12x12 Queens Puzzle #50

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 20-step reasoning is written out below.

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Step-by-step solution for puzzle #50

What follows is a complete solve of puzzle #50, worked the way a person works it rather than the way a computer does. It runs to 20 deductions — 12 queen placements and 8 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 shadow, pairing argument on rows, region confined to one line, last square in a region.

Show the full walkthrough (9 steps) — contains the solution

  1. Step 1. Wherever indigo ends up among its 4 squares, the same squares fall within reach of it — 2 squares in total, impossible regardless of how the colour resolves.

  2. Step 2. Khaki is down to 3 candidates in rows 8 and 9, columns 1 and 2, and they overlap enough to cover 2 squares elsewhere. Cross those out without deciding anything about khaki itself.

  3. Step 3. The orange region has 4 squares left, spread across rows 9 and 10, columns 10–12. 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.

    Puzzle #50 after step 3: 0 of 12 queens placed
    The board after step 3 — 0 of 12 queens placed.

  4. Step 4. Here is the pairing argument. The indigo and amber regions have no open squares outside rows 1 and 2 — 2 colours confined to 2 rows. Between them they must take one row each, in some order, so every other colour is shut out of all of them: 11 squares come off in one stroke.

  5. Step 5. Blue cannot leave row 3 — every one of its open squares (2 open squares) sits there. That row belongs to blue, so every square on it owned by another colour is dead: 10 squares in all.

  6. Step 6. The mint region has 6 squares left, spread across rows 4–6, columns 1–3. 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.

    Puzzle #50 after step 6: 0 of 12 queens placed
    The board after step 6 — 0 of 12 queens placed.

  7. Step 7. Orange, sea green, teal, and rose are now boxed into rows 9–12 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 11 squares at once.

  8. Step 8. Pale yellow is down to 3 candidates in rows 7 and 8, columns 2 and 3, and they overlap enough to cover 3 squares elsewhere. Cross those out without deciding anything about pale yellow itself.

  9. Step 9. From here the board cascades. Keep alternating the region sweep and the line sweep and 12 queens fall out in order without any new idea being needed: khaki has one square left, so its queen takes row 8, column 1; blue has one square left, so its queen takes row 3, column 5; pale yellow has one square left, so its queen takes row 7, column 3; mint has one square left, so its queen takes row 4, column 2; rose has one square left, so its queen takes row 12, column 4; red has one square left, so its queen takes row 6, column 7; indigo has one square left, so its queen takes row 1, column 6; sea green has one square left, so its queen takes row 10, column 8; orange has one square left, so its queen takes row 9, column 12; amber has one square left, so its queen takes row 2, column 10; teal has one square left, so its queen takes row 11, column 11; slate has one square left, so its queen takes row 5, column 9. 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 5, column 9.

    Puzzle #50 after step 9: 12 of 12 queens placed
    The board after step 9 — 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 #50

Board #50 of the 12x12 bank carries a easy 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, #50 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 #50 are: khaki (3 squares), indigo (4 squares), orange (4 squares), amber (8 squares), pale yellow (8 squares), mint (9 squares), teal (9 squares), rose (9 squares), blue (12 squares), sea green (13 squares), red (22 squares), slate (43 squares). An even split would hand every color 12 squares, so the khaki region is running 9 squares under that average while the slate region is the roomiest area on the grid with 43 squares.

Why does the split matter? Because a region's square count has no bearing on how many queens it gets — the answer is always one. So khaki, with 3 squares, is under far more pressure than slate with 43. A 40-square gap like this one rewards players who start where the choices are fewest.

Look at arrangement as well as area. Teal is the densest region on this grid at 90% of a 2×5 frame; pale yellow is the loosest, occupying only 53% of its 5×3 frame. The loose one reaches into more rows and columns, which is exactly why it usually settles last.

Region by region

Below is every color on #50 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.

Khaki occupies 3 squares within rows 8–9, columns 1–2.

Indigo: 4 squares across rows 1–2, columns 5–7.

Orange covers 4 squares, spanning 2 rows and 3 columns (rows 9–10, columns 10–12).

Amber occupies 8 squares within rows 1–2, columns 8–12.

Pale yellow: 8 squares across rows 7–11, columns 2–4.

Mint covers 9 squares, spanning 5 rows and 3 columns (rows 3–7, columns 1–3).

Teal occupies 9 squares within rows 11–12, columns 8–12.

Rose: 9 squares across rows 10–12, columns 1–5.

Blue covers 12 squares, spanning 3 rows and 6 columns (rows 1–3, columns 1–6).

Sea green occupies 13 squares within rows 9–12, columns 3–8.

Red: 22 squares across rows 3–8, columns 2–7.

Slate covers 43 squares, spanning 9 rows and 7 columns (rows 2–10, columns 6–12).

Where to start on this board

Khaki is the natural opening on #50: it is the smallest region on the grid at 3 squares, boxed into rows 8–9 and columns 1–2. Since one of those squares must hold a queen, that block of 2 rows and 2 columns is the most contested part of the board.

With 2 rows and 2 columns of room, khaki needs narrowing rather than solving outright. Test its 3 squares against the neighbours: a candidate that would strand another color is dead, and eliminating even two of them tightens the whole corner of the board around rows 8–9.

Work outward to the other flat regions next. Indigo, amber, orange 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 #50

A quick way to find the next move is to count how many different colors touch each line. On this board, rows 1, 4, 5, 6 and 12 are the narrowest, touched by only 3 colors. Column 9 is the tightest column, with 3 colors.

The fewer colors a line touches, the sooner it surrenders its queen. A row meeting just 3 colors has to be claimed by one of them, which pushes every remaining region into the other 11 rows. Row 10, meeting 5 colors, is the opposite case — the busiest line on #50 and the last one you should expect to crack.

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.

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.

Say the reason out loud: "this region has one square left", "this column has one square left". If no such sentence is available, the eliminating is not finished. One more pass of X marks is almost always quicker than committing to a placement you cannot defend.

Why puzzle #50 is rated easy

What earns a board its rating is the shape of its opening. Here that opening offers no single-line region at all, a 3-square smallest color, a tightest row touched by 3 colors, and a region-size spread of 40. 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.

Learn the pairing argument and you will use it on every board, this one included. If two colors can only sit inside the same two rows, between them they consume both rows and every other color is shut out. It generalises to any matching count — three colors across three rows, four across four. On #50, start hunting for it near row 1.

Here is a shape check that gives nothing away: when #50 is solved, 4 queens sit on the outer edge of the grid and 8 sit inside it, and no queen lands in a corner. A work-in-progress board that clusters its queens in one quadrant while leaving others bare is usually carrying a mistake.

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 #50?

Puzzle #50 is rated easy. Its smallest color region holds 3 squares, its tightest row is touched by 3 colors, and no region is confined to a single row or column, so the opening move takes some hunting.

Does 12x12 puzzle #50 have only one solution?

Yes. Every puzzle in the 12x12 collection, including #50, 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 #50?

Start with the khaki region — the most constrained color on this board, with 3 squares spanning rows 8–9 and columns 1–2. Narrowing the smallest region first removes the most squares elsewhere on the grid.