12x12 Queens Puzzle #115
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 17-step reasoning is written out below.
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Step-by-step solution for puzzle #115
What follows is a complete solve of puzzle #115, worked the way a person works it rather than the way a computer does. It runs to 17 deductions — 12 queen placements and 5 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 shadow.
Techniques this board needs: last square in a region, region confined to one line, region shadow.
Show the full walkthrough (9 steps) — contains the solution
Step 1. Only row 1, column 11 is still open in indigo, and since each colour must take a queen, that settles it. That clears row 1, column 11, the rest of the indigo region and every square adjacent to it — diagonals included.
Step 2. The pale yellow region is down to one open square, at row 7, column 12. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 7 and column 12, the remaining pale yellow squares, and the ring of neighbours around row 7, column 12.
Step 3. Only row 10, column 10 is still open in sea green, and since each colour must take a queen, that settles it. Everything else in row 10, in column 10, in sea green and in the ring around that square is now dead.
The board after step 3 — 3 of 12 queens placed. Step 4. All of the amber region's remaining squares (2 open squares) lie in row 2. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 9 squares come off.
Step 5. Blue is down to 3 candidates in rows 3 and 4, columns 1 and 2, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about blue itself.
Step 6. The mint region has 4 squares left, spread across rows 3 and 4, columns 7–9. 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 6 — 3 of 12 queens placed. Step 7. Wherever slate ends up among its 4 squares, the same squares fall within reach of it — 1 square in total, impossible regardless of how the colour resolves.
Step 8. All of the red region's remaining squares (4 open squares) lie in column 1. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 4 squares come off.
Step 9. From here the board cascades. Keep alternating the region sweep and the line sweep and 9 queens fall out in order without any new idea being needed: blue has one square left, so its queen takes row 3, column 2; mint has one square left, so its queen takes row 4, column 9; slate has one square left, so its queen takes row 5, column 5; amber has one square left, so its queen takes row 2, column 6; teal has one square left, so its queen takes row 11, column 3; orange has one square left, so its queen takes row 9, column 8; rose has one square left, so its queen takes row 12, column 7; khaki has one square left, so its queen takes row 8, column 4; red has one square left, so its queen takes row 6, column 1. 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 1.
The board after step 9 — 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 #115
12x12 puzzle #115 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.
Like every board on this site, #115 has been verified to have exactly one valid solution, and that solution is reachable by deduction alone. You never have to guess and then unwind; every queen can be justified by something already visible on the grid. What changes from puzzle to puzzle is where the first certainty appears and how long the chain of reasoning runs before the next one — and that is entirely a product of how these particular colors are shaped.
How the colors divide this board
From smallest to largest, the regions on puzzle #115 are: indigo (1 square), pale yellow (3 squares), amber (6 squares), slate (6 squares), red (6 squares), teal (7 squares), blue (10 squares), sea green (10 squares), orange (18 squares), rose (22 squares), mint (26 squares), khaki (29 squares). An even split would hand every color 12 squares, so the indigo region is running 11 squares under that average while the khaki 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. Indigo has only 1 place to put its queen; khaki 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 indigo is the most solid, filling 100% of its 1×1 box, and orange the most diffuse at 45% of its 8×5 box. Solid blocks give clean eliminations; diffuse ones spread across the board and stay open longer.
Region by region
The complete breakdown of each region on this board follows, ordered from tightest to roomiest. Skimming the spans first tells you where the board is crowded and where it has slack.
Indigo covers 1 square, spanning 1 row and 1 column (rows 1–1, columns 11–11). It never leaves row 1, so its queen is locked to that row.
Pale yellow occupies 3 squares within rows 7–8, columns 11–12.
Amber: 6 squares across rows 1–2, columns 4–7.
Slate covers 6 squares, spanning 3 rows and 4 columns (rows 3–5, columns 3–6).
Red occupies 6 squares within rows 5–10, columns 1–1. It sits wholly inside column 1, so its queen must be in that column.
Teal: 7 squares across rows 8–12, columns 1–3.
Blue covers 10 squares, spanning 4 rows and 4 columns (rows 1–4, columns 1–4).
Sea green occupies 10 squares within rows 8–12, columns 10–12.
Orange: 18 squares across rows 4–11, columns 6–10.
Rose covers 22 squares, spanning 5 rows and 9 columns (rows 8–12, columns 2–10).
Mint occupies 26 squares within rows 1–6, columns 7–12.
Khaki: 29 squares across rows 4–10, columns 2–8.
Where to start on this board
Begin where the choices are fewest. On this board that means indigo, which owns just 1 square inside a 1×1 window running from row 1 to row 1 and column 11 to column 11. A queen is guaranteed somewhere in there, so every line that window crosses is under pressure from the very first move.
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. Amber and pale yellow 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 #115
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 2, 3 and 12 are the narrowest, touched by only 3 colors. Columns 1, 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 8 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
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.
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 #115 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 #115 is rated hard
Ratings track how generous the opening is. On #115 you get three regions pinned to a single row or column, a smallest color of 1 square, a tightest row crossed by 3 colors, and a 28-square gap between the largest and smallest regions. Those four numbers largely explain the hard label.
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.
If #115 feels harder than its rating suggests, the usual culprit is incomplete marking rather than a difficult deduction. Check that every queen already on the grid has its full cross of eliminations recorded — including the diagonal neighbours, which are by far the easiest to miss. More stalled solves come from one forgotten diagonal X than from any genuinely deep chain of logic.
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 #115 the place to look for one is around row 2.
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 #115?
Puzzle #115 is rated hard. Its smallest color region holds 1 square, its tightest row is touched by 3 colors, and three of its regions are confined to a single row or column, which gives you a forced move early.
Does 12x12 puzzle #115 have only one solution?
Yes. Every puzzle in the 12x12 collection, including #115, 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 #115?
Start with the indigo region — the most constrained color on this board, with 1 square spanning rows 1–1 and columns 11–11. Narrowing the smallest region first removes the most squares elsewhere on the grid.