11x11 Queens Puzzle #104
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 11-step reasoning is written out below.
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Step-by-step solution for puzzle #104
What follows is a complete solve of puzzle #104, worked the way a person works it rather than the way a computer does. It runs to 11 deductions, every one of them a forced placement. Each step names the rule that forces it, so nothing below is a guess, and the hardest idea required is the last square in a region.
Techniques this board needs: last square in a region.
Show the full walkthrough (11 steps) — contains the solution
Step 1. Only row 2, column 9 is still open in amber, and since each colour must take a queen, that settles it. That clears row 2, column 9, the rest of the amber region and every square adjacent to it — diagonals included.
Step 2. The indigo region is down to one open square, at row 1, column 11. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 1 and column 11, the remaining indigo squares, and the ring of neighbours around row 1, column 11.
Step 3. Only row 7, column 1 is still open in pale yellow, and since each colour must take a queen, that settles it. Everything else in row 7, in column 1, in pale yellow and in the ring around that square is now dead.
Step 4. The red region is down to one open square, at row 6, column 10. Every colour holds exactly one queen, so that square is forced. Row 6 and column 10 are now spoken for, along with the squares touching that queen.
The board after step 4 — 4 of 11 queens placed. Step 5. Only row 5, column 5 is still open in slate, and since each colour must take a queen, that settles it. That clears row 5, column 5, the rest of the slate region and every square adjacent to it — diagonals included.
Step 6. The khaki region is down to one open square, at row 8, column 3. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 8 and column 3, the remaining khaki squares, and the ring of neighbours around row 8, column 3.
Step 7. Only row 11, column 4 is still open in teal, and since each colour must take a queen, that settles it. Everything else in row 11, in column 4, in teal and in the ring around that square is now dead.
The board after step 7 — 7 of 11 queens placed. Step 8. The sea green region is down to one open square, at row 10, column 2. Every colour holds exactly one queen, so that square is forced. Row 10 and column 2 are now spoken for, along with the squares touching that queen.
Step 9. Only row 3, column 6 is still open in blue, and since each colour must take a queen, that settles it. That clears row 3, column 6, the rest of the blue region and every square adjacent to it — diagonals included.
Step 10. The mint region is down to one open square, at row 4, column 8. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 4 and column 8, the remaining mint squares, and the ring of neighbours around row 4, column 8.
Step 11. Only row 9, column 7 is still open in orange, and since each colour must take a queen, that settles it. Everything else in row 9, in column 7, in orange and in the ring around that square is now dead.
The board after step 11 — 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 #104
This is puzzle number 104 in the 11x11 collection, rated easy. The grid holds 121 squares split between eleven colored regions, and a finished board carries eleven queens — one in every row, one in every column, one in every color, and never two of them touching, diagonals included.
Puzzle #104 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 #104 are: amber (1 square), pale yellow (1 square), slate (2 squares), teal (3 squares), indigo (6 squares), sea green (10 squares), red (14 squares), mint (16 squares), khaki (16 squares), orange (25 squares), blue (27 squares). An even split would hand every color 11 squares, so the amber region is running 10 squares under that average while the blue region is the roomiest area on the grid with 27 squares.
One queen per color, regardless of acreage: that is what turns this uneven split into a solving order. Amber is working with 1 square while blue has 27 to spare, a gap of 26. Attack the cramped end and the roomy regions tend to resolve themselves.
Shape matters as much as size. The amber region is the most compact color here, filling 100% of the 1×1 box that encloses it, while red is the most scattered at 39% of its 6×6 box. Compact regions are easy to eliminate around; straggling ones reach into more rows and columns and tend to stay unresolved until late.
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.
Amber occupies 1 square within rows 2–2, columns 9–9. It never leaves row 2, so its queen is locked to that row.
Pale yellow: 1 square across rows 7–7, columns 1–1. It never leaves row 7, so its queen is locked to that row.
Slate covers 2 squares, spanning 2 rows and 1 column (rows 5–6, columns 5–5). It sits wholly inside column 5, so its queen must be in that column.
Teal occupies 3 squares within rows 11–11, columns 3–5. It never leaves row 11, so its queen is locked to that row.
Indigo: 6 squares across rows 1–3, columns 9–11.
Sea green covers 10 squares, spanning 4 rows and 4 columns (rows 8–11, columns 1–4).
Red occupies 14 squares within rows 3–8, columns 6–11.
Mint: 16 squares across rows 1–5, columns 6–10.
Khaki covers 16 squares, spanning 5 rows and 5 columns (rows 5–9, columns 1–5).
Orange occupies 25 squares within rows 8–11, columns 5–11.
Blue: 27 squares across rows 1–6, columns 1–8.
Where to start on this board
Open on the tightest color. Here that is amber, confined to 1 square between rows 2 and 2 and columns 9 and 9. Its queen has nowhere else to go, which means those 1 row and 1 column carry more constraint than anywhere else on #104.
Because amber never leaves row 2, its queen must be in that row — and that instantly settles row 2 for everyone else. Sweep along it and X out every square that is not amber. 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. Pale yellow, teal 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 #104
A quick way to find the next move is to count how many different colors touch each line. On this board, row 10 is the narrowest, touched by only 2 colors. Columns 2 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 5 is the crowded extreme at 5 colors — worth revisiting later, not now.
Working through the middle game
The middle of #104 is where careless play costs time. Every queen you place kills a row, a column and the eight surrounding squares; if you do not mark all of that immediately, you will later "discover" a move that was available several turns ago. Mark first, then look.
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.
Say the reason out loud: "this region has one square left", "this column has one square left". If no such sentence is available, the eliminating is not finished. One more pass of X marks is almost always quicker than committing to a placement you cannot defend.
Why puzzle #104 is rated easy
Ratings track how generous the opening is. On #104 you get six regions pinned to a single row or column, a smallest color of 1 square, a tightest row crossed by 2 colors, and a 26-square gap between the largest and smallest regions. Those four numbers largely explain the easy label.
The scale has nothing to do with maths or luck — every puzzle here is solvable by deduction and has exactly one answer. It measures reasoning depth: how many eliminations must stack up before a placement becomes provable. That depth is what separates a easy board from the rest.
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 row 10 on this board.
A non-spoiling distribution check: solved, #104 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 #104?
Puzzle #104 is rated easy. Its smallest color region holds 1 square, its tightest row is touched by 2 colors, and six of its regions are confined to a single row or column, which gives you a forced move early.
Does 11x11 puzzle #104 have only one solution?
Yes. Every puzzle in the 11x11 collection, including #104, 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 #104?
Start with the amber region — the most constrained color on this board, with 1 square spanning rows 2–2 and columns 9–9. Narrowing the smallest region first removes the most squares elsewhere on the grid.