11x11 Queens Puzzle #239
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 15-step reasoning is written out below.
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Step-by-step solution for puzzle #239
What follows is a complete solve of puzzle #239, worked the way a person works it rather than the way a computer does. It runs to 15 deductions — 11 queen placements and 4 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 confined to one line, region shadow.
Show the full walkthrough (8 steps) — contains the solution
Step 1. Only row 11, column 5 is still open in teal, and since each colour must take a queen, that settles it. That clears row 11, column 5, the rest of the teal region and every square adjacent to it — diagonals included.
Step 2. The sea green region is down to one open square, at row 10, column 1. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 10 and column 1, the remaining sea green squares, and the ring of neighbours around row 10, column 1.
Step 3. Only row 9, column 11 is still open in orange, and since each colour must take a queen, that settles it. Everything else in row 9, in column 11, in orange and in the ring around that square is now dead.
Step 4. 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: 6 squares come off.
The board after step 4 — 3 of 11 queens placed. Step 5. Amber cannot leave row 2 — every one of its open squares (2 open squares) sits there. That row belongs to amber, so every square on it owned by another colour is dead: 8 squares in all.
Step 6. The blue region has 5 squares left, spread across rows 3 and 4, columns 2–4. 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. Pale yellow cannot leave column 2 — every one of its open squares (2 open squares) sits there. That column belongs to pale yellow, so every square in it owned by another colour is dead: 6 squares in all.
Step 8. 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: khaki has one square left, so its queen takes row 8, column 4; blue has one square left, so its queen takes row 3, column 3; pale yellow has one square left, so its queen takes row 7, column 2; red has one square left, so its queen takes row 6, column 6; amber has one square left, so its queen takes row 2, column 7; indigo has one square left, so its queen takes row 1, column 9; slate has one square left, so its queen takes row 5, column 10; mint has one square left, so its queen takes row 4, column 8. 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 8.
The board after step 8 — 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 #239
11x11 puzzle #239 is rated easy. Eleven colored regions cover its 121 squares, and your job is to seat eleven queens so that every row, column and color contains exactly one — with no queen touching another, including diagonally.
There is exactly one way to finish #239, and it has been verified. More importantly, you can reach it without ever gambling: at every stage some square is provably right or provably wrong. Boards differ only in how deep you must dig before that proof appears, and the geometry of these eleven regions is what sets the depth.
How the colors divide this board
From smallest to largest, the regions on puzzle #239 are: teal (1 square), indigo (3 squares), amber (4 squares), pale yellow (4 squares), sea green (5 squares), orange (6 squares), mint (13 squares), blue (17 squares), red (18 squares), khaki (21 squares), slate (29 squares). An even split would hand every color 11 squares, so the teal region is running 10 squares under that average while the slate region is the roomiest area on the grid with 29 squares.
One queen per color, regardless of acreage: that is what turns this uneven split into a solving order. Teal is working with 1 square while slate has 29 to spare, a gap of 28. Attack the cramped end and the roomy regions tend to resolve themselves.
Look at arrangement as well as area. Indigo is the densest region on this grid at 100% of a 1×3 frame; slate is the loosest, occupying only 48% of its 10×6 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.
Teal occupies 1 square within rows 11–11, columns 5–5. It never leaves row 11, so its queen is locked to that row.
Indigo: 3 squares across rows 1–1, columns 7–9. It never leaves row 1, so its queen is locked to that row.
Amber covers 4 squares, spanning 2 rows and 3 columns (rows 1–2, columns 6–8).
Pale yellow occupies 4 squares within rows 7–9, columns 1–2.
Sea green: 5 squares across rows 10–11, columns 1–4.
Orange covers 6 squares, spanning 3 rows and 3 columns (rows 9–11, columns 9–11).
Mint occupies 13 squares within rows 3–6, columns 6–10.
Blue: 17 squares across rows 1–4, columns 1–5.
Red covers 18 squares, spanning 5 rows and 6 columns (rows 3–7, columns 1–6).
Khaki occupies 21 squares within rows 7–11, columns 2–9.
Slate: 29 squares across rows 1–10, columns 6–11.
Where to start on this board
The most constrained color is where a solve should begin, and on #239 that is teal with 1 square. It reaches from row 11 to row 11 and from column 5 to column 5 — 1 row by 1 column. One queen has to live inside that footprint no matter what else happens, which makes those lines the busiest real estate on the board.
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, amber 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 #239
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 2, 5, 6 and 8 are the narrowest, touched by only 3 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 3 colors, so one of that handful must take the row and the rest are squeezed into the other 10 rows. Row 11 sits at the far end with 4 colors crossing it; it will almost certainly be among the last to settle.
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.
With eleven queens to seat and eleven regions competing over 121 squares, keep two questions in rotation. Does any region now have exactly one open square left? That queen is forced. Does any row or column now have exactly one open square left? That queen is forced too. Alternating between the region view and the row-and-column view is what keeps a solve moving, and it is the clearest difference between players who finish 11x11 boards quickly and players who stall halfway.
Resist the plausible-looking queen. On #239 every correct placement has a stated reason behind it, and any move you cannot justify is a guess wearing a disguise. Backing out of a wrong guess on a single-solution board takes far longer than finding the real deduction would have.
Why puzzle #239 is rated easy
The easy label comes out of four measurable things about #239: three of its regions are locked to one row or column, its smallest color spans 1 square, its least crowded row meets 3 colors, and its largest and smallest regions differ by 28. 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.
Stuck on #239 despite the easy rating? The odds strongly favour a bookkeeping error over a hard chain of logic. Re-check each placed queen for its complete set of eliminations, paying particular attention to the four diagonal squares — those are the ones that get overlooked, and one of them is usually sitting on the answer.
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.
Whatever the grid size, the pairing rule is the technique to internalise. When a pair of regions is boxed into the same pair of rows, they split those rows between them and nobody else may enter — and the same holds for columns, or for any n regions confined to n lines. Look for an instance of it around column 11 on this board.
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 #239?
Puzzle #239 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 #239 have only one solution?
Yes. Every puzzle in the 11x11 collection, including #239, 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 #239?
Start with the teal region — the most constrained color on this board, with 1 square spanning rows 11–11 and columns 5–5. Narrowing the smallest region first removes the most squares elsewhere on the grid.