11x11 Queens Puzzle #218
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 #218
What follows is a complete solve of puzzle #218, 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 rows.
Techniques this board needs: last square in a region, region confined to one line, region shadow, pairing argument on rows.
Show the full walkthrough (14 steps) — contains the solution
Step 1. Only row 1, column 11 is still open in indigo, and since each colour must take a queen, that settles it. That clears row 1, column 11, the rest of the indigo region and every square adjacent to it — diagonals included.
Step 2. The khaki region is down to one open square, at row 8, column 1. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 8 and column 1, the remaining khaki squares, and the ring of neighbours around row 8, column 1.
Step 3. Only row 6, column 2 is still open in red, and since each colour must take a queen, that settles it. Everything else in row 6, in column 2, in red and in the ring around that square is now dead.
Step 4. All of the mint region's remaining squares (2 open squares) lie in column 10. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 7 squares come off.
Step 5. Orange is down to 3 candidates in rows 9 and 11, columns 3 and 4, and they overlap enough to cover 2 squares elsewhere. Cross those out without deciding anything about orange itself.
The board after step 5 — 3 of 11 queens placed. Step 6. Here is the pairing argument. The orange, sea green, and teal regions have no open squares outside rows 9–11 — 3 colours confined to 3 rows. Between them they must take one row each, in some order, so every other colour is shut out of all of them: 2 squares come off in one stroke.
Step 7. Pale yellow cannot leave row 7 — every one of its open squares (4 open squares) sits there. That row belongs to pale yellow, so every square on it owned by another colour is dead: 2 squares in all.
Step 8. The slate region is down to one open square, at row 5, column 5. Every colour holds exactly one queen, so that square is forced. Row 5 and column 5 are now spoken for, along with the squares touching that queen.
Step 9. Only row 4, column 10 is still open in mint, and since each colour must take a queen, that settles it. That clears row 4, column 10, the rest of the mint region and every square adjacent to it — diagonals included.
The board after step 9 — 5 of 11 queens placed. Step 10. Wherever blue ends up among its 2 squares, the same squares fall within reach of it — 5 squares in total, impossible regardless of how the colour resolves.
Step 11. Teal is down to 2 candidates in rows 9 and 11, columns 4 and 6, and they overlap enough to cover 2 squares elsewhere. Cross those out without deciding anything about teal itself.
Step 12. All of the orange region's remaining squares (2 open squares) lie in column 3. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 2 squares come off.
Step 13. Amber cannot leave column 4 — every one of its open squares (2 open squares) sits there. That column belongs to amber, so every square in it owned by another colour is dead: 1 square in all.
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: teal has one square left, so its queen takes row 11, column 6; blue has one square left, so its queen takes row 3, column 8; amber has one square left, so its queen takes row 2, column 4; orange has one square left, so its queen takes row 9, column 3; sea green has one square left, so its queen takes row 10, column 9; pale yellow has one square left, so its queen takes row 7, column 7. 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 7.
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 #218
Board #218 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.
As with every puzzle in this collection, #218 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 #218 are: indigo (1 square), khaki (1 square), mint (3 squares), red (6 squares), slate (9 squares), teal (10 squares), orange (12 squares), pale yellow (16 squares), sea green (16 squares), blue (21 squares), amber (26 squares). An even split would hand every color 11 squares, so the indigo region is running 10 squares under that average while the amber region is the roomiest area on the grid with 26 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 amber with 26. A 25-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 1×1 frame; teal is the loosest, occupying only 50% of its 4×5 frame. The loose one reaches into more rows and columns, which is exactly why it usually settles last.
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 easy board.
Indigo occupies 1 square within rows 1–1, columns 11–11. It never leaves row 1, so its queen is locked to that row.
Khaki: 1 square across rows 8–8, columns 1–1. It never leaves row 8, so its queen is locked to that row.
Mint covers 3 squares, spanning 2 rows and 2 columns (rows 4–5, columns 10–11).
Red occupies 6 squares within rows 4–7, columns 1–2.
Slate: 9 squares across rows 5–8, columns 3–6.
Teal covers 10 squares, spanning 4 rows and 5 columns (rows 8–11, columns 3–7).
Orange occupies 12 squares within rows 7–11, columns 1–4.
Pale yellow: 16 squares across rows 6–9, columns 6–11.
Sea green covers 16 squares, spanning 4 rows and 6 columns (rows 8–11, columns 6–11).
Blue occupies 21 squares within rows 1–5, columns 6–11.
Amber: 26 squares across rows 1–5, columns 1–9.
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 11 to column 11. 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. Khaki and mint 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 #218
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 2 and 3 are the narrowest, touched by only 2 colors. Columns 2 and 5 are the tightest columns, with 3 colors.
Those lines matter because a row touched by few colors gives its queen away sooner. If a row meets only 2 colors, then one of those regions has to own it, and every other region is competing for the remaining 10 rows. By contrast row 8 meets 6 colors — the most crowded line here, and the one least likely to resolve early. Spend your attention accordingly.
Working through the middle game
Once two or three queens are down, the board changes character. Each queen removes an entire row, an entire column and the ring of up to eight squares around it, so the grid shrinks faster than most people expect. The habit that pays here is marking rather than remembering: after every placement, cross out the full row, the full column and all eight neighbours before hunting for the next move.
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.
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 #218 is rated easy
The easy label comes out of four measurable things about #218: four of its regions are locked to one row or column, its smallest color spans 1 square, 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.
Rating is a measure of chain length, not of chance. With one guaranteed solution and no guessing required, the only thing that changes across the collection is how many eliminations you must link together before a queen is provably forced.
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 #218, start hunting for it near row 2.
As a sanity check rather than a spoiler: the finished solution to #218 puts 3 queens on the outer border and 8 queens in the interior, 1 of them in an actual corner. If your part-finished grid has queens bunched into one area while whole stretches sit empty, something probably went wrong a few moves back.
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 #218?
Puzzle #218 is rated easy. Its smallest color region holds 1 square, its tightest row is touched by 2 colors, and four of its regions are confined to a single row or column, which gives you a forced move early.
Does 11x11 puzzle #218 have only one solution?
Yes. Every puzzle in the 11x11 collection, including #218, 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 #218?
Start with the indigo region — the most constrained color on this board, with 1 square spanning rows 1–1 and columns 11–11. Narrowing the smallest region first removes the most squares elsewhere on the grid.