12x12 Queens Puzzle #158
Difficulty: medium. 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 24-step reasoning is written out below.
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Step-by-step solution for puzzle #158
What follows is a complete solve of puzzle #158, worked the way a person works it rather than the way a computer does. It runs to 24 deductions — 12 queen placements and 12 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 columns, proof by contradiction.
Show the full walkthrough (19 steps) — contains the solution
Step 1. Only row 1, column 3 is still open in indigo, and since each colour must take a queen, that settles it. That clears row 1, column 3, the rest of the indigo region and every square adjacent to it — diagonals included.
Step 2. The mint region is down to one open square, at row 4, column 12. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 4 and column 12, the remaining mint squares, and the ring of neighbours around row 4, column 12.
Step 3. Only row 12, column 7 is still open in rose, and since each colour must take a queen, that settles it. Everything else in row 12, in column 7, in rose and in the ring around that square is now dead.
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: 6 squares come off.
Step 5. Only row 3, column 1 is still open in blue, and since each colour must take a queen, that settles it. That clears row 3, column 1, the rest of the blue region and every square adjacent to it — diagonals included.
The board after step 5 — 4 of 12 queens placed. Step 6. The slate region has 3 squares left, spread across rows 5 and 6, columns 9–11. 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 khaki ends up among its 3 squares, the same squares fall within reach of it — 2 squares in total, impossible regardless of how the colour resolves.
Step 8. All of the slate region's remaining squares (2 open squares) lie in row 5. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 5 squares come off.
Step 9. The teal region has 3 squares left, spread across rows 8, 9, and 11, columns 2 and 4. 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. Here is the pairing argument. The amber and khaki regions have no open squares outside columns 10 and 11 — 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: 7 squares come off in one stroke.
The board after step 10 — 4 of 12 queens placed. Step 11. Only row 5, column 9 is still open in slate, and since each colour must take a queen, that settles it. Everything else in row 5, in column 9, in slate and in the ring around that square is now dead.
Step 12. The orange region is down to one open square, at row 9, column 8. Every colour holds exactly one queen, so that square is forced. Row 9 and column 8 are now spoken for, along with the squares touching that queen.
Step 13. Wherever red ends up among its 3 squares, the same squares fall within reach of it — 2 squares in total, impossible regardless of how the colour resolves.
Step 14. Teal is down to 2 candidates in rows 8 and 11, columns 2 and 4, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about teal itself.
The board after step 14 — 6 of 12 queens placed. Step 15. Test row 6, column 6 for red: place a queen there, run the forced consequences through, and the khaki region is left with nowhere to put its queen. The assumption breaks, so the square is eliminated.
Step 16. Wherever red 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 17. Pale yellow and teal are now boxed into columns 2 and 4 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 1 square at once.
Step 18. Now a short proof by contradiction. Suppose the red queen went to row 8, column 6. Follow the forced moves that would create and the sea green region is left with nowhere to put its queen — impossible. So that square is ruled out for good.
Step 19. 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: red has one square left, so its queen takes row 6, column 5; sea green has one square left, so its queen takes row 10, column 6; pale yellow has one square left, so its queen takes row 7, column 2; khaki has one square left, so its queen takes row 8, column 11; amber has one square left, so its queen takes row 2, column 10; teal has one square left, so its queen takes row 11, column 4. 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 11, column 4.
The board after step 19 — 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 #158
Board #158 of the 12x12 bank carries a medium 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.
As with every puzzle in this collection, #158 has a single verified solution and needs no guesswork. Each queen follows from something already visible. What the board controls is tempo — how soon the first forced move shows up and how far apart the rest are spaced — and that is a direct consequence of how these colors are cut.
How the colors divide this board
From smallest to largest, the regions on puzzle #158 are: indigo (1 square), mint (1 square), rose (1 square), khaki (7 squares), orange (7 squares), teal (11 squares), amber (13 squares), blue (13 squares), slate (16 squares), pale yellow (19 squares), sea green (26 squares), red (29 squares). An even split would hand every color 12 squares, so the indigo region is running 11 squares under that average while the red region is the roomiest area on the grid with 29 squares.
Every color takes one queen and one only, whatever its size — which is why the 28 square difference between indigo and red is worth noting before you touch the grid. The cramped colors resolve first and hand you information; the roomy ones absorb whatever is left over at the end.
Look at arrangement as well as area. Indigo is the densest region on this grid at 100% of a 1×1 frame; teal is the loosest, occupying only 44% of its 5×5 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.
Indigo occupies 1 square within rows 1–1, columns 3–3. It never leaves row 1, so its queen is locked to that row.
Mint: 1 square across rows 4–4, columns 12–12. It never leaves row 4, so its queen is locked to that row.
Rose covers 1 square, spanning 1 row and 1 column (rows 12–12, columns 7–7). It never leaves row 12, so its queen is locked to that row.
Khaki occupies 7 squares within rows 6–9, columns 10–12.
Orange: 7 squares across rows 7–9, columns 8–11.
Teal covers 11 squares, spanning 5 rows and 5 columns (rows 8–12, columns 1–5).
Amber occupies 13 squares within rows 1–4, columns 7–12.
Blue: 13 squares across rows 1–3, columns 1–6.
Slate covers 16 squares, spanning 5 rows and 6 columns (rows 2–6, columns 7–12).
Pale yellow occupies 19 squares within rows 5–11, columns 1–6.
Sea green: 26 squares across rows 9–12, columns 4–12.
Red covers 29 squares, spanning 7 rows and 9 columns (rows 3–9, columns 1–9).
Where to start on this board
Indigo is the natural opening on #158: it is the smallest region on the grid at 1 square, boxed into rows 1–1 and columns 3–3. 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 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. Mint and rose 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 #158
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 1, 2, 5, 10, 11 and 12 are the narrowest, touched by only 3 colors. Columns 1, 2 and 6 are the tightest columns, with 4 colors.
A line with few colors is a line close to resolving. Where only 3 colors appear, one of them owns the row outright and the others must fit into the remaining 11 rows. Row 9 is the crowded extreme at 6 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.
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 #158 is rated medium
Ratings track how generous the opening is. On #158 you get six 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 medium 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 medium board from the rest.
A board that feels above its rating is nearly always a board with a missing X. Audit every queen on the grid: full row cleared, full column cleared, all eight touching squares cleared. Diagonals are the common omission, and missing one is far more often the cause of a stall than any genuine difficulty in the puzzle.
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.
There is one technique that repays study at every grid size. Two regions restricted to the same two rows must occupy one row apiece, which excludes all other regions from those rows entirely; the identical logic applies to columns and to larger matched sets. It converts slow boards into fast ones, and the likeliest place to find it on #158 is row 1.
A non-spoiling distribution check: solved, #158 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 #158?
Puzzle #158 is rated medium. Its smallest color region holds 1 square, its tightest row is touched by 3 colors, and six of its regions are confined to a single row or column, which gives you a forced move early.
Does 12x12 puzzle #158 have only one solution?
Yes. Every puzzle in the 12x12 collection, including #158, 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 #158?
Start with the indigo region — the most constrained color on this board, with 1 square spanning rows 1–1 and columns 3–3. Narrowing the smallest region first removes the most squares elsewhere on the grid.