12x12 Queens Puzzle #53
Difficulty: easy. 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 #53
What follows is a complete solve of puzzle #53, 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: region confined to one line, last square in a region, pairing argument on rows, last square in a row.
Show the full walkthrough (8 steps) — contains the solution
Step 1. Amber cannot leave row 2 — every one of its open squares (2 open squares) sits there. That row belongs to amber, so every square on it owned by another colour is dead: 14 squares in all.
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: 8 squares come off.
Step 3. Orange cannot leave column 9 — 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: 13 squares in all.
Step 4. The indigo region is down to one open square, at row 1, column 10. Every colour holds exactly one queen, so that square is forced. Row 1 and column 10 are now spoken for, along with the squares touching that queen.
The board after step 4 — 1 of 12 queens placed. Step 5. Only row 2, column 12 is still open in amber, and since each colour must take a queen, that settles it. That clears row 2, column 12, the rest of the amber region and every square adjacent to it — diagonals included.
Step 6. All of the mint region's remaining squares (2 open squares) lie in column 11. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 7 squares come off.
Step 7. Sea green, teal, and rose are now boxed into rows 10–12 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 5 squares at once.
Step 8. From here the board cascades. Keep alternating the region sweep and the line sweep and 10 queens fall out in order without any new idea being needed: orange has one square left, so its queen takes row 9, column 9; khaki has one square left, so its queen takes row 8, column 7; pale yellow has one square left, so its queen takes row 7, column 2; slate has one square left, so its queen takes row 5, column 3; mint has one square left, so its queen takes row 4, column 11; row 10 is down to one square, putting a queen on row 10, column 1; rose has one square left, so its queen takes row 12, column 4; teal has one square left, so its queen takes row 11, column 8; blue has one square left, so its queen takes row 3, column 5; red has one square left, so its queen takes row 6, 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 6, column 6.
The board after step 8 — 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 #53
Puzzle #53 is one of the easy-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.
As with every puzzle in this collection, #53 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 #53 are: amber (2 squares), orange (2 squares), indigo (5 squares), pale yellow (5 squares), rose (5 squares), sea green (6 squares), mint (13 squares), slate (13 squares), teal (13 squares), red (22 squares), blue (27 squares), khaki (31 squares). An even split would hand every color 12 squares, so the amber region is running 10 squares under that average while the khaki region is the roomiest area on the grid with 31 squares.
One queen per color, regardless of acreage: that is what turns this uneven split into a solving order. Amber is working with 2 squares while khaki has 31 to spare, a gap of 29. Attack the cramped end and the roomy regions tend to resolve themselves.
Square count is only half the story — how a color is arranged counts too. Amber is the tidiest shape on #53, packing 100% of its 1×2 bounding box, whereas slate straggles across its 6×5 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 #53 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.
Amber occupies 2 squares within rows 2–2, columns 11–12. It never leaves row 2, so its queen is locked to that row.
Orange: 2 squares across rows 9–10, columns 9–9. It sits wholly inside column 9, so its queen must be in that column.
Indigo covers 5 squares, spanning 2 rows and 4 columns (rows 1–2, columns 9–12).
Pale yellow occupies 5 squares within rows 7–9, columns 1–2.
Rose: 5 squares across rows 11–12, columns 1–4.
Sea green covers 6 squares, spanning 2 rows and 4 columns (rows 10–11, columns 1–4).
Mint occupies 13 squares within rows 2–6, columns 9–12.
Slate: 13 squares across rows 4–9, columns 1–5.
Teal covers 13 squares, spanning 3 rows and 6 columns (rows 10–12, columns 5–10).
Red occupies 22 squares within rows 3–8, columns 4–9.
Blue: 27 squares across rows 1–5, columns 1–8.
Khaki covers 31 squares, spanning 7 rows and 9 columns (rows 6–12, columns 4–12).
Where to start on this board
Open on the tightest color. Here that is amber, confined to 2 squares between rows 2 and 2 and columns 11 and 12. Its queen has nowhere else to go, which means those 1 row and 2 columns carry more constraint than anywhere else on #53.
Because amber never leaves row 2, its queen must be in that row — and that instantly settles row 2 for everyone else. Sweep along it and X out every square that is not amber. 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, orange, sea green 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 #53
A quick way to find the next move is to count how many different colors touch each line. On this board, row 1 is the narrowest, touched by only 2 colors. Columns 3, 6, 7, 8, 10, 11 and 12 are the tightest columns, with 4 colors.
Count colors per line and you have a ranking of where to look. The narrowest rows here see only 2 colors, so one of that handful must take the row and the rest are squeezed into the other 11 rows. Row 11 sits at the far end with 4 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.
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.
A placement without a reason is a guess. Because this board has exactly one solution, a guess that happens to be wrong will not announce itself for several moves — and unwinding it is slower than simply finishing the eliminations first.
Why puzzle #53 is rated easy
What earns a board its rating is the shape of its opening. Here that opening offers two single-line regions, a 2-square smallest color, a tightest row touched by 2 colors, and a region-size spread of 29. Lopsided grids with flat regions fall quickly; balanced ones like this take more patience.
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 easy 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.
Whatever the grid size, the pairing rule is the technique to internalise. When a pair of regions is boxed into the same pair of rows, they split those rows between them and nobody else may enter — and the same holds for columns, or for any n regions confined to n lines. Look for an instance of it around row 1 on this board.
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 #53?
Puzzle #53 is rated easy. Its smallest color region holds 2 squares, its tightest row is touched by 2 colors, and two of its regions are confined to a single row or column, which gives you a forced move early.
Does 12x12 puzzle #53 have only one solution?
Yes. Every puzzle in the 12x12 collection, including #53, 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 #53?
Start with the amber region — the most constrained color on this board, with 2 squares spanning rows 2–2 and columns 11–12. Narrowing the smallest region first removes the most squares elsewhere on the grid.