11x11 Queens Puzzle #298
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 19-step reasoning is written out below.
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Step-by-step solution for puzzle #298
What follows is a complete solve of puzzle #298, 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, line confined to one region, last square in a row.
Show the full walkthrough (14 steps) — contains the solution
Step 1. Only row 11, column 1 is still open in teal, and since each colour must take a queen, that settles it. That clears row 11, column 1, the rest of the teal region and every square adjacent to it — diagonals included.
Step 2. All of the indigo region's remaining squares (3 open squares) lie in row 1. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 8 squares come off.
Step 3. The blue region has 3 squares left, spread across rows 3 and 4, columns 2 and 3. You do not need to know which of them takes the queen: every one of those options attacks the same 3 squares, so they can be crossed out now.
Step 4. Wherever khaki ends up among its 5 squares, the same squares fall within reach of it — 1 square in total, impossible regardless of how the colour resolves.
Step 5. Orange is down to 3 candidates in rows 9 and 10, columns 9 and 10, and they overlap enough to cover 2 squares elsewhere. Cross those out without deciding anything about orange itself.
The board after step 5 — 1 of 11 queens placed. Step 6. Here is the pairing argument. The pale yellow, khaki, orange, and sea green regions have no open squares outside rows 7–10 — 4 colours confined to 4 rows. Between them they must take one row each, in some order, so every other colour is shut out of all of them: 14 squares come off in one stroke.
Step 7. Only row 6, column 5 is still open in red, and since each colour must take a queen, that settles it. Everything else in row 6, in column 5, in red and in the ring around that square is now dead.
Step 8. Here is the pairing argument. The indigo, pale yellow, and orange regions have no open squares outside columns 9–11 — 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: 13 squares come off in one stroke.
Step 9. Row 7 has only pale yellow squares left (2 open squares). The row needs a queen and only pale yellow can provide one, which pins that colour to this row and kills its squares elsewhere: 3 squares.
The board after step 9 — 2 of 11 queens placed. Step 10. Row 8 has a single open square left, at column 3 in the khaki region. Every row needs a queen, so this one is forced. Row 8 and column 3 are now spoken for, along with the squares touching that queen.
Step 11. Only row 3, column 2 is still open in blue, and since each colour must take a queen, that settles it. Everything else in row 3, in column 2, in blue and in the ring around that square is now dead.
Step 12. The amber region is down to one open square, at row 2, column 4. Every colour holds exactly one queen, so that square is forced. Row 2 and column 4 are now spoken for, along with the squares touching that queen.
Step 13. Wherever mint ends up among its 2 squares, the same squares fall within reach of it — 2 squares in total, impossible regardless of how the colour resolves.
Step 14. From here the board cascades. Keep alternating the region sweep and the line sweep and 6 queens fall out in order without any new idea being needed: slate has one square left, so its queen takes row 5, column 8; mint has one square left, so its queen takes row 4, column 6; sea green has one square left, so its queen takes row 10, column 7; orange has one square left, so its queen takes row 9, column 10; pale yellow has one square left, so its queen takes row 7, column 11; indigo has one square left, so its queen takes row 1, column 9. 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 1, column 9.
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 #298
Board #298 of the 11x11 bank carries a easy 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.
Puzzle #298 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 #298 are: teal (1 square), indigo (3 squares), blue (3 squares), pale yellow (6 squares), orange (6 squares), khaki (12 squares), red (13 squares), sea green (14 squares), mint (16 squares), slate (23 squares), amber (24 squares). An even split would hand every color 11 squares, so the teal region is running 10 squares under that average while the amber region is the roomiest area on the grid with 24 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 1 square, is under far more pressure than amber with 24. A 23-square gap like this one rewards players who start where the choices are fewest.
Look at arrangement as well as area. Indigo is the densest region on this grid at 100% of a 1×3 frame; mint is the loosest, occupying only 44% of its 6×6 frame. The loose one reaches into more rows and columns, which is exactly why it usually settles last.
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.
Teal covers 1 square, spanning 1 row and 1 column (rows 11–11, columns 1–1). It never leaves row 11, so its queen is locked to that row.
Indigo occupies 3 squares within rows 1–1, columns 9–11. It never leaves row 1, so its queen is locked to that row.
Blue: 3 squares across rows 3–4, columns 2–3.
Pale yellow covers 6 squares, spanning 4 rows and 2 columns (rows 7–10, columns 10–11).
Orange occupies 6 squares within rows 9–11, columns 9–11.
Khaki: 12 squares across rows 8–11, columns 1–4.
Red covers 13 squares, spanning 4 rows and 6 columns (rows 6–9, columns 3–8).
Sea green occupies 14 squares within rows 7–11, columns 5–9.
Mint: 16 squares across rows 1–6, columns 3–8.
Slate covers 23 squares, spanning 6 rows and 5 columns (rows 2–7, columns 7–11).
Amber occupies 24 squares within rows 1–8, columns 1–6.
Where to start on this board
Begin where the choices are fewest. On this board that means teal, which owns just 1 square inside a 1×1 window running from row 11 to row 11 and column 1 to column 1. A queen is guaranteed somewhere in there, so every line that window crosses is under pressure from the very first move.
Because teal never leaves row 11, its queen must be in that row — and that instantly settles row 11 for everyone else. Sweep along it and X out every square that is not teal. 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 and blue 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 #298
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 1, 2 and 5 are the narrowest, touched by only 3 colors. Columns 1 and 2 are the tightest columns, with 3 colors.
Count colors per line and you have a ranking of where to look. The narrowest rows here see only 3 colors, so one of that handful must take the row and the rest are squeezed into the other 10 rows. Row 9 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
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 #298 is rated easy
Ratings track how generous the opening is. On #298 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 23-square gap between the largest and smallest regions. Those four numbers largely explain the easy label.
Nothing about the rating involves computation or chance. Each grid has a single solution reachable by pure logic; the rating simply measures how far ahead you have to reason. Easy boards resolve a queen every step or two, while hard ones can ask you to carry three unfinished lines of thought before any of them pays off.
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 #298, start hunting for it near row 1.
Use this as a rough check on your progress: the completed board has 3 queens around the border and 8 queens in the middle, including 1 in a corner. 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 #298?
Puzzle #298 is rated easy. 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 #298 have only one solution?
Yes. Every puzzle in the 11x11 collection, including #298, 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 #298?
Start with the teal region — the most constrained color on this board, with 1 square spanning rows 11–11 and columns 1–1. Narrowing the smallest region first removes the most squares elsewhere on the grid.