11x11 Queens Puzzle #214
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 21-step reasoning is written out below.
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Step-by-step solution for puzzle #214
What follows is a complete solve of puzzle #214, worked the way a person works it rather than the way a computer does. It runs to 21 deductions — 11 queen placements and 10 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: region shadow, last square in a region, region confined to one line, pairing argument on rows, pairing argument on columns.
Show the full walkthrough (14 steps) — contains the solution
Step 1. Wherever indigo ends up among its 3 squares, the same squares fall within reach of it — 2 squares in total, impossible regardless of how the colour resolves.
Step 2. The blue region is down to one open square, at row 3, column 2. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 3 and column 2, the remaining blue squares, and the ring of neighbours around row 3, column 2.
Step 3. Only row 1, column 1 is still open in indigo, and since each colour must take a queen, that settles it. Everything else in row 1, in column 1, in indigo and in the ring around that square is now dead.
Step 4. The amber region is down to one open square, at row 2, column 5. Every colour holds exactly one queen, so that square is forced. Row 2 and column 5 are now spoken for, along with the squares touching that queen.
Step 5. Mint is down to 3 candidates in rows 4 and 5, columns 3 and 4, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about mint itself.
The board after step 5 — 3 of 11 queens placed. Step 6. The slate region has 5 squares left, spread across rows 4 and 5, columns 7–9. 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 7. Wherever pale yellow 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 8. All of the orange region's remaining squares (2 open squares) lie in row 9. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 10 squares come off.
Step 9. Mint and slate are now boxed into rows 4 and 5 and nothing else. That is 2 colours needing 2 rows, so they fill those rows between them — which locks every remaining colour out and removes 6 squares at once.
The board after step 9 — 3 of 11 queens placed. Step 10. Wherever red ends up among its 3 squares, the same squares fall within reach of it — 1 square in total, impossible regardless of how the colour resolves.
Step 11. Sea green and teal are now boxed into rows 10 and 11 and nothing else. That is 2 colours needing 2 rows, so they fill those rows between them — which locks every remaining colour out and removes 2 squares at once.
Step 12. Here is the pairing argument. The mint and pale yellow regions have no open squares outside columns 3 and 4 — 2 colours confined to 2 columns. Between them they must take one column each, in some order, so every other colour is shut out of all of them: 3 squares come off in one stroke.
Step 13. Red cannot leave column 6 — every one of its open squares (2 open squares) sits there. That column belongs to red, so every square in it owned by another colour is dead: 4 squares in all.
Step 14. From here the board cascades. Keep alternating the region sweep and the line sweep and 8 queens fall out in order without any new idea being needed: 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 9; 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 4; pale yellow has one square left, so its queen takes row 7, column 3; red has one square left, so its queen takes row 6, column 6; khaki has one square left, so its queen takes row 8, column 11; 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 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 #214
Board #214 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.
Like every board on this site, #214 has been verified to have exactly one valid solution, and that solution is reachable by deduction alone. You never have to guess and then unwind; every queen can be justified by something already visible on the grid. What changes from puzzle to puzzle is where the first certainty appears and how long the chain of reasoning runs before the next one — and that is entirely a product of how these particular colors are shaped.
How the colors divide this board
From smallest to largest, the regions on puzzle #214 are: blue (2 squares), orange (2 squares), indigo (3 squares), slate (5 squares), amber (8 squares), teal (10 squares), mint (15 squares), pale yellow (15 squares), sea green (15 squares), red (21 squares), khaki (25 squares). An even split would hand every color 11 squares, so the blue region is running 9 squares under that average while the khaki region is the roomiest area on the grid with 25 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 blue, with 2 squares, is under far more pressure than khaki with 25. A 23-square gap like this one rewards players who start where the choices are fewest.
Look at arrangement as well as area. Blue is the densest region on this grid at 100% of a 1×2 frame; red is the loosest, occupying only 39% of its 6×9 frame. The loose one reaches into more rows and columns, which is exactly why it usually settles last.
Region by region
Below is every color on #214 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.
Blue covers 2 squares, spanning 1 row and 2 columns (rows 3–3, columns 1–2). It never leaves row 3, so its queen is locked to that row.
Orange occupies 2 squares within rows 9–9, columns 8–9. It never leaves row 9, so its queen is locked to that row.
Indigo: 3 squares across rows 1–2, columns 1–2.
Slate covers 5 squares, spanning 2 rows and 3 columns (rows 4–5, columns 7–9).
Amber occupies 8 squares within rows 1–2, columns 5–11.
Teal: 10 squares across rows 9–11, columns 7–11.
Mint covers 15 squares, spanning 5 rows and 5 columns (rows 1–5, columns 1–5).
Pale yellow occupies 15 squares within rows 7–11, columns 1–4.
Sea green: 15 squares across rows 8–11, columns 3–8.
Red covers 21 squares, spanning 6 rows and 9 columns (rows 2–7, columns 1–9).
Khaki occupies 25 squares within rows 2–8, columns 6–11.
Where to start on this board
Begin where the choices are fewest. On this board that means blue, which owns just 2 squares inside a 1×2 window running from row 3 to row 3 and column 1 to column 2. A queen is guaranteed somewhere in there, so every line that window crosses is under pressure from the very first move.
Because blue never leaves row 3, its queen must be in that row — and that instantly settles row 3 for everyone else. Sweep along it and X out every square that is not blue. 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. Orange, indigo, amber 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 #214
A quick way to find the next move is to count how many different colors touch each line. On this board, row 6 is the narrowest, touched by only 2 colors. Columns 10 and 11 are the tightest columns, with 3 colors.
A line with few colors is a line close to resolving. Where only 2 colors appear, one of them owns the row outright and the others must fit into the remaining 10 rows. Row 2 is the crowded extreme at 5 colors — worth revisiting later, not now.
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 #214 is rated medium
What earns a board its rating is the shape of its opening. Here that opening offers two single-line regions, a 2-square smallest color, a tightest row touched by 2 colors, and a region-size spread of 23. Lopsided grids with flat regions fall quickly; balanced ones like this take more patience.
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.
If #214 feels harder than its rating suggests, the usual culprit is incomplete marking rather than a difficult deduction. Check that every queen already on the grid has its full cross of eliminations recorded — including the diagonal neighbours, which are by far the easiest to miss. More stalled solves come from one forgotten diagonal X than from any genuinely deep chain of logic.
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 #214, start hunting for it near row 6.
A non-spoiling distribution check: solved, #214 carries 3 queens on the perimeter against 8 queens inside, 1 of them cornered. 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 #214?
Puzzle #214 is rated medium. Its smallest color region holds 2 squares, its tightest row is touched by 2 colors, and two of its regions are confined to a single row or column, which gives you a forced move early.
Does 11x11 puzzle #214 have only one solution?
Yes. Every puzzle in the 11x11 collection, including #214, 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 #214?
Start with the blue region — the most constrained color on this board, with 2 squares spanning rows 3–3 and columns 1–2. Narrowing the smallest region first removes the most squares elsewhere on the grid.