12x12 Queens Puzzle #83

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 16-step reasoning is written out below.

Previous puzzle · All 12x12 puzzles · Next puzzle

Step-by-step solution for puzzle #83

What follows is a complete solve of puzzle #83, worked the way a person works it rather than the way a computer does. It runs to 16 deductions — 12 queen placements and 4 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 region confined to one line.

Techniques this board needs: last square in a region, region confined to one line.

Show the full walkthrough (7 steps) — contains the solution

  1. Step 1. The board opens by cascading. Each of these placements is forced the moment the one before it is marked, so the whole run is really a single sweep repeated: indigo has one square left, so its queen takes row 1, column 6; mint has one square left, so its queen takes row 4, column 11; rose has one square left, so its queen takes row 12, column 3; sea green has one square left, so its queen takes row 10, column 2. 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 10, column 2.

  2. Step 2. Amber cannot leave row 2 — every one of its open squares (3 open squares) sits there. That row belongs to amber, so every square on it owned by another colour is dead: 3 squares in all.

  3. Step 3. All of the blue region's remaining squares (2 open squares) lie in row 3. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 4 squares come off.

  4. Step 4. Only row 5, column 1 is still open in slate, and since each colour must take a queen, that settles it. Everything else in row 5, in column 1, in slate and in the ring around that square is now dead.

    Puzzle #83 after step 4: 5 of 12 queens placed
    The board after step 4 — 5 of 12 queens placed.

  5. Step 5. All of the orange region's remaining squares (2 open squares) lie in column 5. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 3 squares come off.

  6. Step 6. Teal cannot leave row 11 — every one of its open squares (5 open squares) sits there. That row belongs to teal, so every square on it owned by another colour is dead: 1 square in all.

  7. Step 7. 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: orange has one square left, so its queen takes row 9, column 5; khaki has one square left, so its queen takes row 8, column 12; red has one square left, so its queen takes row 6, column 10; amber has one square left, so its queen takes row 2, column 9; blue has one square left, so its queen takes row 3, column 7; teal has one square left, so its queen takes row 11, column 8; pale yellow has one square left, so its queen takes row 7, 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 7, column 4.

    Puzzle #83 after step 7: 12 of 12 queens placed
    The board after step 7 — 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 #83

12x12 puzzle #83 is rated easy. Twelve colored regions cover its 144 squares, and your job is to seat twelve queens so that every row, column and color contains exactly one — with no queen touching another, including diagonally.

Like every board on this site, #83 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 #83 are: indigo (1 square), mint (1 square), rose (1 square), sea green (5 squares), khaki (7 squares), amber (12 squares), red (14 squares), orange (14 squares), blue (17 squares), teal (17 squares), slate (18 squares), pale yellow (37 squares). An even split would hand every color 12 squares, so the indigo region is running 11 squares under that average while the pale yellow region is the roomiest area on the grid with 37 squares.

That imbalance is the first thing to read, because every region takes exactly one queen regardless of how much space it owns. Indigo has only 1 place to put its queen; pale yellow has 37. The spread between them on this board is 36 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 indigo is the most solid, filling 100% of its 1×1 box, and pale yellow the most diffuse at 46% of its 8×10 box. Solid blocks give clean eliminations; diffuse ones spread across the board and stay open longer.

Region by region

Here is the full footprint of every color on puzzle #83, smallest first. Reading these spans before you place anything is the quickest way to see which parts of the grid are genuinely contested.

Indigo occupies 1 square within rows 1–1, columns 6–6. It never leaves row 1, so its queen is locked to that row.

Mint: 1 square across rows 4–4, columns 11–11. 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 3–3). It never leaves row 12, so its queen is locked to that row.

Sea green occupies 5 squares within rows 10–12, columns 1–3.

Khaki: 7 squares across rows 8–9, columns 8–12.

Amber covers 12 squares, spanning 4 rows and 4 columns (rows 1–4, columns 9–12).

Red occupies 14 squares within rows 3–7, columns 7–12.

Orange: 14 squares across rows 8–12, columns 3–7.

Blue covers 17 squares, spanning 5 rows and 5 columns (rows 1–5, columns 4–8).

Teal occupies 17 squares within rows 10–12, columns 7–12.

Slate: 18 squares across rows 1–7, columns 1–5.

Pale yellow covers 37 squares, spanning 8 rows and 10 columns (rows 4–11, columns 1–10).

Where to start on this board

Begin where the choices are fewest. On this board that means indigo, which owns just 1 square inside a 1×1 window running from row 1 to row 1 and column 6 to column 6. A queen is guaranteed somewhere in there, so every line that window crosses is under pressure from the very first move.

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, rose and khaki 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 #83

A quick way to find the next move is to count how many different colors touch each line. On this board, rows 2, 6, 7, 8 and 9 are the narrowest, touched by only 3 colors. Columns 1 and 2 are the tightest columns, with 3 colors.

Count colors per line and you have a ranking of where to look. The narrowest rows here see only 3 colors, so one of that handful must take the row and the rest are squeezed into the other 11 rows. Row 4 sits at the far end with 6 colors crossing it; it will almost certainly be among the last to settle.

Working through the middle game

The middle of #83 is where careless play costs time. Every queen you place kills a row, a column and the eight surrounding squares; if you do not mark all of that immediately, you will later "discover" a move that was available several turns ago. Mark first, then look.

With twelve queens to seat and twelve regions competing over 144 squares, keep two questions in rotation. Does any region now have exactly one open square left? That queen is forced. Does any row or column now have exactly one open square left? That queen is forced too. Alternating between the region view and the row-and-column view is what keeps a solve moving, and it is the clearest difference between players who finish 12x12 boards quickly and players who stall halfway.

Resist the plausible-looking queen. On #83 every correct placement has a stated reason behind it, and any move you cannot justify is a guess wearing a disguise. Backing out of a wrong guess on a single-solution board takes far longer than finding the real deduction would have.

Why puzzle #83 is rated easy

The rating reflects how much the board concedes up front. Puzzle #83 has six regions confined to a single row or column, its smallest color holds 1 square, its tightest row meets just 3 colors, and the gap between its largest and smallest regions is 36 squares. Flat, lopsided boards open quickly; even, sprawling ones make you earn the first placement.

Rating is a measure of chain length, not of chance. With one guaranteed solution and no guessing required, the only thing that changes across the collection is how many eliminations you must link together before a queen is provably forced.

If #83 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.

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 #83 the place to look for one is around row 2.

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

  1. The board is an N×N grid divided into N colored regions.
  2. Place exactly one queen (♛) in each row, each column, and each colored region.
  3. No two queens may touch each other — not horizontally, vertically, or diagonally.
  4. 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.
  5. There is always exactly one valid solution. Use logic, never guessing, to find it.

Full rules · Strategy library · Puzzle statistics

Questions about this puzzle

How hard is 12x12 Queens puzzle #83?

Puzzle #83 is rated easy. 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 #83 have only one solution?

Yes. Every puzzle in the 12x12 collection, including #83, 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 #83?

Start with the indigo region — the most constrained color on this board, with 1 square spanning rows 1–1 and columns 6–6. Narrowing the smallest region first removes the most squares elsewhere on the grid.