11x11 Queens Puzzle #144
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 #144
What follows is a complete solve of puzzle #144, 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 proof by contradiction.
Techniques this board needs: last square in a region, region shadow, proof by contradiction, region confined to one line, pairing argument on rows, pairing argument on columns.
Show the full walkthrough (15 steps) — contains the solution
Step 1. Only row 2, column 7 is still open in amber, and since each colour must take a queen, that settles it. That clears row 2, column 7, the rest of the amber region and every square adjacent to it — diagonals included.
Step 2. Pale yellow is down to 4 candidates in rows 6 and 7, columns 1–3, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about pale yellow itself.
Step 3. Test row 1, column 10 for indigo: place a queen there, run the forced consequences through, and the khaki region is left with nowhere to put its queen. The assumption breaks, so the square is eliminated.
Step 4. Now a short proof by contradiction. Suppose the indigo queen went to row 1, column 11. Follow the forced moves that would create and the khaki region is left with nowhere to put its queen — impossible. So that square is ruled out for good.
Step 5. Test row 3, column 11 for indigo: place a queen there, run the forced consequences through, and the mint region is left with nowhere to put its queen. The assumption breaks, so the square is eliminated.
The board after step 5 — 1 of 11 queens placed. Step 6. The indigo region has 2 squares left, spread across rows 1 and 4, columns 9 and 11. 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 7. Test row 4, column 11 for indigo: place a queen there, run the forced consequences through, and the mint region is left with nowhere to put its queen. The assumption breaks, so the square is eliminated.
Step 8. The indigo region is down to one open square, at row 1, column 9. Every colour holds exactly one queen, so that square is forced. Row 1 and column 9 are now spoken for, along with the squares touching that queen.
Step 9. The mint region has 4 squares left, spread across rows 3–5, columns 1 and 2. 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 10. All of the pale yellow region's remaining squares (3 open squares) lie in row 7. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 7 squares come off.
The board after step 10 — 2 of 11 queens placed. Step 11. Blue, mint, slate, and red are now boxed into rows 3–6 and nothing else. That is 4 colours needing 4 rows, so they fill those rows between them — which locks every remaining colour out and removes 4 squares at once.
Step 12. The khaki region is down to one open square, at row 8, column 11. Every colour holds exactly one queen, so that square is forced. Row 8 and column 11 are now spoken for, along with the squares touching that queen.
Step 13. Only row 10, column 10 is still open in sea green, and since each colour must take a queen, that settles it. That clears row 10, column 10, the rest of the sea green region and every square adjacent to it — diagonals included.
Step 14. Here is the pairing argument. The mint and orange regions have no open squares outside columns 1 and 2 — 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: 4 squares come off in one stroke.
Step 15. From here the board cascades. Keep alternating the region sweep and the line sweep and 7 queens fall out in order without any new idea being needed: pale yellow has one square left, so its queen takes row 7, column 3; blue has one square left, so its queen takes row 3, column 4; slate has one square left, so its queen takes row 5, column 5; mint has one square left, so its queen takes row 4, column 1; red has one square left, so its queen takes row 6, column 8; orange has one square left, so its queen takes row 9, column 2; teal has one square left, so its queen takes row 11, column 6. 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 11, column 6.
The board after step 15 — 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 #144
This is puzzle number 144 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 #144 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 #144 are: amber (1 square), pale yellow (4 squares), slate (8 squares), khaki (8 squares), sea green (8 squares), mint (9 squares), orange (10 squares), indigo (11 squares), blue (16 squares), red (21 squares), teal (25 squares). An even split would hand every color 11 squares, so the amber region is running 10 squares under that average while the teal region is the roomiest area on the grid with 25 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 teal has 25 to spare, a gap of 24. Attack the cramped end and the roomy regions tend to resolve themselves.
A region's outline can constrain it more than its size does. Here amber is the most solid, filling 100% of its 1×1 box, and sea green the most diffuse at 50% of its 4×4 box. Solid blocks give clean eliminations; diffuse ones spread across the board and stay open longer.
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 hard board.
Amber: 1 square across rows 2–2, columns 7–7. It never leaves row 2, so its queen is locked to that row.
Pale yellow covers 4 squares, spanning 2 rows and 3 columns (rows 6–7, columns 1–3).
Slate occupies 8 squares within rows 3–7, columns 4–5.
Khaki: 8 squares across rows 5–8, columns 9–11.
Sea green covers 8 squares, spanning 4 rows and 4 columns (rows 8–11, columns 8–11).
Mint occupies 9 squares within rows 1–6, columns 1–2.
Orange: 10 squares across rows 8–11, columns 1–5.
Indigo covers 11 squares, spanning 4 rows and 5 columns (rows 1–4, columns 7–11).
Blue occupies 16 squares within rows 1–6, columns 2–6.
Red: 21 squares across rows 3–7, columns 5–10.
Teal covers 25 squares, spanning 4 rows and 9 columns (rows 8–11, columns 2–10).
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 7 and 7. Its queen has nowhere else to go, which means those 1 row and 1 column carry more constraint than anywhere else on #144.
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 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 #144
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 1, 9, 10 and 11 are the narrowest, touched by only 3 colors. Columns 1, 6 and 11 are the tightest columns, with 3 colors.
The fewer colors a line touches, the sooner it surrenders its queen. A row meeting just 3 colors has to be claimed by one of them, which pushes every remaining region into the other 10 rows. Row 6, meeting 6 colors, is the opposite case — the busiest line on #144 and the last one you should expect to crack.
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.
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 #144 is rated hard
The hard label comes out of four measurable things about #144: two 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 24. Boards that score tight on those measures give up their first queen fast.
Difficulty in Queens is never arithmetic and never luck. Every board has one solution and none require guessing. What varies is the length of the chain you must follow before the next queen becomes certain — one or two steps on an easy board, five or six on a hard one, sometimes with several partial eliminations held in play at once.
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 1 on this board.
Here is a shape check that gives nothing away: when #144 is solved, 4 queens sit on the outer edge of the grid and 7 sit inside it, and no queen lands in a corner. A work-in-progress board that clusters its queens in one quadrant while leaving others bare is usually carrying a mistake.
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 #144?
Puzzle #144 is rated hard. Its smallest color region holds 1 square, 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 #144 have only one solution?
Yes. Every puzzle in the 11x11 collection, including #144, 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 #144?
Start with the amber region — the most constrained color on this board, with 1 square spanning rows 2–2 and columns 7–7. Narrowing the smallest region first removes the most squares elsewhere on the grid.