11x11 Queens Puzzle #235
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 19-step reasoning is written out below.
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Step-by-step solution for puzzle #235
What follows is a complete solve of puzzle #235, worked the way a person works it rather than the way a computer does. It runs to 19 deductions — 11 queen placements and 8 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 pairing argument on columns.
Techniques this board needs: last square in a region, region shadow, region confined to one line, pairing argument on columns, line confined to one region, last square in a row.
Show the full walkthrough (15 steps) — contains the solution
Step 1. Only row 1, column 5 is still open in indigo, and since each colour must take a queen, that settles it. That clears row 1, column 5, the rest of the indigo region and every square adjacent to it — diagonals included.
Step 2. The pale yellow region is down to one open square, at row 7, column 11. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 7 and column 11, the remaining pale yellow squares, and the ring of neighbours around row 7, column 11.
Step 3. The amber region has 4 squares left, spread across rows 2–4, columns 8 and 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 4. Wherever orange ends up among its 7 squares, the same squares fall within reach of it — 1 square in total, impossible regardless of how the colour resolves.
Step 5. Sea green cannot leave column 10 — every one of its open squares (2 open squares) sits there. That column belongs to sea green, so every square in it owned by another colour is dead: 7 squares in all.
The board after step 5 — 2 of 11 queens placed. Step 6. The slate region has 3 squares left, spread across rows 4 and 5, columns 8 and 9. 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. Amber and slate are now boxed into columns 8 and 9 and nothing else. That is 2 colours needing 2 columns, so they fill those columns between them — which locks every remaining colour out and removes 7 squares at once.
Step 8. The red region is down to one open square, at row 6, column 6. Every colour holds exactly one queen, so that square is forced. Row 6 and column 6 are now spoken for, along with the squares touching that queen.
Step 9. Mint cannot leave column 7 — every one of its open squares (3 open squares) sits there. That column belongs to mint, so every square in it owned by another colour is dead: 3 squares in all.
Step 10. The orange region is down to one open square, at row 9, column 4. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 9 and column 4, the remaining orange squares, and the ring of neighbours around row 9, column 4.
The board after step 10 — 4 of 11 queens placed. Step 11. Only row 10, column 10 is still open in sea green, and since each colour must take a queen, that settles it. Everything else in row 10, in column 10, in sea green and in the ring around that square is now dead.
Step 12. Every open square left in row 11 (3 open squares) belongs to the teal region. Since that row must contain a queen, teal is the colour that supplies it — so teal squares anywhere else on the board are out, 1 square in all.
Step 13. Look along row 8: one square survives, row 8, column 1, which belongs to khaki. A row cannot be left empty, so the queen goes there. Everything else in row 8, in column 1, in khaki and in the ring around that square is now dead.
Step 14. Every open square left in row 5 (2 open squares) belongs to the slate region. Since that row must contain a queen, slate is the colour that supplies it — so slate squares anywhere else on the board are out, 1 square in all.
Step 15. 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: row 4 is down to one square, putting a queen on row 4, column 7; slate has one square left, so its queen takes row 5, column 9; amber has one square left, so its queen takes row 2, column 8; blue has one square left, so its queen takes row 3, column 2; teal has one square left, so its queen takes row 11, 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 11, column 3.
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 #235
11x11 puzzle #235 is rated hard. 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, #235 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 #235 are: indigo (1 square), pale yellow (1 square), sea green (7 squares), orange (9 squares), mint (10 squares), amber (11 squares), teal (13 squares), slate (14 squares), blue (15 squares), khaki (19 squares), red (21 squares). An even split would hand every color 11 squares, so the indigo region is running 10 squares under that average while the red region is the roomiest area on the grid with 21 squares.
That imbalance is the first thing to read, because every region takes exactly one queen regardless of how much space it owns. Indigo has only 1 place to put its queen; red has 21. The spread between them on this board is 20 squares, and the wider that spread runs, the more it pays to solve from the small end inward.
Look at arrangement as well as area. Indigo is the densest region on this grid at 100% of a 1×1 frame; red is the loosest, occupying only 43% of its 7×7 frame. The loose one reaches into more rows and columns, which is exactly why it usually settles last.
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.
Indigo covers 1 square, spanning 1 row and 1 column (rows 1–1, columns 5–5). It never leaves row 1, so its queen is locked to that row.
Pale yellow occupies 1 square within rows 7–7, columns 11–11. It never leaves row 7, so its queen is locked to that row.
Sea green: 7 squares across rows 8–11, columns 10–11.
Orange covers 9 squares, spanning 4 rows and 4 columns (rows 8–11, columns 4–7).
Mint occupies 10 squares within rows 2–6, columns 5–8.
Amber: 11 squares across rows 1–4, columns 6–11.
Teal covers 13 squares, spanning 4 rows and 6 columns (rows 8–11, columns 1–6).
Slate occupies 14 squares within rows 2–7, columns 8–11.
Blue: 15 squares across rows 1–5, columns 1–5.
Khaki covers 19 squares, spanning 7 rows and 4 columns (rows 3–9, columns 1–4).
Red occupies 21 squares within rows 5–11, columns 4–10.
Where to start on this board
The most constrained color is where a solve should begin, and on #235 that is indigo with 1 square. It reaches from row 1 to row 1 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 indigo never leaves row 1, its queen must be in that row — and that instantly settles row 1 for everyone else. Sweep along it and X out every square that is not indigo. 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 #235
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 3 colors. Columns 1, 2, 3 and 9 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 3 colors, so one of that handful must take the row and the rest are squeezed into the other 10 rows. Row 9 sits at the far end with 5 colors crossing it; it will almost certainly be among the last to settle.
Working through the middle game
The middle of #235 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.
Resist the plausible-looking queen. On #235 every correct placement has a stated reason behind it, and any move you cannot justify is a guess wearing a disguise. Backing out of a wrong guess on a single-solution board takes far longer than finding the real deduction would have.
Why puzzle #235 is rated hard
The hard label comes out of four measurable things about #235: four 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 20. 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 #235 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 #235 the place to look for one is around row 1.
Use this as a rough check on your progress: the completed board has 4 queens around the border and 7 queens in the middle, and nothing in the corners. 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 #235?
Puzzle #235 is rated hard. Its smallest color region holds 1 square, its tightest row is touched by 3 colors, and four of its regions are confined to a single row or column, which gives you a forced move early.
Does 11x11 puzzle #235 have only one solution?
Yes. Every puzzle in the 11x11 collection, including #235, 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 #235?
Start with the indigo region — the most constrained color on this board, with 1 square spanning rows 1–1 and columns 5–5. Narrowing the smallest region first removes the most squares elsewhere on the grid.