11x11 Queens Puzzle #189
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 20-step reasoning is written out below.
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Step-by-step solution for puzzle #189
What follows is a complete solve of puzzle #189, worked the way a person works it rather than the way a computer does. It runs to 20 deductions — 11 queen placements and 9 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 rows.
Techniques this board needs: last square in a region, region confined to one line, region shadow, pairing argument on rows, line confined to one region, last square in a row, last square in a column.
Show the full walkthrough (12 steps) — contains the solution
Step 1. Only row 2, column 11 is still open in amber, and since each colour must take a queen, that settles it. That clears row 2, column 11, the rest of the amber region and every square adjacent to it — diagonals included.
Step 2. The red region is down to one open square, at row 6, column 9. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 6 and column 9, the remaining red squares, and the ring of neighbours around row 6, column 9.
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: 6 squares in all.
Step 4. All of the pale yellow region's remaining squares (2 open squares) lie in row 7. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 6 squares come off.
The board after step 4 — 2 of 11 queens placed. Step 5. Khaki is down to 3 candidates in rows 8 and 9, columns 7 and 8, and they overlap enough to cover 2 squares elsewhere. Cross those out without deciding anything about khaki itself.
Step 6. The sea green region has 3 squares left, spread across rows 10 and 11, 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. Teal cannot leave column 5 — every one of its open squares (2 open squares) sits there. That column belongs to teal, so every square in it owned by another colour is dead: 9 squares in all.
Step 8. Here is the pairing argument. The sea green and teal regions have no open squares outside rows 10 and 11 — 2 colours confined to 2 rows. Between them they must take one row each, in some order, so every other colour is shut out of all of them: 8 squares come off in one stroke.
The board after step 8 — 2 of 11 queens placed. Step 9. Column 10 has only mint squares left (3 open squares). The column needs a queen and only mint can provide one, which pins that colour to this column and kills its squares elsewhere: 3 squares.
Step 10. Every open square left in row 3 (4 open squares) belongs to the blue region. Since that row must contain a queen, blue is the colour that supplies it — so blue squares anywhere else on the board are out, 8 squares in all.
Step 11. Row 5 has only slate squares left (2 open squares). The row needs a queen and only slate can provide one, which pins that colour to this row and kills its squares elsewhere: 3 squares.
Step 12. 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: row 4 is down to one square, putting a queen on row 4, column 10; column 8 is down to one square, putting a queen on row 8, column 8; column 7 is down to one square, putting a queen on row 5, column 7; column 6 is down to one square, putting a queen on row 9, column 6; teal has one square left, so its queen takes row 11, column 5; sea green has one square left, so its queen takes row 10, column 1; pale yellow has one square left, so its queen takes row 7, column 3; indigo has one square left, so its queen takes row 1, column 2; blue has one square left, so its queen takes row 3, column 4. 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 3, column 4.
The board after step 12 — 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 #189
Puzzle #189 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.
Puzzle #189 has been checked to admit exactly one arrangement of queens, and every step toward it is deducible from what is already on the board. There is no point at which you are expected to pick a square and hope. The only thing that differs between boards is how quickly the first certainty surfaces, and that depends entirely on the shapes the colors happen to take here.
How the colors divide this board
From smallest to largest, the regions on puzzle #189 are: amber (1 square), red (1 square), teal (2 squares), sea green (3 squares), indigo (4 squares), pale yellow (6 squares), khaki (7 squares), slate (9 squares), blue (24 squares), mint (29 squares), orange (35 squares). An even split would hand every color 11 squares, so the amber region is running 10 squares under that average while the orange region is the roomiest area on the grid with 35 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 amber, with 1 square, is under far more pressure than orange with 35. A 34-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 2×2 box that encloses it, while mint is the most scattered at 54% of its 9×6 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
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.
Amber: 1 square across rows 2–2, columns 11–11. It never leaves row 2, so its queen is locked to that row.
Red covers 1 square, spanning 1 row and 1 column (rows 6–6, columns 9–9). It never leaves row 6, so its queen is locked to that row.
Teal occupies 2 squares within rows 10–11, columns 5–5. It sits wholly inside column 5, so its queen must be in that column.
Sea green: 3 squares across rows 10–11, columns 1–2.
Indigo covers 4 squares, spanning 2 rows and 2 columns (rows 1–2, columns 2–3).
Pale yellow occupies 6 squares within rows 6–7, columns 1–4.
Khaki: 7 squares across rows 7–9, columns 5–8.
Slate covers 9 squares, spanning 3 rows and 4 columns (rows 4–6, columns 6–9).
Blue occupies 24 squares within rows 1–6, columns 1–6.
Mint: 29 squares across rows 1–9, columns 6–11.
Orange covers 35 squares, spanning 5 rows and 11 columns (rows 7–11, columns 1–11).
Where to start on this board
Amber is the natural opening on #189: it is the smallest region on the grid at 1 square, boxed into rows 2–2 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 amber never leaves row 2, its queen must be in that row — and that instantly settles row 2 for everyone else. Sweep along it and X out every square that is not amber. 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, indigo, pale yellow and sea green 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 #189
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 10 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 6 sits at the far end with 5 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 #189 is rated easy
Ratings track how generous the opening is. On #189 you get five regions pinned to a single row or column, a smallest color of 1 square, a tightest row crossed by 2 colors, and a 34-square gap between the largest and smallest regions. Those four numbers largely explain the easy label.
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.
When a board plays tougher than its label, look for a missed mark before you look for a clever deduction. Walk back over every queen you have placed and confirm the full row, the full column and all eight surrounding squares are crossed out. The diagonal neighbours are the ones players skip, and a single skipped diagonal will hide the next forced move indefinitely.
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 #189, start hunting for it near row 3.
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 #189?
Puzzle #189 is rated easy. 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 #189 have only one solution?
Yes. Every puzzle in the 11x11 collection, including #189, 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 #189?
Start with the amber region — the most constrained color on this board, with 1 square spanning rows 2–2 and columns 11–11. Narrowing the smallest region first removes the most squares elsewhere on the grid.