11x11 Queens Puzzle #128
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 16-step reasoning is written out below.
Previous puzzle · All 11x11 puzzles · Next puzzle
Step-by-step solution for puzzle #128
What follows is a complete solve of puzzle #128, 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 region shadow.
Techniques this board needs: last square in a region, region confined to one line, region shadow, last square in a row.
Show the full walkthrough (13 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 4; amber has one square left, so its queen takes row 2, column 11; blue has one square left, so its queen takes row 3, column 6; slate has one square left, so its queen takes row 5, 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 5, column 10.
Step 2. Mint cannot leave row 4 — every one of its open squares (2 open squares) sits there. That row belongs to mint, so every square on it owned by another colour is dead: 2 squares in all.
Step 3. The red region has 5 squares left, spread across rows 6 and 7, columns 3, 5, 7, and 9. 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 4. Sea green cannot leave column 1 — every one of its open squares (2 open squares) sits there. That column belongs to sea green, so every square in it owned by another colour is dead: 7 squares in all.
The board after step 4 — 4 of 11 queens placed. Step 5. The mint region is down to one open square, at row 4, column 2. Every colour holds exactly one queen, so that square is forced. Row 4 and column 2 are now spoken for, along with the squares touching that queen.
Step 6. Only row 8, column 3 is still open in khaki, and since each colour must take a queen, that settles it. That clears row 8, column 3, the rest of the khaki region and every square adjacent to it — diagonals included.
Step 7. All of the pale yellow region's remaining squares (4 open squares) lie in column 5. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 1 square come off.
Step 8. Look along row 6: one square survives, row 6, column 7, which belongs to red. A row cannot be left empty, so the queen goes there. That clears row 6, column 7, the rest of the red region and every square adjacent to it — diagonals included.
Step 9. Row 7 has a single open square left, at column 5 in the pale yellow region. Every row needs a queen, so this one is forced. Cross out the whole of row 7 and column 5, the remaining pale yellow squares, and the ring of neighbours around row 7, column 5.
The board after step 9 — 8 of 11 queens placed. Step 10. Orange cannot leave column 8 — every one of its open squares (2 open squares) sits there. That column belongs to orange, so every square in it owned by another colour is dead: 3 squares in all.
Step 11. The teal region is down to one open square, at row 11, column 9. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 11 and column 9, the remaining teal squares, and the ring of neighbours around row 11, column 9.
Step 12. Only row 9, column 8 is still open in orange, and since each colour must take a queen, that settles it. Everything else in row 9, in column 8, in orange and in the ring around that square is now dead.
Step 13. 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. Row 10 and column 1 are now spoken for, along with the squares touching that queen.
The board after step 13 — 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 #128
This is puzzle number 128 in the 11x11 collection, rated hard. 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 #128 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 #128 are: indigo (1 square), sea green (2 squares), amber (5 squares), slate (9 squares), teal (10 squares), blue (11 squares), khaki (13 squares), orange (14 squares), mint (16 squares), pale yellow (16 squares), red (24 squares). An even split would hand every color 11 squares, so the indigo region is running 10 squares under that average while the red region is the roomiest area on the grid with 24 squares.
Every color takes one queen and one only, whatever its size — which is why the 23 square difference between indigo and red 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 orange the most diffuse at 39% of its 6×6 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 4–4. It never leaves row 1, so its queen is locked to that row.
Sea green: 2 squares across rows 10–11, columns 1–1. It sits wholly inside column 1, so its queen must be in that column.
Amber covers 5 squares, spanning 2 rows and 4 columns (rows 1–2, columns 8–11).
Slate occupies 9 squares within rows 3–7, columns 8–11.
Teal: 10 squares across rows 9–11, columns 8–11.
Blue covers 11 squares, spanning 3 rows and 7 columns (rows 1–3, columns 4–10).
Khaki occupies 13 squares within rows 6–11, columns 1–4.
Orange: 14 squares across rows 6–11, columns 6–11.
Mint covers 16 squares, spanning 5 rows and 5 columns (rows 1–5, columns 1–5).
Pale yellow occupies 16 squares within rows 6–11, columns 3–6.
Red: 24 squares across rows 3–7, columns 3–10.
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 4 and 4. Its queen has nowhere else to go, which means those 1 row and 1 column carry more constraint than anywhere else on #128.
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. 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 #128
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 2, 4, 5 and 8 are the narrowest, touched by only 3 colors. Column 2 is the tightest column, with 2 colors.
Those lines matter because a row touched by few colors gives its queen away sooner. If a row meets only 3 colors, then one of those regions has to own it, and every other region is competing for the remaining 10 rows. By contrast row 11 meets 5 colors — the most crowded line here, and the one least likely to resolve early. Spend your attention accordingly.
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.
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 #128 is rated hard
Ratings track how generous the opening is. On #128 you get three regions pinned to a single row or column, a smallest color of 1 square, a tightest row crossed by 3 colors, and a 23-square gap between the largest and smallest regions. Those four numbers largely explain the hard label.
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.
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 #128 is column 2.
As a sanity check rather than a spoiler: the finished solution to #128 puts 4 queens on the outer border and 7 queens in the interior, with none in a corner. If your part-finished grid has queens bunched into one area while whole stretches sit empty, something probably went wrong a few moves back.
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.
Full rules · Strategy library · Puzzle statistics
Questions about this puzzle
How hard is 11x11 Queens puzzle #128?
Puzzle #128 is rated hard. 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 #128 have only one solution?
Yes. Every puzzle in the 11x11 collection, including #128, 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 #128?
Start with the indigo region — the most constrained color on this board, with 1 square spanning rows 1–1 and columns 4–4. Narrowing the smallest region first removes the most squares elsewhere on the grid.