11x11 Queens Puzzle #204
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 25-step reasoning is written out below.
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Step-by-step solution for puzzle #204
What follows is a complete solve of puzzle #204, worked the way a person works it rather than the way a computer does. It runs to 25 deductions — 11 queen placements and 14 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, region confined to one line, pairing argument on columns, proof by contradiction.
Show the full walkthrough (20 steps) — contains the solution
Step 1. Only row 11, column 11 is still open in teal, and since each colour must take a queen, that settles it. That clears row 11, column 11, the rest of the teal region and every square adjacent to it — diagonals included.
Step 2. Indigo is down to 6 candidates in rows 1 and 2, columns 4–8, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about indigo itself.
Step 3. The red region has 5 squares left, spread across rows 5 and 6, columns 4–6. 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. All of the khaki region's remaining squares (2 open squares) lie in column 10. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 8 squares come off.
Step 5. Amber is down to 3 candidates in rows 1 and 2, columns 8 and 9, and they overlap enough to cover 2 squares elsewhere. Cross those out without deciding anything about amber itself.
The board after step 5 — 1 of 11 queens placed. Step 6. The indigo region has 5 squares left, spread across rows 1 and 2, columns 4–7. 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. Sea green cannot leave column 9 — 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: 8 squares in all.
Step 8. The amber region is down to one open square, at row 2, column 8. Every colour holds exactly one queen, so that square is forced. Row 2 and column 8 are now spoken for, along with the squares touching that queen.
Step 9. 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: 3 squares in all.
Step 10. 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: 6 squares come off.
The board after step 10 — 2 of 11 queens placed. Step 11. Mint cannot leave row 4 — every one of its open squares (2 open squares) sits there. That row belongs to mint, so every square on it owned by another colour is dead: 5 squares in all.
Step 12. All of the slate region's remaining squares (3 open squares) lie in column 7. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 4 squares come off.
Step 13. Wherever red ends up among its 3 squares, the same squares fall within reach of it — 1 square in total, impossible regardless of how the colour resolves.
Step 14. Here is the pairing argument. The indigo, red, and pale yellow regions have no open squares outside columns 4–6 — 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: 7 squares come off in one stroke.
Step 15. Only row 4, column 3 is still open in mint, and since each colour must take a queen, that settles it. Everything else in row 4, in column 3, in mint and in the ring around that square is now dead.
The board after step 15 — 3 of 11 queens placed. Step 16. The blue region is down to one open square, at row 3, column 1. Every colour holds exactly one queen, so that square is forced. Row 3 and column 1 are now spoken for, along with the squares touching that queen.
Step 17. Test row 1, column 6 for indigo: place a queen there, run the forced consequences through, and the sea green region is left with nowhere to put its queen. The assumption breaks, so the square is eliminated.
Step 18. The indigo region is down to one open square, at row 1, column 5. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 1 and column 5, the remaining indigo squares, and the ring of neighbours around row 1, column 5.
Step 19. Wherever pale yellow ends up among its 3 squares, the same squares fall within reach of it — 1 square in total, impossible regardless of how the colour resolves.
Step 20. 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: slate has one square left, so its queen takes row 5, column 7; red has one square left, so its queen takes row 6, column 4; khaki has one square left, so its queen takes row 8, column 10; pale yellow has one square left, so its queen takes row 7, column 6; sea green has one square left, so its queen takes row 10, column 9; orange has one square left, so its queen takes row 9, column 2. 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 9, column 2.
The board after step 20 — 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 #204
This is puzzle number 204 in the 11x11 collection, rated hard. 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 #204, 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 #204 are: teal (1 square), red (5 squares), indigo (6 squares), blue (6 squares), khaki (6 squares), amber (8 squares), sea green (8 squares), mint (9 squares), pale yellow (13 squares), orange (29 squares), slate (30 squares). An even split would hand every color 11 squares, so the teal region is running 10 squares under that average while the slate region is the roomiest area on the grid with 30 squares.
Every color takes one queen and one only, whatever its size — which is why the 29 square difference between teal and slate 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 blue region is the most compact color here, filling 100% of the 3×2 box that encloses it, while pale yellow is the most scattered at 52% 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 #204, smallest first. Reading these spans before you place anything is the quickest way to see which parts of the grid are genuinely contested.
Teal: 1 square across rows 11–11, columns 11–11. It never leaves row 11, so its queen is locked to that row.
Red covers 5 squares, spanning 2 rows and 3 columns (rows 5–6, columns 4–6).
Indigo occupies 6 squares within rows 1–2, columns 4–8.
Blue: 6 squares across rows 1–3, columns 1–2.
Khaki covers 6 squares, spanning 4 rows and 2 columns (rows 6–9, columns 10–11).
Amber occupies 8 squares within rows 1–3, columns 8–11.
Sea green: 8 squares across rows 9–11, columns 8–11.
Mint covers 9 squares, spanning 4 rows and 4 columns (rows 1–4, columns 2–5).
Pale yellow occupies 13 squares within rows 7–11, columns 4–8.
Orange: 29 squares across rows 4–11, columns 1–6.
Slate covers 30 squares, spanning 8 rows and 7 columns (rows 2–9, columns 5–11).
Where to start on this board
Open on the tightest color. Here that is teal, confined to 1 square between rows 11 and 11 and columns 11 and 11. Its queen has nowhere else to go, which means those 1 row and 1 column carry more constraint than anywhere else on #204.
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 and red 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 #204
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 4, 5 and 10 are the narrowest, touched by only 3 colors. Columns 1 and 3 are the tightest columns, with 2 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
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.
Resist the plausible-looking queen. On #204 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 #204 is rated hard
The rating reflects how much the board concedes up front. Puzzle #204 has two regions confined to a single row or column, its smallest color holds 1 square, its tightest row meets just 3 colors, and the gap between its largest and smallest regions is 29 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.
Stuck on #204 despite the hard 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.
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 #204 is column 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 #204?
Puzzle #204 is rated hard. Its smallest color region holds 1 square, its tightest row is touched by 3 colors, and two of its regions are confined to a single row or column, which gives you a forced move early.
Does 11x11 puzzle #204 have only one solution?
Yes. Every puzzle in the 11x11 collection, including #204, 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 #204?
Start with the teal region — the most constrained color on this board, with 1 square spanning rows 11–11 and columns 11–11. Narrowing the smallest region first removes the most squares elsewhere on the grid.