12x12 Queens Puzzle #253

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 21-step reasoning is written out below.

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Step-by-step solution for puzzle #253

What follows is a complete solve of puzzle #253, worked the way a person works it rather than the way a computer does. It runs to 21 deductions — 12 queen placements and 9 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, region confined to one line, pairing argument on rows, line confined to one region, last square in a column, last square in a row.

Show the full walkthrough (11 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: teal has one square left, so its queen takes row 11, column 1; mint has one square left, so its queen takes row 4, column 2; sea green has one square left, so its queen takes row 10, column 10; indigo has one square left, so its queen takes row 1, column 11. 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 1, column 11.

  2. Step 2. Amber is down to 5 candidates in rows 2, 3, and 5, columns 3–5, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about amber itself.

  3. Step 3. The red region has 6 squares left, spread across rows 5–7, columns 3–6. 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.

  4. Step 4. Wherever khaki ends up among its 3 squares, the same squares fall within reach of it — 1 square in total, impossible regardless of how the colour resolves.

    Puzzle #253 after step 4: 4 of 12 queens placed
    The board after step 4 — 4 of 12 queens placed.

  5. Step 5. All of the rose region's remaining squares (2 open squares) lie in row 12. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 6 squares come off.

  6. Step 6. The orange region has 3 squares left, spread across rows 8 and 9, columns 5 and 6. 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.

  7. Step 7. All of the khaki region's remaining squares (2 open squares) lie in column 3. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 2 squares come off.

    Puzzle #253 after step 7: 4 of 12 queens placed
    The board after step 7 — 4 of 12 queens placed.

  8. Step 8. Khaki and orange are now boxed into rows 8 and 9 and nothing else. That is 2 colours needing 2 rows, so they fill those rows between them — which locks every remaining colour out and removes 7 squares at once.

  9. Step 9. The pale yellow region has 4 squares left, spread across rows 6 and 7, columns 5, 6, and 9. 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.

  10. Step 10. Column 7 has only slate squares left (5 open squares). The column needs a queen and only slate can provide one, which pins that colour to this column and kills its squares elsewhere: 9 squares.

  11. Step 11. From here the board cascades. Keep alternating the region sweep and the line sweep and 8 queens fall out in order without any new idea being needed: column 8 is down to one square, putting a queen on row 3, column 8; row 2 is down to one square, putting a queen on row 2, column 4; row 5 is down to one square, putting a queen on row 5, column 7; red has one square left, so its queen takes row 6, column 5; pale yellow has one square left, so its queen takes row 7, column 9; orange has one square left, so its queen takes row 9, column 6; khaki has one square left, so its queen takes row 8, column 3; rose has one square left, so its queen takes row 12, 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 12, column 12.

    Puzzle #253 after step 11: 12 of 12 queens placed
    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 #253

Puzzle #253 is one of the medium-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, #253 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 #253 are: teal (1 square), indigo (2 squares), sea green (4 squares), rose (5 squares), mint (6 squares), red (6 squares), khaki (15 squares), amber (17 squares), blue (17 squares), orange (18 squares), slate (26 squares), pale yellow (27 squares). An even split would hand every color 12 squares, so the teal region is running 11 squares under that average while the pale yellow region is the roomiest area on the grid with 27 squares.

Every color takes one queen and one only, whatever its size — which is why the 26 square difference between teal and pale yellow 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 1×2 frame; pale yellow is the loosest, occupying only 48% of its 7×8 frame. The loose one reaches into more rows and columns, which is exactly why it usually settles last.

Region by region

Here is the full footprint of every color on puzzle #253, smallest first. Reading these spans before you place anything is the quickest way to see which parts of the grid are genuinely contested.

Teal covers 1 square, spanning 1 row and 1 column (rows 11–11, columns 1–1). It never leaves row 11, so its queen is locked to that row.

Indigo occupies 2 squares within rows 1–1, columns 10–11. It never leaves row 1, so its queen is locked to that row.

Sea green: 4 squares across rows 10–11, columns 8–10.

Rose covers 5 squares, spanning 2 rows and 4 columns (rows 11–12, columns 9–12).

Mint occupies 6 squares within rows 3–7, columns 1–2.

Red: 6 squares across rows 5–7, columns 3–6.

Khaki covers 15 squares, spanning 6 rows and 4 columns (rows 5–10, columns 1–4).

Amber occupies 17 squares within rows 1–5, columns 1–5.

Blue: 17 squares across rows 1–4, columns 5–12.

Orange covers 18 squares, spanning 5 rows and 6 columns (rows 8–12, columns 1–6).

Slate occupies 26 squares within rows 2–7, columns 6–12.

Pale yellow: 27 squares across rows 6–12, columns 5–12.

Where to start on this board

Open on the tightest color. Here that is teal, confined to 1 square between rows 11 and 11 and columns 1 and 1. Its queen has nowhere else to go, which means those 1 row and 1 column carry more constraint than anywhere else on #253.

Because teal never leaves row 11, its queen must be in that row — and that instantly settles row 11 for everyone else. Sweep along it and X out every square that is not teal. 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, 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 #253

A quick way to find the next move is to count how many different colors touch each line. On this board, rows 1, 2, 8, 9 and 12 are the narrowest, touched by only 3 colors. Column 7 is the tightest column, 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 11 sits at the far end with 5 colors crossing it; it will almost certainly be among the last to settle.

Working through the middle game

The middle of #253 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.

Two checks, run alternately, will carry you through the 144 squares of this grid. First: has any of the twelve regions been reduced to a single open square? Second: has any row or column? Either answer forces a queen. Players who stall on 12x12 boards almost always run one of those checks and forget the other.

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 #253 is rated medium

The rating reflects how much the board concedes up front. Puzzle #253 has three 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 26 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.

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 #253 is row 1.

Use this as a rough check on your progress: the completed board has 3 queens around the border and 9 queens in the middle, including 1 in a corner. 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.

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Questions about this puzzle

How hard is 12x12 Queens puzzle #253?

Puzzle #253 is rated medium. 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 #253 have only one solution?

Yes. Every puzzle in the 12x12 collection, including #253, 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 #253?

Start with the teal region — the most constrained color on this board, with 1 square spanning rows 11–11 and columns 1–1. Narrowing the smallest region first removes the most squares elsewhere on the grid.