11x11 Queens Puzzle #93
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 19-step reasoning is written out below.
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Step-by-step solution for puzzle #93
What follows is a complete solve of puzzle #93, 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 pairing argument on columns.
Techniques this board needs: last square in a region, region confined to one line, region shadow, pairing argument on rows, pairing argument on columns.
Show the full walkthrough (11 steps) — contains the solution
Step 1. Only row 1, column 10 is still open in indigo, and since each colour must take a queen, that settles it. That clears row 1, column 10, the rest of the indigo region and every square adjacent to it — diagonals included.
Step 2. All of the blue region's remaining squares (2 open squares) lie in column 11. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 7 squares come off.
Step 3. Only row 6, column 9 is still open in red, and since each colour must take a queen, that settles it. Everything else in row 6, in column 9, in red and in the ring around that square is now dead.
Step 4. All of the slate region's remaining squares (2 open squares) lie in row 5. 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. Sea green is down to 3 candidates in rows 10 and 11, columns 6 and 7, and they overlap enough to cover 3 squares elsewhere. Cross those out without deciding anything about sea green itself.
Step 6. All of the teal region's remaining squares (3 open squares) lie in row 11. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 5 squares come off.
Step 7. Sea green cannot leave row 10 — every one of its open squares (2 open squares) sits there. That row belongs to sea green, so every square on it owned by another colour is dead: 5 squares in all.
The board after step 7 — 2 of 11 queens placed. Step 8. Pale yellow is down to 4 candidates in rows 7–9, columns 1 and 2, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about pale yellow itself.
Step 9. Amber, blue, and mint are now boxed into rows 2–4 and nothing else. That is 3 colours needing 3 rows, so they fill those rows between them — which locks every remaining colour out and removes 4 squares at once.
Step 10. Here is the pairing argument. The slate, pale yellow, and teal regions have no open squares outside columns 1–3 — 3 colours confined to 3 columns. Between them they must take one column each, in some order, so every other colour is shut out of all of them: 12 squares come off in one stroke.
Step 11. 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: mint has one square left, so its queen takes row 4, column 4; blue has one square left, so its queen takes row 3, column 11; slate has one square left, so its queen takes row 5, column 1; pale yellow has one square left, so its queen takes row 7, column 2; orange has one square left, so its queen takes row 9, column 5; sea green has one square left, so its queen takes row 10, column 7; khaki has one square left, so its queen takes row 8, column 8; amber has one square left, so its queen takes row 2, column 6; 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.
The board after step 11 — 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 #93
Puzzle #93 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 #93, 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 #93 are: indigo (1 square), sea green (3 squares), teal (3 squares), slate (5 squares), pale yellow (6 squares), red (7 squares), blue (9 squares), mint (14 squares), orange (17 squares), amber (18 squares), khaki (38 squares). An even split would hand every color 11 squares, so the indigo region is running 10 squares under that average while the khaki region is the roomiest area on the grid with 38 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 khaki with 38. A 37-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 1×1 box that encloses it, while mint is the most scattered at 58% of its 6×4 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
Below is every color on #93 with its exact reach, smallest region first. It is worth a slow read: the spans reveal which rows and columns several regions are fighting over.
Indigo: 1 square across rows 1–1, columns 10–10. It never leaves row 1, so its queen is locked to that row.
Sea green covers 3 squares, spanning 2 rows and 2 columns (rows 10–11, columns 6–7).
Teal occupies 3 squares within rows 11–11, columns 1–3. It never leaves row 11, so its queen is locked to that row.
Slate: 5 squares across rows 5–6, columns 1–3.
Pale yellow covers 6 squares, spanning 4 rows and 2 columns (rows 7–10, columns 1–2).
Red occupies 7 squares within rows 5–7, columns 9–11.
Blue: 9 squares across rows 1–4, columns 9–11.
Mint covers 14 squares, spanning 6 rows and 4 columns (rows 1–6, columns 1–4).
Orange occupies 17 squares within rows 5–11, columns 2–5.
Amber: 18 squares across rows 1–4, columns 3–9.
Khaki covers 38 squares, spanning 9 rows and 7 columns (rows 3–11, columns 5–11).
Where to start on this board
Indigo is the natural opening on #93: it is the smallest region on the grid at 1 square, boxed into rows 1–1 and columns 10–10. 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. Teal, slate 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 #93
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 2, 8 and 9 are the narrowest, touched by only 3 colors. Column 8 is the tightest column, with 2 colors.
The fewer colors a line touches, the sooner it surrenders its queen. A row meeting just 3 colors has to be claimed by one of them, which pushes every remaining region into the other 10 rows. Row 6, meeting 5 colors, is the opposite case — the busiest line on #93 and the last one you should expect to crack.
Working through the middle game
The middle of #93 is where careless play costs time. Every queen you place kills a row, a column and the eight surrounding squares; if you do not mark all of that immediately, you will later "discover" a move that was available several turns ago. Mark first, then look.
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 #93 is rated medium
What earns a board its rating is the shape of its opening. Here that opening offers three single-line regions, a 1-square smallest color, a tightest row touched by 3 colors, and a region-size spread of 37. Lopsided grids with flat regions fall quickly; balanced ones like this take more patience.
The scale has nothing to do with maths or luck — every puzzle here is solvable by deduction and has exactly one answer. It measures reasoning depth: how many eliminations must stack up before a placement becomes provable. That depth is what separates a medium board from the rest.
Stuck on #93 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.
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 #93, start hunting for it near column 8.
Here is a shape check that gives nothing away: when #93 is solved, 4 queens sit on the outer edge of the grid and 7 sit inside it, and no queen lands in a corner. A work-in-progress board that clusters its queens in one quadrant while leaving others bare is usually carrying a mistake.
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 #93?
Puzzle #93 is rated medium. Its smallest color region holds 1 square, its tightest row is touched by 3 colors, and three of its regions are confined to a single row or column, which gives you a forced move early.
Does 11x11 puzzle #93 have only one solution?
Yes. Every puzzle in the 11x11 collection, including #93, 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 #93?
Start with the indigo region — the most constrained color on this board, with 1 square spanning rows 1–1 and columns 10–10. Narrowing the smallest region first removes the most squares elsewhere on the grid.