12x12 Queens Puzzle #178
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 24-step reasoning is written out below.
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Step-by-step solution for puzzle #178
What follows is a complete solve of puzzle #178, 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 pairing argument on columns.
Techniques this board needs: last square in a region, region shadow, region confined to one line, pairing argument on columns, line confined to one region, pairing argument on rows.
Show the full walkthrough (19 steps) — contains the solution
Step 1. Only row 12, column 1 is still open in rose, and since each colour must take a queen, that settles it. That clears row 12, column 1, the rest of the rose region and every square adjacent to it — diagonals included.
Step 2. Red is down to 3 candidates in rows 6 and 7, columns 8 and 9, and they overlap enough to cover 3 squares elsewhere. Cross those out without deciding anything about red itself.
Step 3. The pale yellow region has 3 squares left, spread across rows 7 and 8, columns 10 and 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 4. 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: 9 squares come off.
Step 5. Orange cannot leave column 12 — every one of its open squares (2 open squares) sits there. That column belongs to orange, so every square in it owned by another colour is dead: 9 squares in all.
The board after step 5 — 1 of 12 queens placed. Step 6. The slate region has 3 squares left, spread across rows 1, 2, and 5, columns 10 and 11. You do not need to know which of them takes the queen: every one of those options attacks the same 4 squares, so they can be crossed out now.
Step 7. Wherever amber 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. Here is the pairing argument. The slate and pale yellow 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: 8 squares come off in one stroke.
Step 9. Only row 2, column 9 is still open in amber, and since each colour must take a queen, that settles it. That clears row 2, column 9, the rest of the amber region and every square adjacent to it — diagonals included.
Step 10. The red region is down to one open square, at row 6, column 8. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 6 and column 8, the remaining red squares, and the ring of neighbours around row 6, column 8.
The board after step 10 — 3 of 12 queens placed. Step 11. Khaki is down to 5 candidates in rows 7–10, columns 6 and 7, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about khaki itself.
Step 12. Every open square left in row 11 (5 open squares) belongs to the teal region. Since that row must contain a queen, teal is the colour that supplies it — so teal squares anywhere else on the board are out, 2 squares in all.
Step 13. Indigo, blue, mint, and slate are now boxed into rows 1, 3, 4, and 5 and nothing else. That is 4 colours needing 4 rows, so they fill those rows between them — which locks every remaining colour out and removes 1 square at once.
Step 14. Here is the pairing argument. The mint and khaki regions have no open squares outside columns 6 and 7 — 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 14 — 3 of 12 queens placed. Step 15. 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: indigo has one square left, so its queen takes row 1, column 5; slate has one square left, so its queen takes row 5, column 10; mint has one square left, so its queen takes row 4, column 7; pale yellow has one square left, so its queen takes row 7, column 11; khaki has one square left, so its queen takes row 8, 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.
Step 16. Sea green cannot leave row 10 — every one of its open squares (2 open squares) sits there. That row belongs to sea green, so every square on it owned by another colour is dead: 1 square in all.
Step 17. The teal region is down to one open square, at row 11, column 4. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 11 and column 4, the remaining teal squares, and the ring of neighbours around row 11, column 4.
Step 18. 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 19. The blue region is down to one open square, at row 3, column 3. Every colour holds exactly one queen, so that square is forced. Row 3 and column 3 are now spoken for, along with the squares touching that queen.
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 #178
Board #178 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.
As with every puzzle in this collection, #178 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 #178 are: rose (1 square), red (3 squares), pale yellow (3 squares), orange (3 squares), indigo (7 squares), amber (8 squares), teal (11 squares), slate (13 squares), mint (14 squares), blue (24 squares), khaki (28 squares), sea green (29 squares). An even split would hand every color 12 squares, so the rose region is running 11 squares under that average while the sea green 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. Rose has only 1 place to put its queen; sea green 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 rose is the most solid, filling 100% of its 1×1 box, and slate the most diffuse at 46% of its 7×4 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.
Rose covers 1 square, spanning 1 row and 1 column (rows 12–12, columns 1–1). It never leaves row 12, so its queen is locked to that row.
Red occupies 3 squares within rows 6–7, columns 8–9.
Pale yellow: 3 squares across rows 7–8, columns 10–11.
Orange covers 3 squares, spanning 2 rows and 2 columns (rows 8–9, columns 11–12).
Indigo occupies 7 squares within rows 1–4, columns 5–7.
Amber: 8 squares across rows 1–5, columns 9–11.
Teal covers 11 squares, spanning 3 rows and 5 columns (rows 10–12, columns 3–7).
Slate occupies 13 squares within rows 1–7, columns 9–12.
Mint: 14 squares across rows 1–6, columns 6–9.
Blue covers 24 squares, spanning 6 rows and 5 columns (rows 1–6, columns 1–5).
Khaki occupies 28 squares within rows 7–12, columns 6–12.
Sea green: 29 squares across rows 5–12, columns 1–6.
Where to start on this board
Rose is the natural opening on #178: it is the smallest region on the grid at 1 square, boxed into rows 12–12 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 rose never leaves row 12, its queen must be in that row — and that instantly settles row 12 for everyone else. Sweep along it and X out every square that is not rose. 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. Red, pale yellow and orange 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 #178
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 9, 10 and 11 are the narrowest, touched by only 3 colors. Column 2 is the tightest column, with 2 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 7 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.
The whole middle game reduces to two sweeps. Sweep the twelve colors looking for one with a single square left; sweep the twelve rows and twelve columns looking for the same. Each sweep feeds the next, and switching between them deliberately — rather than drifting — is what separates a fast 12x12 solve from a stalled one.
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 #178 is rated hard
The hard label comes out of four measurable things about #178: two 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 28. Boards that score tight on those measures give up their first queen fast.
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.
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.
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 #178 the place to look for one is around column 2.
A non-spoiling distribution check: solved, #178 carries 3 queens on the perimeter against 9 queens inside, 1 of them cornered. 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 #178?
Puzzle #178 is rated hard. Its smallest color region holds 1 square, its tightest row is touched by 3 colors, and two of its regions are confined to a single row or column, which gives you a forced move early.
Does 12x12 puzzle #178 have only one solution?
Yes. Every puzzle in the 12x12 collection, including #178, 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 #178?
Start with the rose region — the most constrained color on this board, with 1 square spanning rows 12–12 and columns 1–1. Narrowing the smallest region first removes the most squares elsewhere on the grid.