11x11 Queens Puzzle #3
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 18-step reasoning is written out below.
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Step-by-step solution for puzzle #3
What follows is a complete solve of puzzle #3, worked the way a person works it rather than the way a computer does. It runs to 18 deductions — 11 queen placements and 7 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: last square in a region, region confined to one line, region shadow, line confined to one region, last square in a column.
Show the full walkthrough (9 steps) — contains the solution
Step 1. Only row 6, column 4 is still open in red, and since each colour must take a queen, that settles it. That clears row 6, column 4, the rest of the red region and every square adjacent to it — diagonals included.
Step 2. 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: 10 squares come off.
Step 3. The pale yellow region has 5 squares left, spread across rows 7, 8, and 10, columns 2, 3, 5, and 6. 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.
The board after step 3 — 1 of 11 queens placed. Step 4. All of the khaki region's remaining squares (2 open squares) lie in column 9. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 11 squares come off.
Step 5. Teal cannot leave row 11 — every one of its open squares (4 open squares) sits there. That row belongs to teal, so every square on it owned by another colour is dead: 5 squares in all.
Step 6. The sea green region has 3 squares left, spread across rows 9 and 10, columns 8 and 10. 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.
The board after step 6 — 1 of 11 queens placed. Step 7. Wherever orange ends up among its 6 squares, the same squares fall within reach of it — 1 square in total, impossible regardless of how the colour resolves.
Step 8. Every open square left in column 11 (8 open squares) belongs to the mint region. Since that column must contain a queen, mint is the colour that supplies it — so mint squares anywhere else on the board are out, 9 squares in all.
Step 9. 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: column 10 is down to one square, putting a queen on row 10, column 10; pale yellow has one square left, so its queen takes row 7, column 6; indigo has one square left, so its queen takes row 1, column 5; khaki has one square left, so its queen takes row 8, column 9; orange has one square left, so its queen takes row 9, column 7; slate has one square left, so its queen takes row 5, column 2; teal has one square left, so its queen takes row 11, column 8; blue has one square left, so its queen takes row 3, column 3; amber has one square left, so its queen takes row 2, column 1; mint has one square left, so its queen takes row 4, column 11. 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 11.
The board after step 9 — 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 #3
11x11 puzzle #3 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.
Puzzle #3 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 #3 are: red (1 square), indigo (2 squares), khaki (4 squares), amber (6 squares), sea green (7 squares), teal (7 squares), orange (9 squares), pale yellow (13 squares), slate (18 squares), blue (25 squares), mint (29 squares). An even split would hand every color 11 squares, so the red region is running 10 squares under that average while the mint 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. Red is working with 1 square while mint 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 1×2 frame; pale yellow is the loosest, occupying only 43% of its 5×6 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.
Red: 1 square across rows 6–6, columns 4–4. It never leaves row 6, so its queen is locked to that row.
Indigo covers 2 squares, spanning 1 row and 2 columns (rows 1–1, columns 5–6). It never leaves row 1, so its queen is locked to that row.
Khaki occupies 4 squares within rows 6–8, columns 8–9.
Amber: 6 squares across rows 2–5, columns 1–3.
Sea green covers 7 squares, spanning 3 rows and 4 columns (rows 9–11, columns 8–11).
Teal occupies 7 squares within rows 10–11, columns 4–9.
Orange: 9 squares across rows 7–10, columns 5–8.
Pale yellow covers 13 squares, spanning 5 rows and 6 columns (rows 6–10, columns 2–7).
Slate occupies 18 squares within rows 5–11, columns 1–3.
Blue: 25 squares across rows 1–5, columns 1–9.
Mint covers 29 squares, spanning 10 rows and 5 columns (rows 1–10, columns 7–11).
Where to start on this board
The most constrained color is where a solve should begin, and on #3 that is red with 1 square. It reaches from row 6 to row 6 and from column 4 to column 4 — 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 red never leaves row 6, its queen must be in that row — and that instantly settles row 6 for everyone else. Sweep along it and X out every square that is not red. 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 teal 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 #3
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 1, 2, 3, 4 and 11 are the narrowest, touched by only 3 colors. Columns 10 and 11 are the tightest columns, 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 10 sits at the far end with 6 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.
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 #3 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 #3 is rated easy
The easy label comes out of four measurable things about #3: 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.
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.
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 10 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 #3?
Puzzle #3 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 #3 have only one solution?
Yes. Every puzzle in the 11x11 collection, including #3, 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 #3?
Start with the red region — the most constrained color on this board, with 1 square spanning rows 6–6 and columns 4–4. Narrowing the smallest region first removes the most squares elsewhere on the grid.