11x11 Queens Puzzle #229
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 30-step reasoning is written out below.
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Step-by-step solution for puzzle #229
What follows is a complete solve of puzzle #229, worked the way a person works it rather than the way a computer does. It runs to 30 deductions — 11 queen placements and 19 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, region shadow, pairing argument on rows, proof by contradiction, last square in a region, line confined to one region, last square in a column.
Show the full walkthrough (23 steps) — contains the solution
Step 1. Indigo cannot leave column 5 — every one of its open squares (2 open squares) sits there. That column belongs to indigo, so every square in it owned by another colour is dead: 13 squares in all.
Step 2. Amber is down to 3 candidates in rows 1 and 2, columns 2 and 3, and they overlap enough to cover 2 squares elsewhere. Cross those out without deciding anything about amber itself.
Step 3. The blue region has 4 squares left, spread across rows 3–5, columns 4, 6, and 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 4. Wherever red ends up among its 5 squares, the same squares fall within reach of it — 2 squares in total, impossible regardless of how the colour resolves.
Step 5. Pale yellow is down to 7 candidates in rows 4–7, columns 9–11, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about pale yellow itself.
Step 6. Here is the pairing argument. The indigo and amber regions have no open squares outside rows 1 and 2 — 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: 11 squares come off in one stroke.
The board after step 6 — 0 of 11 queens placed. Step 7. Test row 4, column 7 for blue: place a queen there, run the forced consequences through, and the teal region is left with nowhere to put its queen. The assumption breaks, so the square is eliminated.
Step 8. Now a short proof by contradiction. Suppose the blue queen went to row 5, column 6. Follow the forced moves that would create and the teal region is left with nowhere to put its queen — impossible. So that square is ruled out for good.
Step 9. The blue region has 2 squares left, spread across rows 3 and 4, columns 4 and 6. 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 10. Here is the pairing argument. The blue and mint regions have no open squares outside rows 3 and 4 — 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: 6 squares come off in one stroke.
Step 11. Test row 1, column 2 for amber: place a queen there, run the forced consequences through, and column 1 runs out of open squares entirely. The assumption breaks, so the square is eliminated.
Step 12. Now a short proof by contradiction. Suppose the mint queen went to row 3, column 8. Follow the forced moves that would create and the orange region is left with nowhere to put its queen — impossible. So that square is ruled out for good.
The board after step 12 — 0 of 11 queens placed. Step 13. Test row 2, column 5 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 14. 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 15. Only row 2, column 2 is still open in amber, and since each colour must take a queen, that settles it. Everything else in row 2, in column 2, in amber and in the ring around that square is now dead.
Step 16. Every open square left in column 3 (7 open squares) belongs to the khaki region. Since that column must contain a queen, khaki is the colour that supplies it — so khaki squares anywhere else on the board are out, 16 squares in all.
Step 17. Column 1 has only slate squares left (2 open squares). The column needs a queen and only slate can provide one, which pins that colour to this column and kills its squares elsewhere: 1 square.
The board after step 17 — 2 of 11 queens placed. Step 18. Column 4 now has exactly one open square, row 3, column 4, in the blue region. Columns must each hold a queen, so that placement is forced. That clears row 3, column 4, the rest of the blue region and every square adjacent to it — diagonals included.
Step 19. Column 6 has only sea green squares left (2 open squares). The column needs a queen and only sea green can provide one, which pins that colour to this column and kills its squares elsewhere: 4 squares.
Step 20. All of the sea green region's remaining squares (2 open squares) lie in column 6. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 1 square come off.
Step 21. Column 7 has only red squares left (2 open squares). The column needs a queen and only red can provide one, which pins that colour to this column and kills its squares elsewhere: 3 squares.
Step 22. Here is the pairing argument. The slate and red regions have no open squares outside rows 5 and 6 — 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.
Step 23. From here the board cascades. Keep alternating the region sweep and the line sweep and 8 queens fall out in order without any new idea being needed: pale yellow has one square left, so its queen takes row 7, column 10; orange has one square left, so its queen takes row 9, column 11; mint has one square left, so its queen takes row 4, column 8; red has one square left, so its queen takes row 6, column 7; slate has one square left, so its queen takes row 5, column 1; sea green has one square left, so its queen takes row 10, column 6; teal has one square left, so its queen takes row 11, column 9; khaki has one square left, so its queen takes row 8, 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 8, column 3.
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 #229
Puzzle #229 is one of the hard-rated boards in the 11x11 set. Eleven colors divide its 121 squares, and you win by placing eleven queens so that each row, each column and each color holds exactly one, with no two queens adjacent in any direction.
As with every puzzle in this collection, #229 has a single verified solution and needs no guesswork. Each queen follows from something already visible. What the board controls is tempo — how soon the first forced move shows up and how far apart the rest are spaced — and that is a direct consequence of how these colors are cut.
How the colors divide this board
From smallest to largest, the regions on puzzle #229 are: indigo (2 squares), amber (4 squares), red (5 squares), sea green (6 squares), pale yellow (7 squares), blue (8 squares), orange (8 squares), teal (8 squares), slate (14 squares), mint (23 squares), khaki (36 squares). An even split would hand every color 11 squares, so the indigo region is running 9 squares under that average while the khaki region is the roomiest area on the grid with 36 squares.
Why does the split matter? Because a region's square count has no bearing on how many queens it gets — the answer is always one. So indigo, with 2 squares, is under far more pressure than khaki with 36. A 34-square gap like this one rewards players who start where the choices are fewest.
Shape matters as much as size. The indigo region is the most compact color here, filling 100% of the 2×1 box that encloses it, while sea green is the most scattered at 50% of its 3×4 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
Below is every color on #229 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.
Indigo covers 2 squares, spanning 2 rows and 1 column (rows 1–2, columns 5–5). It sits wholly inside column 5, so its queen must be in that column.
Amber occupies 4 squares within rows 1–2, columns 2–4.
Red: 5 squares across rows 5–8, columns 7–8.
Sea green covers 6 squares, spanning 3 rows and 4 columns (rows 8–10, columns 6–9).
Pale yellow occupies 7 squares within rows 4–7, columns 9–11.
Blue: 8 squares across rows 2–5, columns 4–7.
Orange covers 8 squares, spanning 4 rows and 3 columns (rows 7–10, columns 9–11).
Teal occupies 8 squares within rows 10–11, columns 7–11.
Slate: 14 squares across rows 1–6, columns 1–4.
Mint covers 23 squares, spanning 5 rows and 6 columns (rows 1–5, columns 6–11).
Khaki occupies 36 squares within rows 5–11, columns 1–7.
Where to start on this board
Indigo is the natural opening on #229: it is the smallest region on the grid at 2 squares, boxed into rows 1–2 and columns 5–5. Since one of those squares must hold a queen, that block of 2 rows and 1 column is the most contested part of the board.
Because indigo stays inside column 5, its queen belongs to that column and no other region may use it. Cross out the rest of column 5 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. Amber 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 #229
A quick way to find the next move is to count how many different colors touch each line. On this board, row 11 is the narrowest, touched by only 2 colors. Column 1 is the tightest column, with 2 colors.
A line with few colors is a line close to resolving. Where only 2 colors appear, one of them owns the row outright and the others must fit into the remaining 10 rows. Row 5 is the crowded extreme at 6 colors — worth revisiting later, not now.
Working through the middle game
After the first few queens the puzzle becomes bookkeeping. A placed queen wipes its row, its column and every square it touches — as many as eight neighbours — so the space collapses quickly. Record those eliminations on the board instead of carrying them in your head, and the next forced move tends to announce itself.
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.
A placement without a reason is a guess. Because this board has exactly one solution, a guess that happens to be wrong will not announce itself for several moves — and unwinding it is slower than simply finishing the eliminations first.
Why puzzle #229 is rated hard
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 34. Lopsided grids with flat regions fall quickly; balanced ones like this take more patience.
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.
A board that feels above its rating is nearly always a board with a missing X. Audit every queen on the grid: full row cleared, full column cleared, all eight touching squares cleared. Diagonals are the common omission, and missing one is far more often the cause of a stall than any genuine difficulty in the puzzle.
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.
Learn the pairing argument and you will use it on every board, this one included. If two colors can only sit inside the same two rows, between them they consume both rows and every other color is shut out. It generalises to any matching count — three colors across three rows, four across four. On #229, start hunting for it near row 11.
A non-spoiling distribution check: solved, #229 carries 4 queens on the perimeter against 7 queens inside, with the corners empty. Because no two queens may touch, real solutions always look fairly evenly spread — a lopsided board in progress is a warning sign.
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 #229?
Puzzle #229 is rated hard. 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 #229 have only one solution?
Yes. Every puzzle in the 11x11 collection, including #229, 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 #229?
Start with the indigo region — the most constrained color on this board, with 2 squares spanning rows 1–2 and columns 5–5. Narrowing the smallest region first removes the most squares elsewhere on the grid.