11x11 Queens Puzzle #278
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 16-step reasoning is written out below.
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Step-by-step solution for puzzle #278
What follows is a complete solve of puzzle #278, worked the way a person works it rather than the way a computer does. It runs to 16 deductions — 11 queen placements and 5 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.
Show the full walkthrough (10 steps) — contains the solution
Step 1. Only row 1, column 8 is still open in indigo, and since each colour must take a queen, that settles it. That clears row 1, column 8, the rest of the indigo region and every square adjacent to it — diagonals included.
Step 2. Amber is down to 3 candidates in rows 2 and 3, columns 7, 10, and 11, and they overlap enough to cover 3 squares elsewhere. Cross those out without deciding anything about amber itself.
Step 3. 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 9; amber has one square left, so its queen takes row 2, column 11; slate has one square left, so its queen takes row 5, column 7; mint has one square left, so its queen takes row 4, column 1. 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 1.
The board after step 3 — 5 of 11 queens placed. Step 4. Wherever red 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 5. The pale yellow region is down to one open square, at row 7, column 2. Every colour holds exactly one queen, so that square is forced. Row 7 and column 2 are now spoken for, along with the squares touching that queen.
Step 6. Only row 10, column 3 is still open in sea green, and since each colour must take a queen, that settles it. That clears row 10, column 3, the rest of the sea green region and every square adjacent to it — diagonals included.
Step 7. All of the red region's remaining squares (2 open squares) lie in row 6. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 1 square come off.
The board after step 7 — 7 of 11 queens placed. Step 8. Khaki is down to 2 candidates in rows 8 and 9, columns 4 and 5, and they overlap enough to cover 2 squares elsewhere. Cross those out without deciding anything about khaki itself.
Step 9. The orange region has 2 squares left, spread across rows 9 and 11, columns 5 and 6. You do not need to know which of them takes the queen: every one of those options attacks the same 2 squares, so they can be crossed out now.
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: khaki has one square left, so its queen takes row 8, column 4; red has one square left, so its queen takes row 6, column 5; orange has one square left, so its queen takes row 9, column 6; teal has one square left, so its queen takes row 11, 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 11, column 10.
The board after step 10 — 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 #278
Board #278 of the 11x11 bank carries a medium rating. Its 121 squares are shared between eleven colored regions, and the solution places eleven queens: one per row, one per column, one per region, none of them side by side or corner to corner.
As with every puzzle in this collection, #278 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 #278 are: indigo (1 square), blue (4 squares), pale yellow (6 squares), sea green (6 squares), mint (7 squares), slate (8 squares), amber (11 squares), khaki (12 squares), teal (12 squares), orange (25 squares), red (29 squares). An even split would hand every color 11 squares, so the indigo region is running 10 squares under that average while the red region is the roomiest area on the grid with 29 squares.
That imbalance is the first thing to read, because every region takes exactly one queen regardless of how much space it owns. Indigo has only 1 place to put its queen; red has 29. The spread between them on this board is 28 squares, and the wider that spread runs, the more it pays to solve from the small end inward.
Square count is only half the story — how a color is arranged counts too. Indigo is the tidiest shape on #278, packing 100% of its 1×1 bounding box, whereas khaki straggles across its 5×5 box at just 48%. Tidy blocks are easy to work around; scattered ones touch more lines and resist resolution.
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.
Indigo occupies 1 square within rows 1–1, columns 8–8. It never leaves row 1, so its queen is locked to that row.
Blue: 4 squares across rows 3–3, columns 8–11. It never leaves row 3, so its queen is locked to that row.
Pale yellow covers 6 squares, spanning 4 rows and 2 columns (rows 6–9, columns 1–2).
Sea green occupies 6 squares within rows 9–11, columns 1–3.
Mint: 7 squares across rows 1–5, columns 1–2.
Slate covers 8 squares, spanning 2 rows and 5 columns (rows 4–5, columns 7–11).
Amber occupies 11 squares within rows 1–3, columns 6–11.
Khaki: 12 squares across rows 7–11, columns 2–6.
Teal covers 12 squares, spanning 4 rows and 6 columns (rows 8–11, columns 6–11).
Orange occupies 25 squares within rows 5–11, columns 5–11.
Red: 29 squares across rows 1–7, columns 2–7.
Where to start on this board
Begin where the choices are fewest. On this board that means indigo, which owns just 1 square inside a 1×1 window running from row 1 to row 1 and column 8 to column 8. A queen is guaranteed somewhere in there, so every line that window crosses is under pressure from the very first move.
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. Blue and slate 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 #278
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 2, 4 and 6 are the narrowest, touched by only 3 colors. Column 4 is the tightest column, with 2 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 9 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.
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.
Say the reason out loud: "this region has one square left", "this column has one square left". If no such sentence is available, the eliminating is not finished. One more pass of X marks is almost always quicker than committing to a placement you cannot defend.
Why puzzle #278 is rated medium
Ratings track how generous the opening is. On #278 you get three regions pinned to a single row or column, a smallest color of 1 square, a tightest row crossed by 3 colors, and a 28-square gap between the largest and smallest regions. Those four numbers largely explain the medium label.
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.
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.
One pattern is worth learning at every size, and it is available here. When two regions can only fit inside the same two rows, they must take one row each — which locks every other region out of both. The same argument works for columns, and for any matching count: three regions sharing three rows, four sharing four. Spotting these pairings turns a slow grind into a quick cascade, and on #278 the place to look for one is around column 4.
A non-spoiling distribution check: solved, #278 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 #278?
Puzzle #278 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 #278 have only one solution?
Yes. Every puzzle in the 11x11 collection, including #278, 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 #278?
Start with the indigo region — the most constrained color on this board, with 1 square spanning rows 1–1 and columns 8–8. Narrowing the smallest region first removes the most squares elsewhere on the grid.