12x12 Queens Puzzle #153
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 #153
What follows is a complete solve of puzzle #153, 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 pairing argument on rows.
Techniques this board needs: last square in a region, region shadow, pairing argument on rows, region confined to one line.
Show the full walkthrough (11 steps) — contains the solution
Step 1. Only row 3, column 8 is still open in blue, and since each colour must take a queen, that settles it. That clears row 3, column 8, the rest of the blue 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. The amber region has 3 squares left, spread across rows 1 and 2, columns 10 and 11. 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 red ends up among its 2 squares, the same squares fall within reach of it — 3 squares in total, impossible regardless of how the colour resolves.
The board after step 4 — 2 of 12 queens placed. Step 5. Indigo, amber, and slate are now boxed into rows 1, 2, and 5 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 6 squares at once.
Step 6. The red region is down to one open square, at row 6, column 11. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 6 and column 11, the remaining red squares, and the ring of neighbours around row 6, column 11.
Step 7. Only row 2, column 10 is still open in amber, and since each colour must take a queen, that settles it. Everything else in row 2, in column 10, in amber and in the ring around that square is now dead.
The board after step 7 — 4 of 12 queens placed. Step 8. The rose region is down to one open square, at row 12, column 9. Every colour holds exactly one queen, so that square is forced. Row 12 and column 9 are now spoken for, along with the squares touching that queen.
Step 9. Pale yellow cannot leave row 7 — every one of its open squares (2 open squares) sits there. That row belongs to pale yellow, so every square on it owned by another colour is dead: 7 squares in all.
Step 10. All of the teal region's remaining squares (2 open squares) lie in row 11. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 6 squares come off.
Step 11. From here the board cascades. Keep alternating the region sweep and the line sweep and 7 queens fall out in order without any new idea being needed: sea green has one square left, so its queen takes row 10, column 2; khaki has one square left, so its queen takes row 8, column 1; indigo has one square left, so its queen takes row 1, column 3; slate has one square left, so its queen takes row 5, column 7; pale yellow has one square left, so its queen takes row 7, column 4; teal has one square left, so its queen takes row 11, column 5; orange has one square left, so its queen takes row 9, column 6. 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 6.
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 #153
Puzzle #153 is one of the hard-rated boards in the 12x12 set. Twelve colors divide its 144 squares, and you win by placing twelve queens so that each row, each column and each color holds exactly one, with no two queens adjacent in any direction.
There is exactly one way to finish #153, and it has been verified. More importantly, you can reach it without ever gambling: at every stage some square is provably right or provably wrong. Boards differ only in how deep you must dig before that proof appears, and the geometry of these twelve regions is what sets the depth.
How the colors divide this board
From smallest to largest, the regions on puzzle #153 are: blue (1 square), mint (2 squares), teal (6 squares), sea green (7 squares), red (9 squares), amber (11 squares), pale yellow (11 squares), khaki (12 squares), indigo (18 squares), rose (18 squares), slate (21 squares), orange (28 squares). An even split would hand every color 12 squares, so the blue region is running 11 squares under that average while the orange region is the roomiest area on the grid with 28 squares.
Every color takes one queen and one only, whatever its size — which is why the 27 square difference between blue and orange 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.
Square count is only half the story — how a color is arranged counts too. Blue is the tidiest shape on #153, packing 100% of its 1×1 bounding box, whereas slate straggles across its 7×7 box at just 43%. Tidy blocks are easy to work around; scattered ones touch more lines and resist resolution.
Region by region
Below is every color on #153 with its exact reach, smallest region first. It is worth a slow read: the spans reveal which rows and columns several regions are fighting over.
Blue: 1 square across rows 3–3, columns 8–8. It never leaves row 3, so its queen is locked to that row.
Mint covers 2 squares, spanning 2 rows and 1 column (rows 3–4, columns 12–12). It sits wholly inside column 12, so its queen must be in that column.
Teal occupies 6 squares within rows 11–12, columns 4–7.
Sea green: 7 squares across rows 10–12, columns 1–3.
Red covers 9 squares, spanning 6 rows and 3 columns (rows 4–9, columns 10–12).
Amber occupies 11 squares within rows 1–4, columns 9–12.
Pale yellow: 11 squares across rows 4–7, columns 3–6.
Khaki covers 12 squares, spanning 6 rows and 3 columns (rows 5–10, columns 1–3).
Indigo occupies 18 squares within rows 1–5, columns 1–5.
Rose: 18 squares across rows 6–12, columns 8–12.
Slate covers 21 squares, spanning 7 rows and 7 columns (rows 1–7, columns 4–10).
Orange occupies 28 squares within rows 6–11, columns 3–10.
Where to start on this board
Open on the tightest color. Here that is blue, confined to 1 square between rows 3 and 3 and columns 8 and 8. Its queen has nowhere else to go, which means those 1 row and 1 column carry more constraint than anywhere else on #153.
Because blue never leaves row 3, its queen must be in that row — and that instantly settles row 3 for everyone else. Sweep along it and X out every square that is not blue. 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 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 #153
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 1, 2 and 12 are the narrowest, touched by only 3 colors. Columns 1, 2, 7 and 11 are the tightest columns, with 3 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 6 colors — worth revisiting later, not now.
Working through the middle game
Past the opening, treat this as an elimination exercise rather than a placement exercise. Each queen takes out a row, a column and its eight neighbours, and the value of a move is measured by how much it removes. Cross everything out as you go and let the board do the remembering.
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 #153 is rated hard
What earns a board its rating is the shape of its opening. Here that opening offers three single-line regions, a 1-square smallest color, a tightest row touched by 3 colors, and a region-size spread of 27. Lopsided grids with flat regions fall quickly; balanced ones like this take more patience.
Difficulty in Queens is never arithmetic and never luck. Every board has one solution and none require guessing. What varies is the length of the chain you must follow before the next queen becomes certain — one or two steps on an easy board, five or six on a hard one, sometimes with several partial eliminations held in play at once.
Stuck on #153 despite the hard rating? The odds strongly favour a bookkeeping error over a hard chain of logic. Re-check each placed queen for its complete set of eliminations, paying particular attention to the four diagonal squares — those are the ones that get overlooked, and one of them is usually sitting on the answer.
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 #153 is row 1.
A non-spoiling distribution check: solved, #153 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 #153?
Puzzle #153 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 #153 have only one solution?
Yes. Every puzzle in the 12x12 collection, including #153, 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 #153?
Start with the blue region — the most constrained color on this board, with 1 square spanning rows 3–3 and columns 8–8. Narrowing the smallest region first removes the most squares elsewhere on the grid.