11x11 Queens Puzzle #89
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 #89
What follows is a complete solve of puzzle #89, 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 shadow, region confined to one line, last square in a row.
Show the full walkthrough (14 steps) — contains the solution
Step 1. Only row 9, column 4 is still open in orange, and since each colour must take a queen, that settles it. That clears row 9, column 4, the rest of the orange region and every square adjacent to it — diagonals included.
Step 2. Khaki is down to 3 candidates in rows 7 and 8, columns 1 and 2, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about khaki itself.
Step 3. 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 4. The teal region is down to one open square, at row 11, column 3. Every colour holds exactly one queen, so that square is forced. Row 11 and column 3 are now spoken for, along with the squares touching that queen.
Step 5. Only row 10, column 1 is still open in sea green, and since each colour must take a queen, that settles it. That clears row 10, column 1, the rest of the sea green region and every square adjacent to it — diagonals included.
The board after step 5 — 3 of 11 queens placed. Step 6. The khaki region is down to one open square, at row 8, column 2. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 8 and column 2, the remaining khaki squares, and the ring of neighbours around row 8, column 2.
Step 7. Mint cannot leave column 5 — every one of its open squares (2 open squares) sits there. That column belongs to mint, so every square in it owned by another colour is dead: 7 squares in all.
Step 8. All of the pale yellow region's remaining squares (2 open squares) lie in column 6. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 5 squares come off.
Step 9. Indigo cannot leave column 7 — every one of its open squares (2 open squares) sits there. That column belongs to indigo, so every square in it owned by another colour is dead: 5 squares in all.
The board after step 9 — 4 of 11 queens placed. Step 10. 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: blue has one square left, so its queen takes row 3, column 8; indigo has one square left, so its queen takes row 1, column 7; amber has one square left, so its queen takes row 2, column 10; mint has one square left, so its queen takes row 4, column 5. 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 4, column 5.
Step 11. Slate is down to 2 candidates in rows 5 and 7, columns 9 and 11, and they overlap enough to cover 2 squares elsewhere. Cross those out without deciding anything about slate itself.
Step 12. Look along row 5: one square survives, row 5, column 11, which belongs to slate. A row cannot be left empty, so the queen goes there. That clears row 5, column 11, the rest of the slate region and every square adjacent to it — diagonals included.
Step 13. 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. Row 6 and column 9 are now spoken for, along with the squares touching that queen.
Step 14. Only row 7, column 6 is still open in pale yellow, and since each colour must take a queen, that settles it. That clears row 7, column 6, the rest of the pale yellow region and every square adjacent to it — diagonals included.
The board after step 14 — 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 #89
Puzzle #89 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.
There is exactly one way to finish #89, 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 #89 are: orange (1 square), sea green (3 squares), khaki (4 squares), indigo (7 squares), amber (7 squares), blue (8 squares), teal (8 squares), slate (13 squares), pale yellow (19 squares), red (23 squares), mint (28 squares). An even split would hand every color 11 squares, so the orange region is running 10 squares under that average while the mint region is the roomiest area on the grid with 28 squares.
Every color takes one queen and one only, whatever its size — which is why the 27 square difference between orange and mint is worth noting before you touch the grid. The cramped colors resolve first and hand you information; the roomy ones absorb whatever is left over at the end.
Shape matters as much as size. The orange region is the most compact color here, filling 100% of the 1×1 box that encloses it, while teal is the most scattered at 53% of its 3×5 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
Here is the full footprint of every color on puzzle #89, smallest first. Reading these spans before you place anything is the quickest way to see which parts of the grid are genuinely contested.
Orange occupies 1 square within rows 9–9, columns 4–4. It never leaves row 9, so its queen is locked to that row.
Sea green: 3 squares across rows 10–11, columns 1–2.
Khaki covers 4 squares, spanning 2 rows and 3 columns (rows 7–8, columns 1–3).
Indigo occupies 7 squares within rows 1–2, columns 4–7.
Amber: 7 squares across rows 1–2, columns 8–11.
Blue covers 8 squares, spanning 3 rows and 4 columns (rows 3–5, columns 5–8).
Teal occupies 8 squares within rows 9–11, columns 1–5.
Slate: 13 squares across rows 2–7, columns 8–11.
Pale yellow covers 19 squares, spanning 6 rows and 5 columns (rows 6–11, columns 4–8).
Red occupies 23 squares within rows 5–11, columns 7–11.
Mint: 28 squares across rows 1–7, columns 1–5.
Where to start on this board
Orange is the natural opening on #89: it is the smallest region on the grid at 1 square, boxed into rows 9–9 and columns 4–4. 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 orange never leaves row 9, its queen must be in that row — and that instantly settles row 9 for everyone else. Sweep along it and X out every square that is not orange. 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, amber, khaki 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 #89
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 1, 3, 4 and 8 are the narrowest, touched by only 3 colors. Columns 3, 6, 9, 10 and 11 are the tightest columns, with 3 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 7 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.
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.
The trap on a board like this is placing a queen that is merely plausible. Every placement should be traceable to an elimination you can point at. If you cannot name the rule that forced it, you are guessing — and on a single-solution grid a guess costs more to unwind than the deduction would have taken to find.
Why puzzle #89 is rated medium
The rating reflects how much the board concedes up front. Puzzle #89 has two 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 27 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.
Stuck on #89 despite the medium 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.
There is one technique that repays study at every grid size. Two regions restricted to the same two rows must occupy one row apiece, which excludes all other regions from those rows entirely; the identical logic applies to columns and to larger matched sets. It converts slow boards into fast ones, and the likeliest place to find it on #89 is row 1.
A non-spoiling distribution check: solved, #89 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 #89?
Puzzle #89 is rated medium. 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 #89 have only one solution?
Yes. Every puzzle in the 11x11 collection, including #89, 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 #89?
Start with the orange region — the most constrained color on this board, with 1 square spanning rows 9–9 and columns 4–4. Narrowing the smallest region first removes the most squares elsewhere on the grid.