11x11 Queens Puzzle #44
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 16-step reasoning is written out below.
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Step-by-step solution for puzzle #44
What follows is a complete solve of puzzle #44, worked the way a person works it rather than the way a computer does. It runs to 16 deductions — 11 queen placements and 5 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: last square in a region, region shadow, line confined to one region, pairing argument on rows, pairing argument on columns.
Show the full walkthrough (8 steps) — contains the solution
Step 1. The board opens by cascading. Each of these placements is forced the moment the one before it is marked, so the whole run is really a single sweep repeated: indigo has one square left, so its queen takes row 1, column 6; teal has one square left, so its queen takes row 11, column 2; sea green has one square left, so its queen takes row 10, column 4; orange has one square left, so its queen takes row 9, 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 9, column 10.
Step 2. Pale yellow is down to 3 candidates in rows 7 and 8, columns 7 and 8, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about pale yellow itself.
Step 3. Every open square left in column 5 (6 open squares) belongs to the slate region. Since that column must contain a queen, slate is the colour that supplies it — so slate squares anywhere else on the board are out, 7 squares in all.
Step 4. Pale yellow and khaki are now boxed into rows 7 and 8 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 4 squares at once.
The board after step 4 — 4 of 11 queens placed. Step 5. The red region is down to one open square, at row 6, column 11. Every colour holds exactly one queen, so that square is forced. Row 6 and column 11 are now spoken for, along with the squares touching that queen.
Step 6. The blue region has 2 squares left, spread across rows 2 and 3, columns 3 and 9. You do not need to know which of them takes the queen: every one of those options attacks the same 3 squares, so they can be crossed out now.
Step 7. Here is the pairing argument. The amber and khaki regions have no open squares outside columns 1 and 3 — 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: 1 square come off in one stroke.
Step 8. From here the board cascades. Keep alternating the region sweep and the line sweep and 6 queens fall out in order without any new idea being needed: blue has one square left, so its queen takes row 3, column 9; mint has one square left, so its queen takes row 4, column 7; slate has one square left, so its queen takes row 5, column 5; amber has one square left, so its queen takes row 2, column 1; khaki has one square left, so its queen takes row 8, column 3; pale yellow has one square left, so its queen takes row 7, 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 7, 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 #44
This is puzzle number 44 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 #44 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 #44 are: indigo (1 square), teal (1 square), pale yellow (6 squares), orange (7 squares), sea green (9 squares), red (10 squares), amber (14 squares), mint (14 squares), khaki (15 squares), blue (17 squares), slate (27 squares). An even split would hand every color 11 squares, so the indigo region is running 10 squares under that average while the slate region is the roomiest area on the grid with 27 squares.
Every color takes one queen and one only, whatever its size — which is why the 26 square difference between indigo and slate is worth noting before you touch the grid. The cramped colors resolve first and hand you information; the roomy ones absorb whatever is left over at the end.
A region's outline can constrain it more than its size does. Here indigo is the most solid, filling 100% of its 1×1 box, and mint the most diffuse at 47% of its 5×6 box. Solid blocks give clean eliminations; diffuse ones spread across the board and stay open longer.
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 occupies 1 square within rows 1–1, columns 6–6. It never leaves row 1, so its queen is locked to that row.
Teal: 1 square across rows 11–11, columns 2–2. It never leaves row 11, so its queen is locked to that row.
Pale yellow covers 6 squares, spanning 4 rows and 3 columns (rows 7–10, columns 7–9).
Orange occupies 7 squares within rows 9–11, columns 9–11.
Sea green: 9 squares across rows 10–11, columns 3–8.
Red covers 10 squares, spanning 5 rows and 3 columns (rows 5–9, columns 9–11).
Amber occupies 14 squares within rows 1–6, columns 1–4.
Mint: 14 squares across rows 2–6, columns 6–11.
Khaki covers 15 squares, spanning 6 rows and 5 columns (rows 6–11, columns 1–5).
Blue occupies 17 squares within rows 1–3, columns 3–11.
Slate: 27 squares across rows 3–10, columns 2–8.
Where to start on this board
Open on the tightest color. Here that is indigo, confined to 1 square between rows 1 and 1 and columns 6 and 6. Its queen has nowhere else to go, which means those 1 row and 1 column carry more constraint than anywhere else on #44.
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. Teal 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 #44
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 1, 2 and 4 are the narrowest, touched by only 3 colors. Column 1 is the tightest column, with 2 colors.
A line with few colors is a line close to resolving. Where only 3 colors appear, one of them owns the row outright and the others must fit into the remaining 10 rows. Row 10 is the crowded extreme at 5 colors — worth revisiting later, not now.
Working through the middle game
The middle of #44 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.
Two checks, run alternately, will carry you through the 121 squares of this grid. First: has any of the eleven regions been reduced to a single open square? Second: has any row or column? Either answer forces a queen. Players who stall on 11x11 boards almost always run one of those checks and forget the other.
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 #44 is rated easy
Ratings track how generous the opening is. On #44 you get four regions pinned to a single row or column, a smallest color of 1 square, a tightest row crossed by 3 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.
There is one technique that repays study at every grid size. Two regions restricted to the same two rows must occupy one row apiece, which excludes all other regions from those rows entirely; the identical logic applies to columns and to larger matched sets. It converts slow boards into fast ones, and the likeliest place to find it on #44 is column 1.
A non-spoiling distribution check: solved, #44 carries 4 queens on the perimeter against 7 queens inside, with the corners empty. 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 #44?
Puzzle #44 is rated easy. Its smallest color region holds 1 square, its tightest row is touched by 3 colors, and four of its regions are confined to a single row or column, which gives you a forced move early.
Does 11x11 puzzle #44 have only one solution?
Yes. Every puzzle in the 11x11 collection, including #44, 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 #44?
Start with the indigo region — the most constrained color on this board, with 1 square spanning rows 1–1 and columns 6–6. Narrowing the smallest region first removes the most squares elsewhere on the grid.