12x12 Queens Puzzle #99
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 18-step reasoning is written out below.
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Step-by-step solution for puzzle #99
What follows is a complete solve of puzzle #99, worked the way a person works it rather than the way a computer does. It runs to 18 deductions — 12 queen placements and 6 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 region confined to one line.
Techniques this board needs: region confined to one line, last square in a region.
Show the full walkthrough (11 steps) — contains the solution
Step 1. Indigo cannot leave row 1 — every one of its open squares (6 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 2. The amber region is down to one open square, at row 2, column 1. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 2 and column 1, the remaining amber squares, and the ring of neighbours around row 2, column 1.
Step 3. Only row 10, column 2 is still open in sea green, and since each colour must take a queen, that settles it. Everything else in row 10, in column 2, in sea green and in the ring around that square is now dead.
Step 4. The pale yellow region is down to one open square, at row 7, column 3. Every colour holds exactly one queen, so that square is forced. Row 7 and column 3 are now spoken for, along with the squares touching that queen.
The board after step 4 — 3 of 12 queens placed. Step 5. Blue cannot leave row 3 — every one of its open squares (2 open squares) sits there. That row belongs to blue, so every square on it owned by another colour is dead: 8 squares in all.
Step 6. All of the mint region's remaining squares (2 open squares) lie in row 4. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 8 squares come off.
Step 7. Only row 5, column 4 is still open in slate, and since each colour must take a queen, that settles it. Everything else in row 5, in column 4, in slate and in the ring around that square is now dead.
The board after step 7 — 4 of 12 queens placed. Step 8. All of the red region's remaining squares (2 open squares) lie in row 6. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 5 squares come off.
Step 9. Khaki cannot leave column 5 — every one of its open squares (2 open squares) sits there. That column belongs to khaki, so every square in it owned by another colour is dead: 2 squares in all.
Step 10. All of the rose region's remaining squares (3 open squares) lie in column 6. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 3 squares come off.
Step 11. 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: mint has one square left, so its queen takes row 4, column 7; blue has one square left, so its queen takes row 3, column 10; red has one square left, so its queen takes row 6, column 11; teal has one square left, so its queen takes row 11, column 8; indigo has one square left, so its queen takes row 1, column 9; khaki has one square left, so its queen takes row 8, column 5; rose has one square left, so its queen takes row 12, column 6; orange has one square left, so its queen takes row 9, column 12. 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 12.
The board after step 11 — 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 #99
12x12 puzzle #99 is rated hard. 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 #99 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 #99 are: pale yellow (3 squares), sea green (4 squares), teal (5 squares), indigo (6 squares), amber (6 squares), blue (8 squares), mint (8 squares), rose (11 squares), red (17 squares), slate (21 squares), khaki (24 squares), orange (31 squares). An even split would hand every color 12 squares, so the pale yellow region is running 9 squares under that average while the orange region is the roomiest area on the grid with 31 squares.
That imbalance is the first thing to read, because every region takes exactly one queen regardless of how much space it owns. Pale yellow has only 3 places to put its queen; orange has 31. 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 indigo is the most solid, filling 100% of its 1×6 box, and khaki the most diffuse at 43% of its 7×8 box. Solid blocks give clean eliminations; diffuse ones spread across the board and stay open longer.
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.
Pale yellow: 3 squares across rows 7–7, columns 1–3. It never leaves row 7, so its queen is locked to that row.
Sea green covers 4 squares, spanning 3 rows and 2 columns (rows 10–12, columns 1–2).
Teal occupies 5 squares within rows 9–12, columns 7–8.
Indigo: 6 squares across rows 1–1, columns 6–11. It never leaves row 1, so its queen is locked to that row.
Amber covers 6 squares, spanning 2 rows and 5 columns (rows 1–2, columns 1–5).
Blue occupies 8 squares within rows 1–3, columns 8–12.
Mint: 8 squares across rows 2–4, columns 5–7.
Rose covers 11 squares, spanning 4 rows and 5 columns (rows 9–12, columns 2–6).
Red occupies 17 squares within rows 3–7, columns 7–12.
Slate: 21 squares across rows 2–7, columns 1–5.
Khaki covers 24 squares, spanning 7 rows and 8 columns (rows 5–11, columns 1–8).
Orange occupies 31 squares within rows 6–12, columns 6–12.
Where to start on this board
Begin where the choices are fewest. On this board that means pale yellow, which owns just 3 squares inside a 1×3 window running from row 7 to row 7 and column 1 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 pale yellow never leaves row 7, its queen must be in that row — and that instantly settles row 7 for everyone else. Sweep along it and X out every square that is not pale yellow. 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 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 #99
A quick way to find the next move is to count how many different colors touch each line. On this board, row 8 is the narrowest, touched by only 2 colors. Column 12 is the tightest column, with 3 colors.
Those lines matter because a row touched by few colors gives its queen away sooner. If a row meets only 2 colors, then one of those regions has to own it, and every other region is competing for the remaining 11 rows. By contrast row 11 meets 5 colors — the most crowded line here, and the one least likely to resolve early. Spend your attention accordingly.
Working through the middle game
The middle of #99 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.
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.
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 #99 is rated hard
The hard label comes out of four measurable things about #99: two of its regions are locked to one row or column, its smallest color spans 3 squares, its least crowded row meets 2 colors, and its largest and smallest regions differ by 28. Boards that score tight on those measures give up their first queen fast.
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 #99 the place to look for one is around row 8.
As a sanity check rather than a spoiler: the finished solution to #99 puts 4 queens on the outer border and 8 queens in the interior, with none in a corner. If your part-finished grid has queens bunched into one area while whole stretches sit empty, something probably went wrong a few moves back.
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 #99?
Puzzle #99 is rated hard. Its smallest color region holds 3 squares, its tightest row is touched by 2 colors, and two of its regions are confined to a single row or column, which gives you a forced move early.
Does 12x12 puzzle #99 have only one solution?
Yes. Every puzzle in the 12x12 collection, including #99, 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 #99?
Start with the pale yellow region — the most constrained color on this board, with 3 squares spanning rows 7–7 and columns 1–3. Narrowing the smallest region first removes the most squares elsewhere on the grid.