12x12 Queens Puzzle #223
Difficulty: easy. Place 12 queens on this 12x12 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 26-step reasoning is written out below.
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Step-by-step solution for puzzle #223
What follows is a complete solve of puzzle #223, worked the way a person works it rather than the way a computer does. It runs to 26 deductions — 12 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 confined to one line, region shadow, pairing argument on rows, proof by contradiction, pairing argument on columns.
Show the full walkthrough (21 steps) — contains the solution
Step 1. Only row 10, column 3 is still open in sea green, and since each colour must take a queen, that settles it. That clears row 10, column 3, the rest of the sea green region and every square adjacent to it — diagonals included.
Step 2. The orange region is down to one open square, at row 9, column 1. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 9 and column 1, the remaining orange squares, and the ring of neighbours around row 9, column 1.
Step 3. Only row 12, column 2 is still open in rose, and since each colour must take a queen, that settles it. Everything else in row 12, in column 2, in rose and in the ring around that square is now dead.
Step 4. All of the blue region's remaining squares (2 open squares) lie in column 8. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 11 squares come off.
Step 5. 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: 5 squares in all.
The board after step 5 — 3 of 12 queens placed. Step 6. The pale yellow region has 3 squares left, spread across rows 7 and 8, columns 9 and 10. 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 7. Wherever slate 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 8. Here is the pairing argument. The pale yellow and khaki regions have no open squares outside rows 7 and 8 — 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: 8 squares come off in one stroke.
Step 9. The slate region has 2 squares left, spread across rows 5 and 6, columns 7 and 9. 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 10. Wherever red ends up among its 2 squares, the same squares fall within reach of it — 3 squares in total, impossible regardless of how the colour resolves.
Step 11. Test row 1, column 9 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.
The board after step 11 — 3 of 12 queens placed. Step 12. Now a short proof by contradiction. Suppose the indigo queen went to row 1, column 10. 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 13. Test row 1, column 11 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 6. Follow the forced moves that would create and the khaki region is left with nowhere to put its queen — impossible. So that square is ruled out for good.
Step 15. Indigo and slate are now boxed into columns 7 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 3 squares at once.
Step 16. The pale yellow region is down to one open square, at row 7, column 10. Every colour holds exactly one queen, so that square is forced. Row 7 and column 10 are now spoken for, along with the squares touching that queen.
The board after step 16 — 4 of 12 queens placed. Step 17. Only row 8, column 12 is still open in khaki, and since each colour must take a queen, that settles it. That clears row 8, column 12, the rest of the khaki region and every square adjacent to it — diagonals included.
Step 18. The teal region is down to one open square, at row 11, column 5. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 11 and column 5, the remaining teal squares, and the ring of neighbours around row 11, column 5.
Step 19. Test row 2, column 7 for indigo: place a queen there, run the forced consequences through, and the slate region is left with nowhere to put its queen. The assumption breaks, so the square is eliminated.
Step 20. Now a short proof by contradiction. Suppose the indigo queen went to row 2, column 9. 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 21. 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: indigo has one square left, so its queen takes row 1, column 7; slate has one square left, so its queen takes row 5, column 9; blue has one square left, so its queen takes row 3, column 8; amber has one square left, so its queen takes row 2, column 4; mint has one square left, so its queen takes row 4, column 11; red has one square left, so its queen takes row 6, column 6. 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 6.
The board after step 21 — 12 of 12 queens placed.
That completes the board: 12 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 12x12 Queens puzzle #223
12x12 puzzle #223 is rated easy. Twelve colored regions cover its 144 squares, and your job is to seat twelve queens so that every row, column and color contains exactly one — with no queen touching another, including diagonally.
Puzzle #223 has been checked to admit exactly one arrangement of queens, and every step toward it is deducible from what is already on the board. There is no point at which you are expected to pick a square and hope. The only thing that differs between boards is how quickly the first certainty surfaces, and that depends entirely on the shapes the colors happen to take here.
How the colors divide this board
From smallest to largest, the regions on puzzle #223 are: sea green (1 square), blue (2 squares), orange (2 squares), slate (7 squares), khaki (8 squares), rose (10 squares), indigo (11 squares), teal (13 squares), mint (16 squares), pale yellow (19 squares), amber (26 squares), red (29 squares). An even split would hand every color 12 squares, so the sea green region is running 11 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. Sea green 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 2×1 box, and red the most diffuse at 40% of its 9×8 box. Solid blocks give clean eliminations; diffuse ones spread across the board and stay open longer.
Region by region
Here is the full footprint of every color on puzzle #223, smallest first. Reading these spans before you place anything is the quickest way to see which parts of the grid are genuinely contested.
Sea green covers 1 square, spanning 1 row and 1 column (rows 10–10, columns 3–3). It never leaves row 10, so its queen is locked to that row.
Blue occupies 2 squares within rows 3–4, columns 8–8. It sits wholly inside column 8, so its queen must be in that column.
Orange: 2 squares across rows 9–10, columns 1–1. It sits wholly inside column 1, so its queen must be in that column.
Slate covers 7 squares, spanning 4 rows and 3 columns (rows 4–7, columns 7–9).
Khaki occupies 8 squares within rows 7–10, columns 10–12.
Rose: 10 squares across rows 8–12, columns 1–3.
Indigo covers 11 squares, spanning 3 rows and 6 columns (rows 1–3, columns 6–11).
Teal occupies 13 squares within rows 10–12, columns 3–8.
Mint: 16 squares across rows 1–6, columns 10–12.
Pale yellow covers 19 squares, spanning 6 rows and 5 columns (rows 7–12, columns 8–12).
Amber occupies 26 squares within rows 1–8, columns 1–7.
Red: 29 squares across rows 3–11, columns 1–8.
Where to start on this board
Begin where the choices are fewest. On this board that means sea green, which owns just 1 square inside a 1×1 window running from row 10 to row 10 and column 3 to column 3. A queen is guaranteed somewhere in there, so every line that window crosses is under pressure from the very first move.
Because sea green never leaves row 10, its queen must be in that row — and that instantly settles row 10 for everyone else. Sweep along it and X out every square that is not sea green. 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. Blue and orange 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 #223
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 1, 2 and 12 are the narrowest, touched by only 3 colors. Columns 2, 4, 5, 9 and 12 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 11 rows. Row 10 sits at the far end with 7 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 twelve queens to seat and twelve regions competing over 144 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 12x12 boards quickly and players who stall halfway.
Resist the plausible-looking queen. On #223 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 #223 is rated easy
The rating reflects how much the board concedes up front. Puzzle #223 has four 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 28 squares. Flat, lopsided boards open quickly; even, sprawling ones make you earn the first placement.
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.
When a board plays tougher than its label, look for a missed mark before you look for a clever deduction. Walk back over every queen you have placed and confirm the full row, the full column and all eight surrounding squares are crossed out. The diagonal neighbours are the ones players skip, and a single skipped diagonal will hide the next forced move indefinitely.
Techniques that work well at 12x12
At 12x12 you are managing 144 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 #223 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 8 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 12x12 Queens puzzle #223?
Puzzle #223 is rated easy. 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 12x12 puzzle #223 have only one solution?
Yes. Every puzzle in the 12x12 collection, including #223, has been verified to have exactly one valid arrangement of twelve queens, and it can always be reached by logic alone — no guessing or backtracking needed.
Where should I place my first queen on puzzle #223?
Start with the sea green region — the most constrained color on this board, with 1 square spanning rows 10–10 and columns 3–3. Narrowing the smallest region first removes the most squares elsewhere on the grid.