11x11 Queens Puzzle #223
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 19-step reasoning is written out below.
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Step-by-step solution for puzzle #223
What follows is a complete solve of puzzle #223, worked the way a person works it rather than the way a computer does. It runs to 19 deductions — 11 queen placements and 8 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 confined to one line, region shadow, proof by contradiction, last square in a row.
Show the full walkthrough (16 steps) — contains the solution
Step 1. Only row 4, column 6 is still open in mint, and since each colour must take a queen, that settles it. That clears row 4, column 6, the rest of the mint region and every square adjacent to it — diagonals included.
Step 2. The blue region is down to one open square, at row 3, column 4. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 3 and column 4, the remaining blue squares, and the ring of neighbours around row 3, column 4.
Step 3. Indigo cannot leave row 1 — every one of its open squares (2 open squares) sits there. That row belongs to indigo, so every square on it owned by another colour is dead: 7 squares in all.
Step 4. The amber region is down to one open square, at row 2, column 11. Every colour holds exactly one queen, so that square is forced. Row 2 and column 11 are now spoken for, along with the squares touching that queen.
Step 5. Sea green is down to 5 candidates in rows 10 and 11, columns 1–3, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about sea green itself.
The board after step 5 — 3 of 11 queens placed. Step 6. All of the teal region's remaining squares (2 open squares) lie in row 11. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 8 squares come off.
Step 7. Wherever pale yellow 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. The sea green region is down to one open square, at row 10, column 1. Every colour holds exactly one queen, so that square is forced. Row 10 and column 1 are now spoken for, along with the squares touching that queen.
Step 9. Pale yellow cannot leave column 3 — 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: 5 squares in all.
Step 10. The indigo region is down to one open square, at row 1, column 5. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 1 and column 5, the remaining indigo squares, and the ring of neighbours around row 1, column 5.
Step 11. Only row 6, column 7 is still open in red, and since each colour must take a queen, that settles it. Everything else in row 6, in column 7, in red and in the ring around that square is now dead.
The board after step 11 — 6 of 11 queens placed. Step 12. The orange region has 4 squares left, spread across rows 8 and 9, columns 8–10. 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 13. Test row 7, column 2 for slate: place a queen there, run the forced consequences through, and column 8 runs out of open squares entirely. The assumption breaks, so the square is eliminated.
Step 14. The slate region is down to one open square, at row 5, column 2. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 5 and column 2, the remaining slate squares, and the ring of neighbours around row 5, column 2.
Step 15. The khaki region has 3 squares left, spread across rows 7 and 8, columns 8–10. 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 16. From here the board cascades. Keep alternating the region sweep and the line sweep and 4 queens fall out in order without any new idea being needed: row 8 is down to one square, putting a queen on row 8, column 8; orange has one square left, so its queen takes row 9, column 10; pale yellow has one square left, so its queen takes row 7, column 3; teal has one square left, so its queen takes row 11, column 9. 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 9.
The board after step 16 — 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 #223
11x11 puzzle #223 is rated easy. Eleven colored regions cover its 121 squares, and your job is to seat eleven queens so that every row, column and color contains exactly one — with no queen touching another, including diagonally.
Like every board on this site, #223 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 #223 are: mint (1 square), teal (4 squares), blue (5 squares), sea green (5 squares), indigo (7 squares), amber (7 squares), red (11 squares), pale yellow (11 squares), orange (16 squares), slate (24 squares), khaki (30 squares). An even split would hand every color 11 squares, so the mint region is running 10 squares under that average while the khaki region is the roomiest area on the grid with 30 squares.
One queen per color, regardless of acreage: that is what turns this uneven split into a solving order. Mint is working with 1 square while khaki has 30 to spare, a gap of 29. Attack the cramped end and the roomy regions tend to resolve themselves.
Look at arrangement as well as area. Mint is the densest region on this grid at 100% of a 1×1 frame; pale yellow is the loosest, occupying only 55% of its 5×4 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.
Mint covers 1 square, spanning 1 row and 1 column (rows 4–4, columns 6–6). It never leaves row 4, so its queen is locked to that row.
Teal occupies 4 squares within rows 10–11, columns 9–11.
Blue: 5 squares across rows 3–4, columns 3–6.
Sea green covers 5 squares, spanning 2 rows and 3 columns (rows 10–11, columns 1–3).
Indigo occupies 7 squares within rows 1–2, columns 3–6.
Amber: 7 squares across rows 1–4, columns 9–11.
Red covers 11 squares, spanning 6 rows and 3 columns (rows 4–9, columns 5–7).
Pale yellow occupies 11 squares within rows 7–11, columns 2–5.
Orange: 16 squares across rows 8–11, columns 6–11.
Slate covers 24 squares, spanning 9 rows and 4 columns (rows 1–9, columns 1–4).
Khaki occupies 30 squares within rows 1–8, columns 7–11.
Where to start on this board
The most constrained color is where a solve should begin, and on #223 that is mint with 1 square. It reaches from row 4 to row 4 and from column 6 to column 6 — 1 row by 1 column. One queen has to live inside that footprint no matter what else happens, which makes those lines the busiest real estate on the board.
Because mint never leaves row 4, its queen must be in that row — and that instantly settles row 4 for everyone else. Sweep along it and X out every square that is not mint. 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, blue, sea green 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 #223
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 1 and 8 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 6 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.
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.
Resist the plausible-looking queen. On #223 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 #223 is rated easy
Ratings track how generous the opening is. On #223 you get two regions pinned to a single row or column, a smallest color of 1 square, a tightest row crossed by 3 colors, and a 29-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.
If #223 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.
Whatever the grid size, the pairing rule is the technique to internalise. When a pair of regions is boxed into the same pair of rows, they split those rows between them and nobody else may enter — and the same holds for columns, or for any n regions confined to n lines. Look for an instance of it around column 1 on this board.
A non-spoiling distribution check: solved, #223 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 #223?
Puzzle #223 is rated easy. Its smallest color region holds 1 square, its tightest row is touched by 3 colors, and two of its regions are confined to a single row or column, which gives you a forced move early.
Does 11x11 puzzle #223 have only one solution?
Yes. Every puzzle in the 11x11 collection, including #223, 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 #223?
Start with the mint region — the most constrained color on this board, with 1 square spanning rows 4–4 and columns 6–6. Narrowing the smallest region first removes the most squares elsewhere on the grid.