11x11 Queens Puzzle #247
Difficulty: hard. 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 #247
What follows is a complete solve of puzzle #247, 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 line confined to one region.
Techniques this board needs: region confined to one line, region shadow, last square in a region, line confined to one region, last square in a row.
Show the full walkthrough (12 steps) — contains the solution
Step 1. Indigo cannot leave row 1 — every one of its open squares (3 open squares) sits there. That row belongs to indigo, so every square on it owned by another colour is dead: 9 squares in all.
Step 2. Mint is down to 3 candidates in rows 4 and 5, columns 2 and 3, and they overlap enough to cover 3 squares elsewhere. Cross those out without deciding anything about mint itself.
Step 3. Red cannot leave column 1 — every one of its open squares (3 open squares) sits there. That column belongs to red, so every square in it owned by another colour is dead: 6 squares in all.
Step 4. All of the teal region's remaining squares (4 open squares) lie in column 2. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 5 squares come off.
The board after step 4 — 0 of 11 queens placed. Step 5. Only row 4, column 3 is still open in mint, and since each colour must take a queen, that settles it. That clears row 4, column 3, the rest of the mint region and every square adjacent to it — diagonals included.
Step 6. The blue region has 3 squares left, spread across rows 2 and 3, columns 10 and 11. 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 7. Wherever amber 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 8. All of the indigo region's remaining squares (2 open squares) lie in row 1. 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 8 — 1 of 11 queens placed. Step 9. Pale yellow cannot leave column 4 — 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: 7 squares in all.
Step 10. Wherever sea green ends up among its 4 squares, the same squares fall within reach of it — 1 square in total, impossible regardless of how the colour resolves.
Step 11. Row 9 has only orange squares left (7 open squares). The row needs a queen and only orange can provide one, which pins that colour to this row and kills its squares elsewhere: 25 squares.
Step 12. From here the board cascades. Keep alternating the region sweep and the line sweep and 10 queens fall out in order without any new idea being needed: row 10 is down to one square, putting a queen on row 10, column 5; row 11 is down to one square, putting a queen on row 11, column 2; row 8 is down to one square, putting a queen on row 8, column 10; blue has one square left, so its queen takes row 3, column 11; slate has one square left, so its queen takes row 5, column 7; indigo has one square left, so its queen takes row 1, column 6; red has one square left, so its queen takes row 6, column 1; pale yellow has one square left, so its queen takes row 7, column 4; orange has one square left, so its queen takes row 9, column 8; amber has one square left, so its queen takes row 2, 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 2, column 9.
The board after step 12 — 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 #247
11x11 puzzle #247 is rated hard. 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 #247, 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 #247 are: indigo (3 squares), mint (3 squares), red (4 squares), blue (5 squares), pale yellow (5 squares), khaki (8 squares), teal (9 squares), amber (11 squares), sea green (11 squares), slate (25 squares), orange (37 squares). An even split would hand every color 11 squares, so the indigo region is running 8 squares under that average while the orange region is the roomiest area on the grid with 37 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 3 places to put its queen; orange has 37. The spread between them on this board is 34 squares, and the wider that spread runs, the more it pays to solve from the small end inward.
Look at arrangement as well as area. Indigo is the densest region on this grid at 100% of a 1×3 frame; amber is the loosest, occupying only 55% 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
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 covers 3 squares, spanning 1 row and 3 columns (rows 1–1, columns 6–8). It never leaves row 1, so its queen is locked to that row.
Mint occupies 3 squares within rows 4–5, columns 2–3.
Red: 4 squares across rows 3–6, columns 1–1. It sits wholly inside column 1, so its queen must be in that column.
Blue covers 5 squares, spanning 3 rows and 2 columns (rows 2–4, columns 10–11).
Pale yellow occupies 5 squares within rows 6–8, columns 3–4.
Khaki: 8 squares across rows 5–8, columns 9–11.
Teal covers 9 squares, spanning 6 rows and 2 columns (rows 6–11, columns 1–2).
Amber occupies 11 squares within rows 1–4, columns 7–11.
Sea green: 11 squares across rows 9–11, columns 2–7.
Slate covers 25 squares, spanning 5 rows and 7 columns (rows 1–5, columns 1–7).
Orange occupies 37 squares within rows 5–11, columns 4–11.
Where to start on this board
The most constrained color is where a solve should begin, and on #247 that is indigo with 3 squares. It reaches from row 1 to row 1 and from column 6 to column 8 — 1 row by 3 columns. 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 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. Mint is no more than two rows tall, so its queen is 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 #247
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 1, 2, 9, 10 and 11 are the narrowest, touched by only 3 colors. Columns 1, 5, 8 and 9 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 6 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
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 #247 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 #247 is rated hard
Ratings track how generous the opening is. On #247 you get two regions pinned to a single row or column, a smallest color of 3 squares, a tightest row crossed by 3 colors, and a 34-square gap between the largest and smallest regions. Those four numbers largely explain the hard 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.
Stuck on #247 despite the hard 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.
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 #247 the place to look for one is around row 1.
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 #247?
Puzzle #247 is rated hard. Its smallest color region holds 3 squares, its tightest row is touched by 3 colors, and two of its regions are confined to a single row or column, which gives you a forced move early.
Does 11x11 puzzle #247 have only one solution?
Yes. Every puzzle in the 11x11 collection, including #247, 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 #247?
Start with the indigo region — the most constrained color on this board, with 3 squares spanning rows 1–1 and columns 6–8. Narrowing the smallest region first removes the most squares elsewhere on the grid.