11x11 Queens Puzzle #293
Difficulty: hard. 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 #293
What follows is a complete solve of puzzle #293, 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 line confined to one region.
Techniques this board needs: region shadow, last square in a region, region confined to one line, line confined to one region, last square in a row.
Show the full walkthrough (11 steps) — contains the solution
Step 1. Wherever indigo ends up among its 4 squares, the same squares fall within reach of it — 2 squares in total, impossible regardless of how the colour resolves.
Step 2. Orange is down to 3 candidates in rows 9 and 10, columns 9 and 10, and they overlap enough to cover 3 squares elsewhere. Cross those out without deciding anything about orange itself.
Step 3. Only row 11, column 10 is still open in teal, and since each colour must take a queen, that settles it. Everything else in row 11, in column 10, in teal and in the ring around that square is now dead.
Step 4. The orange region is down to one open square, at row 9, column 9. Every colour holds exactly one queen, so that square is forced. Row 9 and column 9 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 10, column 6 is still open in sea green, and since each colour must take a queen, that settles it. That clears row 10, column 6, the rest of the sea green region and every square adjacent to it — diagonals included.
Step 6. All of the blue region's remaining squares (3 open squares) lie in column 11. 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 7 is still open in khaki, and since each colour must take a queen, that settles it. Everything else in row 8, in column 7, in khaki and in the ring around that square is now dead.
The board after step 7 — 4 of 11 queens placed. Step 8. All of the mint region's remaining squares (4 open squares) lie in column 8. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 2 squares come off.
Step 9. The red region has 4 squares left, spread across rows 5 and 6, columns 3–5. 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 10. Every open square left in row 7 (5 open squares) belongs to the pale yellow region. Since that row must contain a queen, pale yellow is the colour that supplies it — so pale yellow squares anywhere else on the board are out, 4 squares in all.
Step 11. From here the board cascades. Keep alternating the region sweep and the line sweep and 7 queens fall out in order without any new idea being needed: row 6 is down to one square, putting a queen on row 6, column 5; indigo has one square left, so its queen takes row 1, column 4; row 5 is down to one square, putting a queen on row 5, column 2; amber has one square left, so its queen takes row 2, column 1; blue has one square left, so its queen takes row 3, column 11; mint has one square left, so its queen takes row 4, column 8; pale yellow has one square left, so its queen takes row 7, 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 7, 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 #293
Puzzle #293 is one of the hard-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, #293 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 #293 are: teal (2 squares), orange (3 squares), indigo (4 squares), amber (6 squares), sea green (9 squares), blue (10 squares), mint (11 squares), red (11 squares), slate (15 squares), pale yellow (23 squares), khaki (27 squares). An even split would hand every color 11 squares, so the teal region is running 9 squares under that average while the khaki 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 teal, with 2 squares, is under far more pressure than khaki with 27. A 25-square gap like this one rewards players who start where the choices are fewest.
Shape matters as much as size. The teal region is the most compact color here, filling 100% of the 2×1 box that encloses it, while khaki is the most scattered at 42% of its 8×8 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 hard board.
Teal occupies 2 squares within rows 10–11, columns 10–10. It sits wholly inside column 10, so its queen must be in that column.
Orange: 3 squares across rows 9–10, columns 9–10.
Indigo covers 4 squares, spanning 2 rows and 3 columns (rows 1–2, columns 4–6).
Amber occupies 6 squares within rows 1–3, columns 1–3.
Sea green: 9 squares across rows 10–11, columns 3–9.
Blue covers 10 squares, spanning 4 rows and 3 columns (rows 1–4, columns 9–11).
Mint occupies 11 squares within rows 1–5, columns 6–9.
Red: 11 squares across rows 5–7, columns 3–8.
Slate covers 15 squares, spanning 4 rows and 7 columns (rows 2–5, columns 1–7).
Pale yellow occupies 23 squares within rows 5–11, columns 1–5.
Khaki: 27 squares across rows 4–11, columns 4–11.
Where to start on this board
Teal is the natural opening on #293: it is the smallest region on the grid at 2 squares, boxed into rows 10–11 and columns 10–10. Since one of those squares must hold a queen, that block of 2 rows and 1 column is the most contested part of the board.
Because teal stays inside column 10, its queen belongs to that column and no other region may use it. Cross out the rest of column 10 straight away. Any color that was relying on those squares now has a visibly smaller footprint, and that shrinkage is where your second deduction comes from.
Work outward to the other flat regions next. Indigo, orange 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 #293
A quick way to find the next move is to count how many different colors touch each line. On this board, row 8 is 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 10 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
After the first few queens the puzzle becomes bookkeeping. A placed queen wipes its row, its column and every square it touches — as many as eight neighbours — so the space collapses quickly. Record those eliminations on the board instead of carrying them in your head, and the next forced move tends to announce itself.
Keep alternating between two views of the board. In the region view you ask which of the eleven colors is down to one open square. In the line view you ask the same of each row and column. Both produce forced queens, and each placement refreshes the other view, so cycling between them deliberately is how a 11x11 board unwinds.
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 #293 is rated hard
The hard label comes out of four measurable things about #293: one of its regions is locked to one row or column, its smallest color spans 2 squares, its least crowded row meets 2 colors, and its largest and smallest regions differ by 25. Boards that score tight on those measures give up their first queen fast.
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 hard board from the rest.
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 #293, start hunting for it near row 8.
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 #293?
Puzzle #293 is rated hard. Its smallest color region holds 2 squares, its tightest row is touched by 2 colors, and one of its regions is confined to a single row or column, which gives you a forced move early.
Does 11x11 puzzle #293 have only one solution?
Yes. Every puzzle in the 11x11 collection, including #293, 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 #293?
Start with the teal region — the most constrained color on this board, with 2 squares spanning rows 10–11 and columns 10–10. Narrowing the smallest region first removes the most squares elsewhere on the grid.