11x11 Queens Puzzle #236
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 20-step reasoning is written out below.
Previous puzzle · All 11x11 puzzles · Next puzzle
Step-by-step solution for puzzle #236
What follows is a complete solve of puzzle #236, 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 line confined to one region.
Techniques this board needs: region shadow, region confined to one line, last square in a region, line confined to one region, last square in a row.
Show the full walkthrough (17 steps) — contains the solution
Step 1. Wherever blue ends up among its 4 squares, the same squares fall within reach of it — 1 square in total, impossible regardless of how the colour resolves.
Step 2. Red is down to 3 candidates in rows 5 and 6, columns 5 and 6, and they overlap enough to cover 3 squares elsewhere. Cross those out without deciding anything about red itself.
Step 3. Teal cannot leave row 11 — every one of its open squares (2 open squares) sits there. That row belongs to teal, so every square on it owned by another colour is dead: 11 squares in all.
Step 4. The sea green region is down to one open square, at row 10, column 8. Every colour holds exactly one queen, so that square is forced. Row 10 and column 8 are now spoken for, along with the squares touching that queen.
The board after step 4 — 1 of 11 queens placed. Step 5. Only row 9, column 1 is still open in orange, and since each colour must take a queen, that settles it. That clears row 9, column 1, the rest of the orange region and every square adjacent to it — diagonals included.
Step 6. All of the blue region's remaining squares (2 open squares) lie in row 3. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 10 squares come off.
Step 7. Indigo cannot leave row 1 — every one of its open squares (3 open squares) sits there. That row belongs to indigo, so every square on it owned by another colour is dead: 6 squares in all.
Step 8. All of the slate region's remaining squares (2 open squares) lie in column 9. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 6 squares come off.
Step 9. Only row 8, column 11 is still open in khaki, and since each colour must take a queen, that settles it. That clears row 8, column 11, the rest of the khaki region and every square adjacent to it — diagonals included.
The board after step 9 — 3 of 11 queens placed. Step 10. The teal region is down to one open square, at row 11, column 10. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 11 and column 10, the remaining teal squares, and the ring of neighbours around row 11, column 10.
Step 11. Row 2 has only amber squares left (4 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: 2 squares.
Step 12. 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, 3 squares in all.
Step 13. From here the board cascades. Keep alternating the region sweep and the line sweep and 4 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 4; blue has one square left, so its queen takes row 3, column 2; indigo has one square left, so its queen takes row 1, column 3; row 5 is down to one square, putting a queen on row 5, column 9. 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 5, column 9.
The board after step 13 — 8 of 11 queens placed. Step 14. Red cannot leave row 6 — every one of its open squares (2 open squares) sits there. That row belongs to red, so every square on it owned by another colour is dead: 1 square in all.
Step 15. The pale yellow region is down to one open square, at row 7, column 7. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 7 and column 7, the remaining pale yellow squares, and the ring of neighbours around row 7, column 7.
Step 16. Only row 6, column 5 is still open in red, and since each colour must take a queen, that settles it. Everything else in row 6, in column 5, in red and in the ring around that square is now dead.
Step 17. The amber region is down to one open square, at row 2, column 6. Every colour holds exactly one queen, so that square is forced. Row 2 and column 6 are now spoken for, along with the squares touching that queen.
The board after step 17 — 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 #236
This is puzzle number 236 in the 11x11 collection, rated medium. The grid holds 121 squares split between eleven colored regions, and a finished board carries eleven queens — one in every row, one in every column, one in every color, and never two of them touching, diagonals included.
There is exactly one way to finish #236, and it has been verified. More importantly, you can reach it without ever gambling: at every stage some square is provably right or provably wrong. Boards differ only in how deep you must dig before that proof appears, and the geometry of these eleven regions is what sets the depth.
How the colors divide this board
From smallest to largest, the regions on puzzle #236 are: teal (2 squares), red (3 squares), blue (4 squares), slate (5 squares), orange (5 squares), sea green (6 squares), indigo (7 squares), khaki (8 squares), mint (12 squares), amber (23 squares), pale yellow (46 squares). An even split would hand every color 11 squares, so the teal region is running 9 squares under that average while the pale yellow region is the roomiest area on the grid with 46 squares.
One queen per color, regardless of acreage: that is what turns this uneven split into a solving order. Teal is working with 2 squares while pale yellow has 46 to spare, a gap of 44. Attack the cramped end and the roomy regions tend to resolve themselves.
A region's outline can constrain it more than its size does. Here teal is the most solid, filling 100% of its 1×2 box, and pale yellow the most diffuse at 46% of its 9×11 box. Solid blocks give clean eliminations; diffuse ones spread across the board and stay open longer.
Region by region
The complete breakdown of each region on this board follows, ordered from tightest to roomiest. Skimming the spans first tells you where the board is crowded and where it has slack.
Teal occupies 2 squares within rows 11–11, columns 10–11. It never leaves row 11, so its queen is locked to that row.
Red: 3 squares across rows 5–6, columns 5–6.
Blue covers 4 squares, spanning 2 rows and 3 columns (rows 3–4, columns 1–3).
Slate occupies 5 squares within rows 4–6, columns 8–9.
Orange: 5 squares across rows 9–11, columns 1–2.
Sea green covers 6 squares, spanning 2 rows and 5 columns (rows 10–11, columns 5–9).
Indigo occupies 7 squares within rows 1–2, columns 1–4.
Khaki: 8 squares across rows 8–10, columns 9–11.
Mint covers 12 squares, spanning 4 rows and 5 columns (rows 3–6, columns 1–5).
Amber occupies 23 squares within rows 1–4, columns 4–11.
Pale yellow: 46 squares across rows 3–11, columns 1–11.
Where to start on this board
Open on the tightest color. Here that is teal, confined to 2 squares between rows 11 and 11 and columns 10 and 11. Its queen has nowhere else to go, which means those 1 row and 2 columns carry more constraint than anywhere else on #236.
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, blue, red and sea green 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 #236
A quick way to find the next move is to count how many different colors touch each line. On this board, row 7 is the narrowest, touched by only 1 color. Column 7 is the tightest column, with 3 colors.
Count colors per line and you have a ranking of where to look. The narrowest rows here see only 1 color, so one of that handful must take the row and the rest are squeezed into the other 10 rows. Row 4 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
Past the opening, treat this as an elimination exercise rather than a placement exercise. Each queen takes out a row, a column and its eight neighbours, and the value of a move is measured by how much it removes. Cross everything out as you go and let the board do the remembering.
Two checks, run alternately, will carry you through the 121 squares of this grid. First: has any of the eleven regions been reduced to a single open square? Second: has any row or column? Either answer forces a queen. Players who stall on 11x11 boards almost always run one of those checks and forget the other.
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 #236 is rated medium
Ratings track how generous the opening is. On #236 you get one region pinned to a single row or column, a smallest color of 2 squares, a tightest row crossed by 1 color, and a 44-square gap between the largest and smallest regions. Those four numbers largely explain the medium label.
Difficulty in Queens is never arithmetic and never luck. Every board has one solution and none require guessing. What varies is the length of the chain you must follow before the next queen becomes certain — one or two steps on an easy board, five or six on a hard one, sometimes with several partial eliminations held in play at once.
Stuck on #236 despite the medium rating? The odds strongly favour a bookkeeping error over a hard chain of logic. Re-check each placed queen for its complete set of eliminations, paying particular attention to the four diagonal squares — those are the ones that get overlooked, and one of them is usually sitting on the answer.
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 7 on this board.
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.
Full rules · Strategy library · Puzzle statistics
Questions about this puzzle
How hard is 11x11 Queens puzzle #236?
Puzzle #236 is rated medium. Its smallest color region holds 2 squares, its tightest row is touched by 1 color, and one of its regions is confined to a single row or column, which gives you a forced move early.
Does 11x11 puzzle #236 have only one solution?
Yes. Every puzzle in the 11x11 collection, including #236, 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 #236?
Start with the teal region — the most constrained color on this board, with 2 squares spanning rows 11–11 and columns 10–11. Narrowing the smallest region first removes the most squares elsewhere on the grid.