11x11 Queens Puzzle #49
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 20-step reasoning is written out below.
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Step-by-step solution for puzzle #49
What follows is a complete solve of puzzle #49, worked the way a person works it rather than the way a computer does. It runs to 20 deductions — 11 queen placements and 9 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 confined to one line, region shadow, pairing argument on rows, proof by contradiction, last square in a row.
Show the full walkthrough (15 steps) — contains the solution
Step 1. Only row 9, column 2 is still open in orange, and since each colour must take a queen, that settles it. That clears row 9, column 2, the rest of the orange region and every square adjacent to it — diagonals included.
Step 2. The teal region is down to one open square, at row 11, column 6. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 11 and column 6, the remaining teal squares, and the ring of neighbours around row 11, column 6.
Step 3. Indigo cannot leave row 1 — every one of its open squares (2 open squares) sits there. That row belongs to indigo, so every square on it owned by another colour is dead: 9 squares in all.
Step 4. Wherever mint ends up among its 5 squares, the same squares fall within reach of it — 1 square in total, impossible regardless of how the colour resolves.
Step 5. Pale yellow is down to 3 candidates in rows 7 and 8, columns 4, 5, and 7, and they overlap enough to cover 4 squares elsewhere. Cross those out without deciding anything about pale yellow itself.
The board after step 5 — 2 of 11 queens placed. Step 6. The slate region has 6 squares left, spread across rows 4–6, columns 7–9. 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 7. Wherever sea green ends up among its 2 squares, the same squares fall within reach of it — 2 squares in total, impossible regardless of how the colour resolves.
Step 8. Here is the pairing argument. The pale yellow, khaki, and sea green regions have no open squares outside rows 7, 8, and 10 — 3 colours confined to 3 rows. Between them they must take one row each, in some order, so every other colour is shut out of all of them: 8 squares come off in one stroke.
Step 9. The red region has 3 squares left, spread across rows 5 and 6, columns 10 and 11. 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. Now a short proof by contradiction. Suppose the indigo queen went to row 1, column 8. Follow the forced moves that would create and the blue region is left with nowhere to put its queen — impossible. So that square is ruled out for good.
The board after step 10 — 2 of 11 queens placed. Step 11. 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: indigo has one square left, so its queen takes row 1, column 7; pale yellow has one square left, so its queen takes row 7, column 5; sea green has one square left, so its queen takes row 10, column 4; khaki has one square left, so its queen takes row 8, column 8; slate has one square left, so its queen takes row 5, column 9; red has one square left, so its queen takes row 6, column 11. 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 6, column 11.
Step 12. Mint is down to 2 candidates in rows 3 and 4, columns 1 and 3, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about mint itself.
Step 13. Row 4 has a single open square left, at column 1 in the mint region. Every row needs a queen, so this one is forced. Row 4 and column 1 are now spoken for, along with the squares touching that queen.
Step 14. Only row 2, column 3 is still open in amber, and since each colour must take a queen, that settles it. Everything else in row 2, in column 3, in amber and in the ring around that square is now dead.
Step 15. The blue region is down to one open square, at row 3, column 10. Every colour holds exactly one queen, so that square is forced. Row 3 and column 10 are now spoken for, along with the squares touching that queen.
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 #49
Puzzle #49 is one of the easy-rated boards in the 11x11 set. Eleven colors divide its 121 squares, and you win by placing eleven queens so that each row, each column and each color holds exactly one, with no two queens adjacent in any direction.
As with every puzzle in this collection, #49 has a single verified solution and needs no guesswork. Each queen follows from something already visible. What the board controls is tempo — how soon the first forced move shows up and how far apart the rest are spaced — and that is a direct consequence of how these colors are cut.
How the colors divide this board
From smallest to largest, the regions on puzzle #49 are: orange (1 square), teal (1 square), indigo (2 squares), pale yellow (9 squares), slate (10 squares), khaki (12 squares), mint (13 squares), red (13 squares), sea green (16 squares), blue (19 squares), amber (25 squares). An even split would hand every color 11 squares, so the orange region is running 10 squares under that average while the amber region is the roomiest area on the grid with 25 squares.
Every color takes one queen and one only, whatever its size — which is why the 24 square difference between orange and amber 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.
Shape matters as much as size. The indigo region is the most compact color here, filling 100% of the 1×2 box that encloses it, while khaki is the most scattered at 48% of its 5×5 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
Here is the full footprint of every color on puzzle #49, smallest first. Reading these spans before you place anything is the quickest way to see which parts of the grid are genuinely contested.
Orange covers 1 square, spanning 1 row and 1 column (rows 9–9, columns 2–2). It never leaves row 9, so its queen is locked to that row.
Teal occupies 1 square within rows 11–11, columns 6–6. It never leaves row 11, so its queen is locked to that row.
Indigo: 2 squares across rows 1–1, columns 7–8. It never leaves row 1, so its queen is locked to that row.
Pale yellow covers 9 squares, spanning 3 rows and 4 columns (rows 7–9, columns 4–7).
Slate occupies 10 squares within rows 4–7, columns 6–9.
Khaki: 12 squares across rows 7–11, columns 7–11.
Mint covers 13 squares, spanning 7 rows and 3 columns (rows 3–9, columns 1–3).
Red occupies 13 squares within rows 5–10, columns 9–11.
Sea green: 16 squares across rows 7–11, columns 1–6.
Blue covers 19 squares, spanning 5 rows and 5 columns (rows 1–5, columns 7–11).
Amber occupies 25 squares within rows 1–6, columns 1–6.
Where to start on this board
Orange is the natural opening on #49: it is the smallest region on the grid at 1 square, boxed into rows 9–9 and columns 2–2. Since one of those squares must hold a queen, that block of 1 row and 1 column is the most contested part of the board.
Because orange never leaves row 9, its queen must be in that row — and that instantly settles row 9 for everyone else. Sweep along it and X out every square that is not orange. 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 and teal 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 #49
A quick way to find the next move is to count how many different colors touch each line. On this board, row 2 is the narrowest, touched by only 2 colors. Columns 1, 3, 4, 5, 10 and 11 are the tightest columns, with 3 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 9 meets 6 colors — the most crowded line here, and the one least likely to resolve early. Spend your attention accordingly.
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.
The whole middle game reduces to two sweeps. Sweep the eleven colors looking for one with a single square left; sweep the eleven rows and eleven columns looking for the same. Each sweep feeds the next, and switching between them deliberately — rather than drifting — is what separates a fast 11x11 solve from a stalled one.
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 #49 is rated easy
The rating reflects how much the board concedes up front. Puzzle #49 has five 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 24 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.
A board that feels above its rating is nearly always a board with a missing X. Audit every queen on the grid: full row cleared, full column cleared, all eight touching squares cleared. Diagonals are the common omission, and missing one is far more often the cause of a stall than any genuine difficulty in the puzzle.
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 #49 is row 2.
As a sanity check rather than a spoiler: the finished solution to #49 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.
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Questions about this puzzle
How hard is 11x11 Queens puzzle #49?
Puzzle #49 is rated easy. Its smallest color region holds 1 square, its tightest row is touched by 2 colors, and five of its regions are confined to a single row or column, which gives you a forced move early.
Does 11x11 puzzle #49 have only one solution?
Yes. Every puzzle in the 11x11 collection, including #49, 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 #49?
Start with the orange region — the most constrained color on this board, with 1 square spanning rows 9–9 and columns 2–2. Narrowing the smallest region first removes the most squares elsewhere on the grid.