11x11 Queens Puzzle #297
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 16-step reasoning is written out below.
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Step-by-step solution for puzzle #297
What follows is a complete solve of puzzle #297, worked the way a person works it rather than the way a computer does. It runs to 16 deductions — 11 queen placements and 5 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 line confined to one region.
Techniques this board needs: last square in a region, region confined to one line, region shadow, line confined to one region, last square in a row.
Show the full walkthrough (8 steps) — contains the solution
Step 1. The board opens by cascading. Each of these placements is forced the moment the one before it is marked, so the whole run is really a single sweep repeated: indigo has one square left, so its queen takes row 1, column 11; red has one square left, so its queen takes row 6, column 2; pale yellow has one square left, so its queen takes row 7, column 10; khaki has one square left, so its queen takes row 8, column 7; teal has one square left, so its queen takes row 11, column 3. 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 11, column 3.
Step 2. All of the amber region's remaining squares (2 open squares) lie in row 2. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 6 squares come off.
Step 3. Only row 3, column 9 is still open in blue, and since each colour must take a queen, that settles it. Everything else in row 3, in column 9, in blue and in the ring around that square is now dead.
Step 4. Slate is down to 3 candidates in rows 5 and 9, columns 4 and 5, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about slate itself.
The board after step 4 — 6 of 11 queens placed. Step 5. Orange cannot leave column 1 — every one of its open squares (2 open squares) sits there. That column belongs to orange, so every square in it owned by another colour is dead: 1 square in all.
Step 6. 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 7. Row 4 has only mint squares left (2 open squares). The row needs a queen and only mint can provide one, which pins that colour to this row and kills its squares elsewhere: 2 squares.
Step 8. From here the board cascades. Keep alternating the region sweep and the line sweep and 5 queens fall out in order without any new idea being needed: row 5 is down to one square, putting a queen on row 5, column 4; mint has one square left, so its queen takes row 4, column 6; amber has one square left, so its queen takes row 2, column 5; sea green has one square left, so its queen takes row 10, column 8; 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 8 — 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 #297
Puzzle #297 is one of the easy-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.
There is exactly one way to finish #297, and it has been verified. More importantly, you can reach it without ever gambling: at every stage some square is provably right or provably wrong. Boards differ only in how deep you must dig before that proof appears, and the geometry of these eleven regions is what sets the depth.
How the colors divide this board
From smallest to largest, the regions on puzzle #297 are: indigo (1 square), red (1 square), teal (4 squares), pale yellow (6 squares), amber (7 squares), khaki (7 squares), orange (9 squares), blue (12 squares), slate (16 squares), sea green (26 squares), mint (32 squares). An even split would hand every color 11 squares, so the indigo region is running 10 squares under that average while the mint region is the roomiest area on the grid with 32 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 indigo, with 1 square, is under far more pressure than mint with 32. A 31-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 #297, packing 100% of its 1×1 bounding box, whereas orange straggles across its 6×3 box at just 50%. 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.
Indigo: 1 square across rows 1–1, columns 11–11. It never leaves row 1, so its queen is locked to that row.
Red covers 1 square, spanning 1 row and 1 column (rows 6–6, columns 2–2). It never leaves row 6, so its queen is locked to that row.
Teal occupies 4 squares within rows 9–11, columns 2–3.
Pale yellow: 6 squares across rows 5–8, columns 10–11.
Amber covers 7 squares, spanning 2 rows and 5 columns (rows 1–2, columns 3–7).
Khaki occupies 7 squares within rows 7–8, columns 6–10.
Orange: 9 squares across rows 6–11, columns 1–3.
Blue covers 12 squares, spanning 5 rows and 4 columns (rows 1–5, columns 8–11).
Slate occupies 16 squares within rows 4–9, columns 2–6.
Sea green: 26 squares across rows 8–11, columns 3–11.
Mint covers 32 squares, spanning 6 rows and 9 columns (rows 1–6, columns 1–9).
Where to start on this board
Indigo is the natural opening on #297: it is the smallest region on the grid at 1 square, boxed into rows 1–1 and columns 11–11. 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 indigo never leaves row 1, its queen must be in that row — and that instantly settles row 1 for everyone else. Sweep along it and X out every square that is not indigo. 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. Red, amber and khaki 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 #297
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. Column 1 is the tightest column, with 2 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 8 is the crowded extreme at 5 colors — worth revisiting later, not now.
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.
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.
Resist the plausible-looking queen. On #297 every correct placement has a stated reason behind it, and any move you cannot justify is a guess wearing a disguise. Backing out of a wrong guess on a single-solution board takes far longer than finding the real deduction would have.
Why puzzle #297 is rated easy
Ratings track how generous the opening is. On #297 you get four regions pinned to a single row or column, a smallest color of 1 square, a tightest row crossed by 2 colors, and a 31-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.
Stuck on #297 despite the easy rating? The odds strongly favour a bookkeeping error over a hard chain of logic. Re-check each placed queen for its complete set of eliminations, paying particular attention to the four diagonal squares — those are the ones that get overlooked, and one of them is usually sitting on the answer.
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 #297, start hunting for it near row 3.
A non-spoiling distribution check: solved, #297 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 #297?
Puzzle #297 is rated easy. Its smallest color region holds 1 square, its tightest row is touched by 2 colors, and four of its regions are confined to a single row or column, which gives you a forced move early.
Does 11x11 puzzle #297 have only one solution?
Yes. Every puzzle in the 11x11 collection, including #297, 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 #297?
Start with the indigo region — the most constrained color on this board, with 1 square spanning rows 1–1 and columns 11–11. Narrowing the smallest region first removes the most squares elsewhere on the grid.