11x11 Queens Puzzle #217
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 17-step reasoning is written out below.
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Step-by-step solution for puzzle #217
What follows is a complete solve of puzzle #217, 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 region shadow.
Techniques this board needs: last square in a region, region confined to one line, region shadow.
Show the full walkthrough (13 steps) — contains the solution
Step 1. Only row 4, column 9 is still open in mint, and since each colour must take a queen, that settles it. That clears row 4, column 9, the rest of the mint region and every square adjacent to it — diagonals included.
Step 2. All of the indigo region's remaining squares (2 open squares) lie in row 1. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 10 squares come off.
Step 3. Pale yellow cannot leave column 1 — every one of its open squares (4 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 4. The indigo region is down to one open square, at row 1, column 2. Every colour holds exactly one queen, so that square is forced. Row 1 and column 2 are now spoken for, along with the squares touching that queen.
The board after step 4 — 2 of 11 queens placed. Step 5. Only row 3, column 3 is still open in blue, and since each colour must take a queen, that settles it. That clears row 3, column 3, the rest of the blue region and every square adjacent to it — diagonals included.
Step 6. All of the slate region's remaining squares (2 open squares) lie in column 4. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 5 squares come off.
Step 7. Only row 8, column 5 is still open in khaki, and since each colour must take a queen, that settles it. Everything else in row 8, in column 5, in khaki and in the ring around that square is now dead.
Step 8. The slate region is down to one open square, at row 5, column 4. Every colour holds exactly one queen, so that square is forced. Row 5 and column 4 are now spoken for, along with the squares touching that queen.
Step 9. Red cannot leave row 6 — every one of its open squares (2 open squares) sits there. That row belongs to red, so every square on it owned by another colour is dead: 5 squares in all.
The board after step 9 — 5 of 11 queens placed. Step 10. The pale yellow region is down to one open square, at row 7, column 1. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 7 and column 1, the remaining pale yellow squares, and the ring of neighbours around row 7, column 1.
Step 11. Orange is down to 2 candidates in rows 9 and 10, columns 8 and 10, and they overlap enough to cover 4 squares elsewhere. Cross those out without deciding anything about orange itself.
Step 12. The sea green region has 3 squares left, spread across rows 10 and 11, 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 13. 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: orange has one square left, so its queen takes row 9, column 8; red has one square left, so its queen takes row 6, column 6; teal has one square left, so its queen takes row 11, column 7; sea green has one square left, so its queen takes row 10, column 11; amber has one square left, so its queen takes row 2, 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 2, 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 #217
Puzzle #217 is one of the medium-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, #217 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 #217 are: mint (1 square), indigo (2 squares), khaki (2 squares), pale yellow (4 squares), orange (5 squares), blue (9 squares), sea green (14 squares), slate (19 squares), red (19 squares), teal (19 squares), amber (27 squares). An even split would hand every color 11 squares, so the mint region is running 10 squares under that average while the amber region is the roomiest area on the grid with 27 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 mint, with 1 square, is under far more pressure than amber with 27. A 26-square gap like this one rewards players who start where the choices are fewest.
Shape matters as much as size. The indigo region is the most compact color here, filling 100% of the 1×2 box that encloses it, while slate is the most scattered at 42% of its 9×5 box. Compact regions are easy to eliminate around; straggling ones reach into more rows and columns and tend to stay unresolved until late.
Region by region
Each region's exact extent on this grid is listed below, starting with the most constrained. Knowing which lines a color can and cannot reach is most of the work on a medium board.
Mint covers 1 square, spanning 1 row and 1 column (rows 4–4, columns 9–9). It never leaves row 4, so its queen is locked to that row.
Indigo occupies 2 squares within rows 1–1, columns 1–2. It never leaves row 1, so its queen is locked to that row.
Khaki: 2 squares across rows 8–8, columns 4–5. It never leaves row 8, so its queen is locked to that row.
Pale yellow covers 4 squares, spanning 4 rows and 1 column (rows 5–8, columns 1–1). It sits wholly inside column 1, so its queen must be in that column.
Orange occupies 5 squares within rows 8–10, columns 8–10.
Blue: 9 squares across rows 2–6, columns 1–3.
Sea green covers 14 squares, spanning 7 rows and 3 columns (rows 5–11, columns 9–11).
Slate occupies 19 squares within rows 3–11, columns 1–5.
Red: 19 squares across rows 4–8, columns 4–9.
Teal covers 19 squares, spanning 6 rows and 6 columns (rows 6–11, columns 3–8).
Amber occupies 27 squares within rows 1–5, columns 3–11.
Where to start on this board
Mint is the natural opening on #217: it is the smallest region on the grid at 1 square, boxed into rows 4–4 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 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 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 #217
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 1 and 2 are the narrowest, touched by only 2 colors. Column 11 is the tightest column, with 2 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 7 colors crossing it; it will almost certainly be among the last to settle.
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.
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 #217 is rated medium
The medium label comes out of four measurable things about #217: five of its regions are locked to one row or column, its smallest color spans 1 square, its least crowded row meets 2 colors, and its largest and smallest regions differ by 26. Boards that score tight on those measures give up their first queen fast.
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.
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 #217, start hunting for it near row 1.
Use this as a rough check on your progress: the completed board has 4 queens around the border and 7 queens in the middle, and nothing in the corners. 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 #217?
Puzzle #217 is rated medium. Its smallest color region holds 1 square, its tightest row is touched by 2 colors, and five of its regions are confined to a single row or column, which gives you a forced move early.
Does 11x11 puzzle #217 have only one solution?
Yes. Every puzzle in the 11x11 collection, including #217, 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 #217?
Start with the mint region — the most constrained color on this board, with 1 square spanning rows 4–4 and columns 9–9. Narrowing the smallest region first removes the most squares elsewhere on the grid.