11x11 Queens Puzzle #253
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 #253
What follows is a complete solve of puzzle #253, 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 proof by contradiction.
Techniques this board needs: last square in a region, region shadow, region confined to one line, pairing argument on rows, proof by contradiction, line confined to one region, last square in a column.
Show the full walkthrough (13 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. Indigo is down to 3 candidates in rows 1 and 2, columns 1 and 2, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about indigo itself.
Step 3. The blue region has 4 squares left, spread across rows 1–3, columns 2–4. 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. All of the khaki region's remaining squares (2 open squares) lie in row 8. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 12 squares come off.
The board after step 4 — 1 of 11 queens placed. Step 5. Sea green cannot leave row 10 — every one of its open squares (3 open squares) sits there. That row belongs to sea green, so every square on it owned by another colour is dead: 5 squares in all.
Step 6. Here is the pairing argument. The indigo, amber, blue, and mint regions have no open squares outside rows 1–4 — 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: 11 squares come off in one stroke.
Step 7. Test row 1, column 2 for indigo: place a queen there, run the forced consequences through, and the slate region is left with nowhere to put its queen. The assumption breaks, so the square is eliminated.
Step 8. All of the indigo 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: 4 squares come off.
Step 9. Test row 2, column 1 for indigo: place a queen there, run the forced consequences through, and column 11 runs out of open squares entirely. The assumption breaks, so the square is eliminated.
The board after step 9 — 1 of 11 queens placed. Step 10. The indigo region is down to one open square, at row 1, column 1. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 1 and column 1, the remaining indigo squares, and the ring of neighbours around row 1, column 1.
Step 11. Blue is down to 3 candidates in rows 2 and 3, columns 2–4, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about blue itself.
Step 12. Every open square left in column 10 (4 open squares) belongs to the orange region. Since that column must contain a queen, orange is the colour that supplies it — so orange squares anywhere else on the board are out, 4 squares in all.
Step 13. From here the board cascades. Keep alternating the region sweep and the line sweep and 9 queens fall out in order without any new idea being needed: column 11 is down to one square, putting a queen on row 2, column 11; blue has one square left, so its queen takes row 3, column 2; mint has one square left, so its queen takes row 4, column 5; pale yellow has one square left, so its queen takes row 7, column 4; slate has one square left, so its queen takes row 5, column 3; 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 8; red has one square left, so its queen takes row 6, column 6; orange has one square left, so its queen takes row 9, column 10. 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 10.
The board after step 13 — 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 #253
Puzzle #253 is one of the hard-rated boards in the 11x11 set. Eleven colors divide its 121 squares, and you win by placing eleven queens so that each row, each column and each color holds exactly one, with no two queens adjacent in any direction.
As with every puzzle in this collection, #253 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 #253 are: teal (1 square), khaki (2 squares), indigo (3 squares), blue (5 squares), sea green (9 squares), mint (10 squares), amber (14 squares), pale yellow (16 squares), slate (17 squares), red (20 squares), orange (24 squares). An even split would hand every color 11 squares, so the teal region is running 10 squares under that average while the orange region is the roomiest area on the grid with 24 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 teal, with 1 square, is under far more pressure than orange with 24. A 23-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. Khaki is the tidiest shape on #253, packing 100% of its 1×2 bounding box, whereas red straggles across its 7×7 box at just 41%. Tidy blocks are easy to work around; scattered ones touch more lines and resist resolution.
Region by region
Here is the full footprint of every color on puzzle #253, smallest first. Reading these spans before you place anything is the quickest way to see which parts of the grid are genuinely contested.
Teal covers 1 square, spanning 1 row and 1 column (rows 11–11, columns 9–9). It never leaves row 11, so its queen is locked to that row.
Khaki occupies 2 squares within rows 8–8, columns 7–8. It never leaves row 8, so its queen is locked to that row.
Indigo: 3 squares across rows 1–2, columns 1–2.
Blue covers 5 squares, spanning 3 rows and 3 columns (rows 1–3, columns 2–4).
Sea green occupies 9 squares within rows 9–11, columns 4–8.
Mint: 10 squares across rows 1–4, columns 4–7.
Amber covers 14 squares, spanning 4 rows and 6 columns (rows 1–4, columns 6–11).
Pale yellow occupies 16 squares within rows 7–11, columns 1–4.
Slate: 17 squares across rows 3–7, columns 1–5.
Red covers 20 squares, spanning 7 rows and 7 columns (rows 4–10, columns 3–9).
Orange occupies 24 squares within rows 2–11, columns 9–11.
Where to start on this board
Teal is the natural opening on #253: it is the smallest region on the grid at 1 square, boxed into rows 11–11 and columns 9–9. Since one of those squares must hold a queen, that block of 1 row and 1 column is the most contested part of the board.
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. Khaki and indigo 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 #253
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 5 and 6 are the narrowest, touched by only 3 colors. Columns 10 and 11 are the tightest columns, with 2 colors.
A line with few colors is a line close to resolving. Where only 3 colors appear, one of them owns the row outright and the others must fit into the remaining 10 rows. Row 4 is the crowded extreme at 5 colors — worth revisiting later, not now.
Working through the middle game
Past the opening, treat this as an elimination exercise rather than a placement exercise. Each queen takes out a row, a column and its eight neighbours, and the value of a move is measured by how much it removes. Cross everything out as you go and let the board do the remembering.
Two checks, run alternately, will carry you through the 121 squares of this grid. First: has any of the eleven regions been reduced to a single open square? Second: has any row or column? Either answer forces a queen. Players who stall on 11x11 boards almost always run one of those checks and forget the other.
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 #253 is rated hard
The rating reflects how much the board concedes up front. Puzzle #253 has three regions confined to a single row or column, its smallest color holds 1 square, its tightest row meets just 3 colors, and the gap between its largest and smallest regions is 23 squares. Flat, lopsided boards open quickly; even, sprawling ones make you earn the first placement.
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 #253, start hunting for it near column 10.
A non-spoiling distribution check: solved, #253 carries 3 queens on the perimeter against 8 queens inside, 1 of them cornered. 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 #253?
Puzzle #253 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 #253 have only one solution?
Yes. Every puzzle in the 11x11 collection, including #253, 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 #253?
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.