12x12 Queens Puzzle #244
Difficulty: hard. 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 20-step reasoning is written out below.
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Step-by-step solution for puzzle #244
What follows is a complete solve of puzzle #244, worked the way a person works it rather than the way a computer does. It runs to 20 deductions — 12 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 proof by contradiction.
Techniques this board needs: last square in a region, region confined to one line, pairing argument on rows, last square in a row, region shadow, line confined to one region, proof by contradiction.
Show the full walkthrough (17 steps) — contains the solution
Step 1. Only row 1, column 4 is still open in indigo, and since each colour must take a queen, that settles it. That clears row 1, column 4, the rest of the indigo region and every square adjacent to it — diagonals included.
Step 2. The slate region is down to one open square, at row 5, column 12. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 5 and column 12, the remaining slate squares, and the ring of neighbours around row 5, column 12.
Step 3. Amber cannot leave row 2 — every one of its open squares (2 open squares) sits there. That row belongs to amber, so every square on it owned by another colour is dead: 6 squares in all.
Step 4. All of the teal region's remaining squares (3 open squares) lie in row 11. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 9 squares come off.
The board after step 4 — 2 of 12 queens placed. Step 5. Blue, mint, and red are now boxed into rows 3, 4, and 6 and nothing else. That is 3 colours needing 3 rows, so they fill those rows between them — which locks every remaining colour out and removes 11 squares at once.
Step 6. The pale yellow region is down to one open square, at row 7, column 1. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 7 and column 1, the remaining pale yellow squares, and the ring of neighbours around row 7, column 1.
Step 7. Look along row 6: one square survives, row 6, column 10, which belongs to red. A row cannot be left empty, so the queen goes there. That clears row 6, column 10, the rest of the red region and every square adjacent to it — diagonals included.
Step 8. The amber region is down to one open square, at row 2, column 7. Every colour holds exactly one queen, so that square is forced. Row 2 and column 7 are now spoken for, along with the squares touching that queen.
Step 9. The mint region has 2 squares left, spread across rows 3 and 4, columns 6 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.
The board after step 9 — 5 of 12 queens placed. Step 10. All of the teal region's remaining squares (2 open squares) lie in row 11. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 2 squares come off.
Step 11. Column 2 has only sea green squares left (3 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: 3 squares.
Step 12. Now a short proof by contradiction. Suppose the blue queen went to row 4, column 5. Follow the forced moves that would create and the rose region is left with nowhere to put its queen — impossible. So that square is ruled out for good.
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: blue has one square left, so its queen takes row 3, column 3; mint has one square left, so its queen takes row 4, column 6; teal has one square left, so its queen takes row 11, column 5; khaki has one square left, so its queen takes row 8, column 8. 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 8.
The board after step 13 — 9 of 12 queens placed. Step 14. Orange is down to 3 candidates in rows 9, 10, and 12, columns 9 and 11, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about orange itself.
Step 15. The rose region is down to one open square, at row 12, column 9. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 12 and column 9, the remaining rose squares, and the ring of neighbours around row 12, column 9.
Step 16. Only row 9, column 11 is still open in orange, and since each colour must take a queen, that settles it. Everything else in row 9, in column 11, in orange and in the ring around that square is now dead.
Step 17. The sea green region is down to one open square, at row 10, column 2. Every colour holds exactly one queen, so that square is forced. Row 10 and column 2 are now spoken for, along with the squares touching that queen.
The board after step 17 — 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 #244
This is puzzle number 244 in the 12x12 collection, rated hard. The grid holds 144 squares split between twelve colored regions, and a finished board carries twelve queens — one in every row, one in every column, one in every color, and never two of them touching, diagonals included.
Puzzle #244 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 #244 are: indigo (1 square), slate (1 square), teal (4 squares), pale yellow (7 squares), amber (8 squares), mint (12 squares), rose (14 squares), sea green (17 squares), red (18 squares), khaki (20 squares), blue (21 squares), orange (21 squares). An even split would hand every color 12 squares, so the indigo region is running 11 squares under that average while the orange region is the roomiest area on the grid with 21 squares.
One queen per color, regardless of acreage: that is what turns this uneven split into a solving order. Indigo is working with 1 square while orange has 21 to spare, a gap of 20. Attack the cramped end and the roomy regions tend to resolve themselves.
Shape matters as much as size. The indigo region is the most compact color here, filling 100% of the 1×1 box that encloses it, while pale yellow is the most scattered at 47% of its 5×3 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
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 4–4). It never leaves row 1, so its queen is locked to that row.
Slate occupies 1 square within rows 5–5, columns 12–12. It never leaves row 5, so its queen is locked to that row.
Teal: 4 squares across rows 11–11, columns 4–7. It never leaves row 11, so its queen is locked to that row.
Pale yellow covers 7 squares, spanning 5 rows and 3 columns (rows 3–7, columns 1–3).
Amber occupies 8 squares within rows 1–2, columns 6–11.
Mint: 12 squares across rows 2–5, columns 5–10.
Rose covers 14 squares, spanning 3 rows and 7 columns (rows 10–12, columns 5–11).
Sea green occupies 17 squares within rows 6–12, columns 1–4.
Red: 18 squares across rows 1–7, columns 8–12.
Khaki covers 20 squares, spanning 6 rows and 6 columns (rows 6–11, columns 3–8).
Blue occupies 21 squares within rows 1–6, columns 1–6.
Orange: 21 squares across rows 6–12, columns 8–12.
Where to start on this board
The most constrained color is where a solve should begin, and on #244 that is indigo with 1 square. It reaches from row 1 to row 1 and from column 4 to column 4 — 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. Slate, teal and amber 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 #244
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 8, 9 and 12 are the narrowest, touched by only 3 colors. Columns 1, 2 and 12 are the tightest columns, with 3 colors.
The fewer colors a line touches, the sooner it surrenders its queen. A row meeting just 3 colors has to be claimed by one of them, which pushes every remaining region into the other 11 rows. Row 6, meeting 6 colors, is the opposite case — the busiest line on #244 and the last one you should expect to crack.
Working through the middle game
The middle of #244 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.
Two checks, run alternately, will carry you through the 144 squares of this grid. First: has any of the twelve regions been reduced to a single open square? Second: has any row or column? Either answer forces a queen. Players who stall on 12x12 boards almost always run one of those checks and forget the other.
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 #244 is rated hard
The hard label comes out of four measurable things about #244: five 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.
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.
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.
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 8 on this board.
Here is a shape check that gives nothing away: when #244 is solved, 4 queens sit on the outer edge of the grid and 8 sit inside it, and no queen lands in a corner. A work-in-progress board that clusters its queens in one quadrant while leaving others bare is usually carrying a mistake.
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 #244?
Puzzle #244 is rated hard. Its smallest color region holds 1 square, its tightest row is touched by 3 colors, and five of its regions are confined to a single row or column, which gives you a forced move early.
Does 12x12 puzzle #244 have only one solution?
Yes. Every puzzle in the 12x12 collection, including #244, 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 #244?
Start with the indigo region — the most constrained color on this board, with 1 square spanning rows 1–1 and columns 4–4. Narrowing the smallest region first removes the most squares elsewhere on the grid.