 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: 7 squares come off in one stroke.
Step 9. Indigo and sea green are now boxed into columns 10 and 11 and nothing else. That is 2 colours needing 2 columns, so they fill those columns between them — which locks every remaining colour out and removes 7 squares at once.
The board after step 9 — 0 of 11 queens placed. Step 10. The amber region is down to one open square, at row 2, column 9. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 2 and column 9, the remaining amber squares, and the ring of neighbours around row 2, column 9.
Step 11. Only row 1, column 11 is still open in indigo, and since each colour must take a queen, that settles it. Everything else in row 1, in column 11, in indigo and in the ring around that square is now dead.
Step 12. Here is the pairing argument. The blue and pale yellow regions have no open squares outside columns 1 and 2 — 2 colours confined to 2 columns. Between them they must take one column each, in some order, so every other colour is shut out of all of them: 9 squares come off in one stroke.
Step 13. 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: mint has one square left, so its queen takes row 4, column 3; blue has one square left, so its queen takes row 3, column 1; slate has one square left, so its queen takes row 5, column 8; pale yellow has one square left, so its queen takes row 7, column 2; khaki has one square left, so its queen takes row 8, column 4; orange has one square left, so its queen takes row 9, column 7. 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 7.
The board after step 13 — 8 of 11 queens placed. Step 14. Wherever teal 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 15. Row 11 has a single open square left, at column 6 in the teal region. Every row needs a queen, so this one is forced. Cross out the whole of row 11 and column 6, the remaining teal squares, and the ring of neighbours around row 11, column 6.
Step 16. 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 17. 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. Cross out the whole of row 10 and column 10, the remaining sea green squares, and the ring of neighbours around row 10, column 10.
The board after step 17 — 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 #254
Board #254 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.
Like every board on this site, #254 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 #254 are: blue (2 squares), khaki (3 squares), indigo (4 squares), pale yellow (5 squares), amber (6 squares), slate (7 squares), teal (8 squares), sea green (10 squares), orange (15 squares), mint (25 squares), red (36 squares). An even split would hand every color 11 squares, so the blue region is running 9 squares under that average while the red region is the roomiest area on the grid with 36 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 blue, with 2 squares, is under far more pressure than red with 36. A 34-square gap like this one rewards players who start where the choices are fewest.
Look at arrangement as well as area. Blue is the densest region on this grid at 100% of a 1×2 frame; teal is the loosest, occupying only 40% of its 4×5 frame. The loose one reaches into more rows and columns, which is exactly why it usually settles last.
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.
Blue occupies 2 squares within rows 3–3, columns 1–2. It never leaves row 3, so its queen is locked to that row.
Khaki: 3 squares across rows 8–8, columns 2–4. It never leaves row 8, so its queen is locked to that row.
Indigo covers 4 squares, spanning 3 rows and 2 columns (rows 1–3, columns 10–11).
Pale yellow occupies 5 squares within rows 6–8, columns 1–3.
Amber: 6 squares across rows 2–4, columns 8–11.
Slate covers 7 squares, spanning 2 rows and 5 columns (rows 4–5, columns 7–11).
Teal occupies 8 squares within rows 8–11, columns 4–8.
Sea green: 10 squares across rows 6–10, columns 9–11.
Orange covers 15 squares, spanning 5 rows and 5 columns (rows 7–11, columns 7–11).
Mint occupies 25 squares within rows 1–5, columns 1–10.
Red: 36 squares across rows 3–11, columns 1–9.
Where to start on this board
Begin where the choices are fewest. On this board that means blue, which owns just 2 squares inside a 1×2 window running from row 3 to row 3 and column 1 to column 2. A queen is guaranteed somewhere in there, so every line that window crosses is under pressure from the very first move.
Because blue never leaves row 3, its queen must be in that row — and that instantly settles row 3 for everyone else. Sweep along it and X out every square that is not blue. 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. Khaki and slate 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 #254
A quick way to find the next move is to count how many different colors touch each line. On this board, row 1 is the narrowest, touched by only 2 colors. Columns 5 and 6 are the tightest columns, with 3 colors.
Count colors per line and you have a ranking of where to look. The narrowest rows here see only 2 colors, so one of that handful must take the row and the rest are squeezed into the other 10 rows. Row 8 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
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.
The whole middle game reduces to two sweeps. Sweep the eleven colors looking for one with a single square left; sweep the eleven rows and eleven columns looking for the same. Each sweep feeds the next, and switching between them deliberately — rather than drifting — is what separates a fast 11x11 solve from a stalled one.
A placement without a reason is a guess. Because this board has exactly one solution, a guess that happens to be wrong will not announce itself for several moves — and unwinding it is slower than simply finishing the eliminations first.
Why puzzle #254 is rated medium
Ratings track how generous the opening is. On #254 you get two regions pinned to a single row or column, a smallest color of 2 squares, a tightest row crossed by 2 colors, and a 34-square gap between the largest and smallest regions. Those four numbers largely explain the medium 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.
If #254 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 #254, start hunting for it near row 1.
Use this as a rough check on your progress: the completed board has 3 queens around the border and 8 queens in the middle, including 1 in a corner. 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 #254?
Puzzle #254 is rated medium. Its smallest color region holds 2 squares, its tightest row is touched by 2 colors, and two of its regions are confined to a single row or column, which gives you a forced move early.
Does 11x11 puzzle #254 have only one solution?
Yes. Every puzzle in the 11x11 collection, including #254, 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 #254?
Start with the blue region — the most constrained color on this board, with 2 squares spanning rows 3–3 and columns 1–2. Narrowing the smallest region first removes the most squares elsewhere on the grid.