12x12 Queens Puzzle #118
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 28-step reasoning is written out below.
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Step-by-step solution for puzzle #118
What follows is a complete solve of puzzle #118, worked the way a person works it rather than the way a computer does. It runs to 28 deductions — 12 queen placements and 16 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, line confined to one region, proof by contradiction, last square in a column, pairing argument on columns.
Show the full walkthrough (20 steps) — contains the solution
Step 1. Only row 6, column 1 is still open in red, and since each colour must take a queen, that settles it. That clears row 6, column 1, the rest of the red region and every square adjacent to it — diagonals included.
Step 2. All of the indigo region's remaining squares (2 open squares) lie in row 1. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 11 squares come off.
Step 3. The amber region has 5 squares left, spread across rows 2–4, columns 6–8. 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 teal ends up among its 4 squares, the same squares fall within reach of it — 2 squares in total, impossible regardless of how the colour resolves.
Step 5. Amber, blue, and mint are now boxed into rows 2–4 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 8 squares at once.
The board after step 5 — 1 of 12 queens placed. Step 6. Every open square left in column 2 (5 open squares) belongs to the sea green region. Since that column must contain a queen, sea green is the colour that supplies it — so sea green squares anywhere else on the board are out, 15 squares in all.
Step 7. Test row 2, column 7 for amber: place a queen there, run the forced consequences through, and the mint 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 amber queen went to row 3, column 8. 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 amber region has 3 squares left, spread across rows 2–4, columns 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 10. Now a short proof by contradiction. Suppose the indigo queen went to row 1, column 12. 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.
The board after step 10 — 1 of 12 queens placed. Step 11. Only row 1, column 11 is still open in indigo, and since each colour must take a queen, that settles it. Everything else in row 1, in column 11, in indigo and in the ring around that square is now dead.
Step 12. Now a short proof by contradiction. Suppose the amber queen went to row 3, column 7. 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. Wherever amber ends up among its 2 squares, the same squares fall within reach of it — 1 square in total, impossible regardless of how the colour resolves.
Step 14. Now a short proof by contradiction. Suppose the amber queen went to row 4, column 7. 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 15. 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: amber has one square left, so its queen takes row 2, column 6; column 3 is down to one square, putting a queen on row 5, column 3; pale yellow has one square left, so its queen takes row 7, column 12; khaki has one square left, so its queen takes row 8, column 10. 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 10.
The board after step 15 — 6 of 12 queens placed. Step 16. Rose cannot leave row 12 — every one of its open squares (2 open squares) sits there. That row belongs to rose, so every square on it owned by another colour is dead: 3 squares in all.
Step 17. Teal is down to 2 candidates in rows 10 and 11, columns 7 and 9, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about teal itself.
Step 18. Orange cannot leave row 9 — every one of its open squares (4 open squares) sits there. That row belongs to orange, so every square on it owned by another colour is dead: 1 square in all.
Step 19. Here is the pairing argument. The mint and rose regions have no open squares outside columns 8 and 9 — 2 colours confined to 2 columns. Between them they must take one column each, in some order, so every other colour is shut out of all of them: 2 squares come off in one stroke.
Step 20. 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: teal has one square left, so its queen takes row 11, column 7; sea green has one square left, so its queen takes row 10, column 2; rose has one square left, so its queen takes row 12, column 9; mint has one square left, so its queen takes row 4, column 8; blue has one square left, so its queen takes row 3, column 4; orange has one square left, so its queen takes row 9, column 5. 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 5.
The board after step 20 — 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 #118
Board #118 of the 12x12 bank carries a hard rating. Its 144 squares are shared between twelve colored regions, and the solution places twelve queens: one per row, one per column, one per region, none of them side by side or corner to corner.
Like every board on this site, #118 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 #118 are: red (1 square), indigo (2 squares), teal (4 squares), khaki (7 squares), amber (8 squares), blue (13 squares), orange (13 squares), mint (14 squares), rose (15 squares), pale yellow (16 squares), slate (22 squares), sea green (29 squares). An even split would hand every color 12 squares, so the red region is running 11 squares under that average while the sea green region is the roomiest area on the grid with 29 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 red, with 1 square, is under far more pressure than sea green with 29. A 28-square gap like this one rewards players who start where the choices are fewest.
Look at arrangement as well as area. Indigo is the densest region on this grid at 100% of a 1×2 frame; khaki is the loosest, occupying only 44% of its 4×4 frame. The loose one reaches into more rows and columns, which is exactly why it usually settles last.
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.
Red covers 1 square, spanning 1 row and 1 column (rows 6–6, columns 1–1). It never leaves row 6, so its queen is locked to that row.
Indigo occupies 2 squares within rows 1–1, columns 11–12. It never leaves row 1, so its queen is locked to that row.
Teal: 4 squares across rows 10–11, columns 7–9.
Khaki covers 7 squares, spanning 4 rows and 4 columns (rows 6–9, columns 9–12).
Amber occupies 8 squares within rows 1–4, columns 5–8.
Blue: 13 squares across rows 1–4, columns 1–6.
Orange covers 13 squares, spanning 4 rows and 5 columns (rows 7–10, columns 4–8).
Mint occupies 14 squares within rows 1–4, columns 8–12.
Rose: 15 squares across rows 8–12, columns 8–12.
Pale yellow covers 16 squares, spanning 5 rows and 6 columns (rows 3–7, columns 7–12).
Slate occupies 22 squares within rows 2–8, columns 1–6.
Sea green: 29 squares across rows 6–12, columns 1–7.
Where to start on this board
Red is the natural opening on #118: it is the smallest region on the grid at 1 square, boxed into rows 6–6 and columns 1–1. Since one of those squares must hold a queen, that block of 1 row and 1 column is the most contested part of the board.
Because red never leaves row 6, its queen must be in that row — and that instantly settles row 6 for everyone else. Sweep along it and X out every square that is not red. 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 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 #118
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 5 and 12 are the narrowest, touched by only 2 colors. Columns 2 and 3 are the tightest columns, with 3 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 11 rows. Row 8 is the crowded extreme at 5 colors — worth revisiting later, not now.
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.
Keep alternating between two views of the board. In the region view you ask which of the twelve 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 12x12 board unwinds.
The trap on a board like this is placing a queen that is merely plausible. Every placement should be traceable to an elimination you can point at. If you cannot name the rule that forced it, you are guessing — and on a single-solution grid a guess costs more to unwind than the deduction would have taken to find.
Why puzzle #118 is rated hard
Ratings track how generous the opening is. On #118 you get three regions pinned to a single row or column, a smallest color of 1 square, a tightest row crossed by 2 colors, and a 28-square gap between the largest and smallest regions. Those four numbers largely explain the hard label.
The scale has nothing to do with maths or luck — every puzzle here is solvable by deduction and has exactly one answer. It measures reasoning depth: how many eliminations must stack up before a placement becomes provable. That depth is what separates a hard board from the rest.
If #118 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.
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 #118, start hunting for it near row 5.
A non-spoiling distribution check: solved, #118 carries 4 queens on the perimeter against 8 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 12x12 Queens puzzle #118?
Puzzle #118 is rated hard. Its smallest color region holds 1 square, its tightest row is touched by 2 colors, and three of its regions are confined to a single row or column, which gives you a forced move early.
Does 12x12 puzzle #118 have only one solution?
Yes. Every puzzle in the 12x12 collection, including #118, 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 #118?
Start with the red region — the most constrained color on this board, with 1 square spanning rows 6–6 and columns 1–1. Narrowing the smallest region first removes the most squares elsewhere on the grid.