11x11 Queens Puzzle #282
Difficulty: medium. 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 33-step reasoning is written out below.
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Step-by-step solution for puzzle #282
What follows is a complete solve of puzzle #282, worked the way a person works it rather than the way a computer does. It runs to 33 deductions — 11 queen placements and 22 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: region confined to one line, last square in a region, region shadow, pairing argument on rows, pairing argument on columns, line confined to one region, proof by contradiction.
Show the full walkthrough (25 steps) — contains the solution
Step 1. Amber cannot leave column 1 — every one of its open squares (2 open squares) sits there. That column belongs to amber, so every square in it owned by another colour is dead: 11 squares in all.
Step 2. The red region is down to one open square, at row 6, column 2. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 6 and column 2, the remaining red squares, and the ring of neighbours around row 6, column 2.
Step 3. The mint region has 3 squares left, spread across rows 3 and 4, 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 4. Wherever sea green ends up among its 3 squares, the same squares fall within reach of it — 2 squares in total, impossible regardless of how the colour resolves.
Step 5. Teal is down to 5 candidates in rows 10 and 11, columns 9–11, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about teal itself.
Step 6. Here is the pairing argument. The sea green and teal regions have no open squares outside rows 10 and 11 — 2 colours confined to 2 rows. Between them they must take one row each, in some order, so every other colour is shut out of all of them: 7 squares come off in one stroke.
The board after step 6 — 1 of 11 queens placed. Step 7. Orange cannot leave row 9 — every one of its open squares (4 open squares) sits there. That row belongs to orange, so every square on it owned by another colour is dead: 5 squares in all.
Step 8. Here is the pairing argument. The mint, slate, and teal regions have no open squares outside columns 9–11 — 3 colours confined to 3 columns. Between them they must take one column each, in some order, so every other colour is shut out of all of them: 11 squares come off in one stroke.
Step 9. Khaki cannot leave row 8 — every one of its open squares (4 open squares) sits there. That row belongs to khaki, so every square on it owned by another colour is dead: 2 squares in all.
Step 10. Every open square left in row 7 (5 open squares) belongs to the pale yellow region. Since that row must contain a queen, pale yellow is the colour that supplies it — so pale yellow squares anywhere else on the board are out, 10 squares in all.
Step 11. Test row 2, column 4 for indigo: place a queen there, run the forced consequences through, and row 10 runs out of open squares entirely. The assumption breaks, so the square is eliminated.
Step 12. Now a short proof by contradiction. Suppose the indigo queen went to row 2, column 5. Follow the forced moves that would create and column 3 runs out of open squares entirely — impossible. So that square is ruled out for good.
Step 13. Test row 2, column 6 for indigo: place a queen there, run the forced consequences through, and the orange region is left with nowhere to put its queen. The assumption breaks, so the square is eliminated.
The board after step 13 — 1 of 11 queens placed. Step 14. Now a short proof by contradiction. Suppose the indigo queen went to row 2, column 7. Follow the forced moves that would create and row 1 runs out of open squares entirely — impossible. So that square is ruled out for good.
Step 15. Test row 3, column 5 for indigo: place a queen there, run the forced consequences through, and column 3 runs out of open squares entirely. The assumption breaks, so the square is eliminated.
Step 16. All of the indigo region's remaining squares (3 open squares) lie in row 1. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 3 squares come off.
Step 17. Test row 3, column 1 for amber: 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 18. The amber region is down to one open square, at row 2, column 1. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 2 and column 1, the remaining amber squares, and the ring of neighbours around row 2, column 1.
Step 19. Test row 3, column 6 for blue: place a queen there, run the forced consequences through, and the orange region is left with nowhere to put its queen. The assumption breaks, so the square is eliminated.
The board after step 19 — 2 of 11 queens placed. Step 20. Now a short proof by contradiction. Suppose the blue queen went to row 3, column 8. 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 21. Test row 4, column 5 for blue: place a queen there, run the forced consequences through, and column 6 runs out of open squares entirely. The assumption breaks, so the square is eliminated.
Step 22. Now a short proof by contradiction. Suppose the blue queen went to row 4, column 6. 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 23. Test row 4, column 8 for blue: place a queen there, run the forced consequences through, and column 7 runs out of open squares entirely. The assumption breaks, so the square is eliminated.
Step 24. Now a short proof by contradiction. Suppose the blue queen went to row 5, column 8. 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 25. From here the board cascades. Keep alternating the region sweep and the line sweep and 9 queens fall out in order without any new idea being needed: blue has one square left, so its queen takes row 3, column 7; mint has one square left, so its queen takes row 4, column 11; slate has one square left, so its queen takes row 5, column 9; teal has one square left, so its queen takes row 11, column 10; 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 6; khaki has one square left, so its queen takes row 8, column 8; pale yellow has one square left, so its queen takes row 7, column 5; indigo has one square left, so its queen takes row 1, 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 1, column 3.
The board after step 25 — 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 #282
Board #282 of the 11x11 bank carries a medium rating. Its 121 squares are shared between eleven colored regions, and the solution places eleven queens: one per row, one per column, one per region, none of them side by side or corner to corner.
Like every board on this site, #282 has been verified to have exactly one valid solution, and that solution is reachable by deduction alone. You never have to guess and then unwind; every queen can be justified by something already visible on the grid. What changes from puzzle to puzzle is where the first certainty appears and how long the chain of reasoning runs before the next one — and that is entirely a product of how these particular colors are shaped.
How the colors divide this board
From smallest to largest, the regions on puzzle #282 are: amber (2 squares), mint (3 squares), red (5 squares), teal (5 squares), slate (7 squares), indigo (12 squares), orange (12 squares), sea green (13 squares), blue (17 squares), khaki (19 squares), pale yellow (26 squares). An even split would hand every color 11 squares, so the amber region is running 9 squares under that average while the pale yellow region is the roomiest area on the grid with 26 squares.
Every color takes one queen and one only, whatever its size — which is why the 24 square difference between amber and pale yellow 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.
Square count is only half the story — how a color is arranged counts too. Amber is the tidiest shape on #282, packing 100% of its 2×1 bounding box, whereas blue straggles across its 5×7 box at just 49%. Tidy blocks are easy to work around; scattered ones touch more lines and resist resolution.
Region by region
Below is every color on #282 with its exact reach, smallest region first. It is worth a slow read: the spans reveal which rows and columns several regions are fighting over.
Amber: 2 squares across rows 2–3, columns 1–1. It sits wholly inside column 1, so its queen must be in that column.
Mint covers 3 squares, spanning 2 rows and 2 columns (rows 3–4, columns 10–11).
Red occupies 5 squares within rows 4–7, columns 1–2.
Teal: 5 squares across rows 10–11, columns 9–11.
Slate covers 7 squares, spanning 4 rows and 3 columns (rows 3–6, columns 9–11).
Indigo occupies 12 squares within rows 1–3, columns 1–7.
Orange: 12 squares across rows 9–11, columns 3–8.
Sea green covers 13 squares, spanning 5 rows and 4 columns (rows 7–11, columns 1–4).
Blue occupies 17 squares within rows 1–5, columns 5–11.
Khaki: 19 squares across rows 6–10, columns 5–11.
Pale yellow covers 26 squares, spanning 7 rows and 7 columns (rows 2–8, columns 2–8).
Where to start on this board
Begin where the choices are fewest. On this board that means amber, which owns just 2 squares inside a 2×1 window running from row 2 to row 3 and column 1 to column 1. A queen is guaranteed somewhere in there, so every line that window crosses is under pressure from the very first move.
Because amber stays inside column 1, its queen belongs to that column and no other region may use it. Cross out the rest of column 1 straight away. Any color that was relying on those squares now has a visibly smaller footprint, and that shrinkage is where your second deduction comes from.
Work outward to the other flat regions next. Mint 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 #282
A quick way to find the next move is to count how many different colors touch each line. On this board, row 1 is the narrowest, touched by only 2 colors. Columns 1, 2, 3, 4, 8 and 9 are the tightest columns, with 4 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 3 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.
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.
The trap on a board like this is placing a queen that is merely plausible. Every placement should be traceable to an elimination you can point at. If you cannot name the rule that forced it, you are guessing — and on a single-solution grid a guess costs more to unwind than the deduction would have taken to find.
Why puzzle #282 is rated medium
What earns a board its rating is the shape of its opening. Here that opening offers one single-line region, a 2-square smallest color, a tightest row touched by 2 colors, and a region-size spread of 24. Lopsided grids with flat regions fall quickly; balanced ones like this take more patience.
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 medium board from the rest.
If #282 feels harder than its rating suggests, the usual culprit is incomplete marking rather than a difficult deduction. Check that every queen already on the grid has its full cross of eliminations recorded — including the diagonal neighbours, which are by far the easiest to miss. More stalled solves come from one forgotten diagonal X than from any genuinely deep chain of logic.
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 #282 is row 1.
As a sanity check rather than a spoiler: the finished solution to #282 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 #282?
Puzzle #282 is rated medium. Its smallest color region holds 2 squares, its tightest row is touched by 2 colors, and one of its regions is confined to a single row or column, which gives you a forced move early.
Does 11x11 puzzle #282 have only one solution?
Yes. Every puzzle in the 11x11 collection, including #282, 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 #282?
Start with the amber region — the most constrained color on this board, with 2 squares spanning rows 2–3 and columns 1–1. Narrowing the smallest region first removes the most squares elsewhere on the grid.