11x11 Queens Puzzle #143
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 17-step reasoning is written out below.
Previous puzzle · All 11x11 puzzles · Next puzzle
Step-by-step solution for puzzle #143
What follows is a complete solve of puzzle #143, worked the way a person works it rather than the way a computer does. It runs to 17 deductions — 11 queen placements and 6 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.
Show the full walkthrough (13 steps) — contains the solution
Step 1. Only row 11, column 2 is still open in teal, and since each colour must take a queen, that settles it. That clears row 11, column 2, the rest of the teal 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. Only row 2, column 11 is still open in amber, and since each colour must take a queen, that settles it. Everything else in row 2, in column 11, in amber and in the ring around that square is now dead.
Step 4. 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.
The board after step 4 — 3 of 11 queens placed. Step 5. Mint cannot leave column 10 — every one of its open squares (2 open squares) sits there. That column belongs to mint, so every square in it owned by another colour is dead: 5 squares in all.
Step 6. The khaki region has 3 squares left, spread across rows 8 and 9, columns 7 and 8. 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. Orange cannot leave row 9 — every one of its open squares (2 open squares) sits there. That row belongs to orange, so every square on it owned by another colour is dead: 4 squares in all.
Step 8. The khaki region is down to one open square, at row 8, column 7. Every colour holds exactly one queen, so that square is forced. Row 8 and column 7 are now spoken for, along with the squares touching that queen.
Step 9. The pale yellow region has 3 squares left, spread across rows 6 and 7, columns 1 and 3. 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 9 — 4 of 11 queens placed. Step 10. The sea green region is down to one open square, at row 10, column 4. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 10 and column 4, the remaining sea green squares, and the ring of neighbours around row 10, column 4.
Step 11. Only row 9, column 1 is still open in orange, and since each colour must take a queen, that settles it. Everything else in row 9, in column 1, in orange and in the ring around that square is now dead.
Step 12. All of the pale yellow region's remaining squares (2 open squares) lie in column 3. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 3 squares come off.
Step 13. From here the board cascades. Keep alternating the region sweep and the line sweep and 5 queens fall out in order without any new idea being needed: 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 10; red has one square left, so its queen takes row 6, column 8; blue has one square left, so its queen takes row 3, column 6; pale yellow has one square left, so its queen takes row 7, column 3. 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 3.
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 #143
11x11 puzzle #143 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 #143 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 #143 are: teal (1 square), indigo (2 squares), amber (2 squares), khaki (3 squares), orange (5 squares), mint (8 squares), pale yellow (8 squares), slate (9 squares), sea green (10 squares), blue (30 squares), red (43 squares). An even split would hand every color 11 squares, so the teal region is running 10 squares under that average while the red region is the roomiest area on the grid with 43 squares.
One queen per color, regardless of acreage: that is what turns this uneven split into a solving order. Teal is working with 1 square while red has 43 to spare, a gap of 42. 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; sea green is the loosest, occupying only 50% of its 5×4 frame. The loose one reaches into more rows and columns, which is exactly why it usually settles last.
Region by region
Here is the full footprint of every color on puzzle #143, smallest first. Reading these spans before you place anything is the quickest way to see which parts of the grid are genuinely contested.
Teal occupies 1 square within rows 11–11, columns 2–2. It never leaves row 11, so its queen is locked to that row.
Indigo: 2 squares across rows 1–1, columns 9–10. It never leaves row 1, so its queen is locked to that row.
Amber covers 2 squares, spanning 2 rows and 1 column (rows 1–2, columns 11–11). It sits wholly inside column 11, so its queen must be in that column.
Khaki occupies 3 squares within rows 8–9, columns 7–8.
Orange: 5 squares across rows 9–11, columns 1–3.
Mint covers 8 squares, spanning 4 rows and 3 columns (rows 2–5, columns 9–11).
Pale yellow occupies 8 squares within rows 6–8, columns 1–3.
Slate: 9 squares across rows 4–6, columns 1–5.
Sea green covers 10 squares, spanning 5 rows and 4 columns (rows 7–11, columns 2–5).
Blue occupies 30 squares within rows 1–4, columns 1–9.
Red: 43 squares across rows 4–11, columns 5–11.
Where to start on this board
The most constrained color is where a solve should begin, and on #143 that is teal with 1 square. It reaches from row 11 to row 11 and from column 2 to column 2 — 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 teal never leaves row 11, its queen must be in that row — and that instantly settles row 11 for everyone else. Sweep along it and X out every square that is not teal. 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, amber and khaki 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 #143
A quick way to find the next move is to count how many different colors touch each line. On this board, row 3 is the narrowest, touched by only 2 colors. Column 6 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 2 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 4 colors — the most crowded line here, and the one least likely to resolve early. Spend your attention accordingly.
Working through the middle game
The middle of #143 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 #143 is rated easy
The rating reflects how much the board concedes up front. Puzzle #143 has four regions confined to a single row or column, its smallest color holds 1 square, its tightest row meets just 2 colors, and the gap between its largest and smallest regions is 42 squares. Flat, lopsided boards open quickly; even, sprawling ones make you earn the first placement.
Nothing about the rating involves computation or chance. Each grid has a single solution reachable by pure logic; the rating simply measures how far ahead you have to reason. Easy boards resolve a queen every step or two, while hard ones can ask you to carry three unfinished lines of thought before any of them pays off.
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 3 on this board.
As a sanity check rather than a spoiler: the finished solution to #143 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 #143?
Puzzle #143 is rated easy. Its smallest color region holds 1 square, its tightest row is touched by 2 colors, and four of its regions are confined to a single row or column, which gives you a forced move early.
Does 11x11 puzzle #143 have only one solution?
Yes. Every puzzle in the 11x11 collection, including #143, 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 #143?
Start with the teal region — the most constrained color on this board, with 1 square spanning rows 11–11 and columns 2–2. Narrowing the smallest region first removes the most squares elsewhere on the grid.