11x11 Queens Puzzle #95
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 28-step reasoning is written out below.
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Step-by-step solution for puzzle #95
What follows is a complete solve of puzzle #95, worked the way a person works it rather than the way a computer does. It runs to 28 deductions — 11 queen placements and 17 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, pairing argument on rows, region confined to one line, proof by contradiction, pairing argument on columns, line confined to one region.
Show the full walkthrough (23 steps) — contains the solution
Step 1. Only row 3, column 5 is still open in blue, and since each colour must take a queen, that settles it. That clears row 3, column 5, the rest of the blue region and every square adjacent to it — diagonals included.
Step 2. Mint is down to 5 candidates in rows 4–7, columns 1 and 2, and they overlap enough to cover 2 squares elsewhere. Cross those out without deciding anything about mint itself.
Step 3. The orange region has 4 squares left, spread across rows 9–11, 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. The teal region is down to one open square, at row 11, column 11. Every colour holds exactly one queen, so that square is forced. Row 11 and column 11 are now spoken for, along with the squares touching that queen.
Step 5. Only row 9, column 10 is still open in orange, and since each colour must take a queen, that settles it. That clears row 9, column 10, the rest of the orange region and every square adjacent to it — diagonals included.
Step 6. The indigo region has 5 squares left, spread across rows 1 and 2, 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.
The board after step 6 — 3 of 11 queens placed. Step 7. Wherever slate ends up among its 6 squares, the same squares fall within reach of it — 1 square in total, impossible regardless of how the colour resolves.
Step 8. Pale yellow is down to 4 candidates in rows 7 and 8, columns 7–9, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about pale yellow itself.
Step 9. Khaki and sea green are now boxed into rows 8 and 10 and nothing else. That is 2 colours needing 2 rows, so they fill those rows between them — which locks every remaining colour out and removes 6 squares at once.
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: 4 squares come off.
Step 11. Test row 1, column 7 for indigo: 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 12. Now a short proof by contradiction. Suppose the indigo queen went to row 1, column 9. Follow the forced moves that would create and column 6 runs out of open squares entirely — impossible. So that square is ruled out for good.
The board after step 12 — 3 of 11 queens placed. Step 13. Test row 2, column 7 for indigo: 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 14. Now a short proof by contradiction. Suppose the indigo queen went to row 2, column 9. Follow the forced moves that would create and column 6 runs out of open squares entirely — impossible. So that square is ruled out for good.
Step 15. Only row 1, column 8 is still open in indigo, and since each colour must take a queen, that settles it. Everything else in row 1, in column 8, in indigo and in the ring around that square is now dead.
Step 16. Here is the pairing argument. The amber, mint, and sea green regions have no open squares outside columns 1–3 — 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: 4 squares come off in one stroke.
Step 17. Row 2 has only amber squares left (2 open squares). The row needs a queen and only amber can provide one, which pins that colour to this row and kills its squares elsewhere: 1 square.
The board after step 17 — 4 of 11 queens placed. Step 18. Now a short proof by contradiction. Suppose the amber queen went to row 2, column 1. Follow the forced moves that would create and column 6 runs out of open squares entirely — impossible. So that square is ruled out for good.
Step 19. 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 20. Now a short proof by contradiction. Suppose the mint queen went to row 5, column 1. Follow the forced moves that would create and the slate region is left with nowhere to put its queen — impossible. So that square is ruled out for good.
Step 21. Test row 6, column 1 for mint: 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 mint queen went to row 6, column 2. Follow the forced moves that would create and the red region is left with nowhere to put its queen — impossible. So that square is ruled out for good.
Step 23. 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: mint has one square left, so its queen takes row 4, column 1; sea green has one square left, so its queen takes row 10, column 2; khaki has one square left, so its queen takes row 8, column 7; pale yellow has one square left, so its queen takes row 7, column 9; slate has one square left, so its queen takes row 5, column 6; red has one square left, so its queen takes row 6, column 4. 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 4.
The board after step 23 — 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 #95
11x11 puzzle #95 is rated medium. 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.
Like every board on this site, #95 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 #95 are: blue (1 square), teal (2 squares), orange (4 squares), mint (5 squares), sea green (8 squares), indigo (11 squares), amber (13 squares), slate (13 squares), pale yellow (17 squares), khaki (18 squares), red (29 squares). An even split would hand every color 11 squares, so the blue region is running 10 squares under that average while the red region is the roomiest area on the grid with 29 squares.
That imbalance is the first thing to read, because every region takes exactly one queen regardless of how much space it owns. Blue has only 1 place to put its queen; red has 29. The spread between them on this board is 28 squares, and the wider that spread runs, the more it pays to solve from the small end inward.
A region's outline can constrain it more than its size does. Here blue is the most solid, filling 100% of its 1×1 box, and pale yellow the most diffuse at 43% of its 8×5 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 medium board.
Blue occupies 1 square within rows 3–3, columns 5–5. It never leaves row 3, so its queen is locked to that row.
Teal: 2 squares across rows 10–11, columns 11–11. It sits wholly inside column 11, so its queen must be in that column.
Orange covers 4 squares, spanning 3 rows and 2 columns (rows 9–11, columns 10–11).
Mint occupies 5 squares within rows 4–7, columns 1–2.
Sea green: 8 squares across rows 7–11, columns 1–3.
Indigo covers 11 squares, spanning 3 rows and 6 columns (rows 1–3, columns 6–11).
Amber occupies 13 squares within rows 1–4, columns 1–6.
Slate: 13 squares across rows 2–6, columns 5–10.
Pale yellow covers 17 squares, spanning 8 rows and 5 columns (rows 2–9, columns 7–11).
Khaki occupies 18 squares within rows 8–11, columns 2–9.
Red: 29 squares across rows 2–10, columns 2–8.
Where to start on this board
The most constrained color is where a solve should begin, and on #95 that is blue with 1 square. It reaches from row 3 to row 3 and from column 5 to column 5 — 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 blue never leaves row 3, its queen must be in that row — and that instantly settles row 3 for everyone else. Sweep along it and X out every square that is not blue. 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. Teal 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 #95
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 and 4 are the tightest columns, with 3 colors.
Count colors per line and you have a ranking of where to look. The narrowest rows here see only 2 colors, so one of that handful must take the row and the rest are squeezed into the other 10 rows. Row 3 sits at the far end with 6 colors crossing it; it will almost certainly be among the last to settle.
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.
Keep alternating between two views of the board. In the region view you ask which of the eleven colors is down to one open square. In the line view you ask the same of each row and column. Both produce forced queens, and each placement refreshes the other view, so cycling between them deliberately is how a 11x11 board unwinds.
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 #95 is rated medium
The medium label comes out of four measurable things about #95: three of its regions are locked to one row or column, its smallest color spans 1 square, its least crowded row meets 2 colors, and its largest and smallest regions differ by 28. Boards that score tight on those measures give up their first queen fast.
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.
If #95 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.
One pattern is worth learning at every size, and it is available here. When two regions can only fit inside the same two rows, they must take one row each — which locks every other region out of both. The same argument works for columns, and for any matching count: three regions sharing three rows, four sharing four. Spotting these pairings turns a slow grind into a quick cascade, and on #95 the place to look for one is around row 1.
Use this as a rough check on your progress: the completed board has 3 queens around the border and 8 queens in the middle, including 1 in a corner. Solutions spread out; if yours is bunching up in one region of the grid, retrace a few moves.
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 #95?
Puzzle #95 is rated medium. Its smallest color region holds 1 square, its tightest row is touched by 2 colors, and three of its regions are confined to a single row or column, which gives you a forced move early.
Does 11x11 puzzle #95 have only one solution?
Yes. Every puzzle in the 11x11 collection, including #95, 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 #95?
Start with the blue region — the most constrained color on this board, with 1 square spanning rows 3–3 and columns 5–5. Narrowing the smallest region first removes the most squares elsewhere on the grid.