12x12 Queens Puzzle #154

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 19-step reasoning is written out below.

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Step-by-step solution for puzzle #154

What follows is a complete solve of puzzle #154, worked the way a person works it rather than the way a computer does. It runs to 19 deductions — 12 queen placements and 7 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 line confined to one region.

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

Show the full walkthrough (9 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: red has one square left, so its queen takes row 6, column 7; slate has one square left, so its queen takes row 5, column 12; indigo has one square left, so its queen takes row 1, column 11; amber has one square left, so its queen takes row 2, column 9; rose has one square left, so its queen takes row 12, column 1. 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 1.

  2. Step 2. All of the pale yellow region's remaining squares (2 open squares) lie in row 7. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 4 squares come off.

  3. Step 3. Wherever orange ends up among its 2 squares, the same squares fall within reach of it — 2 squares in total, impossible regardless of how the colour resolves.

    Puzzle #154 after step 3: 5 of 12 queens placed
    The board after step 3 — 5 of 12 queens placed.

  4. Step 4. Sea green is down to 2 candidates in rows 10 and 11, columns 2 and 3, and they overlap enough to cover 3 squares elsewhere. Cross those out without deciding anything about sea green itself.

  5. Step 5. The teal region has 3 squares left, spread across rows 10 and 11, columns 4, 5, and 10. 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.

  6. Step 6. Every open square left in row 3 (5 open squares) belongs to the blue region. Since that row must contain a queen, blue is the colour that supplies it — so blue squares anywhere else on the board are out, 3 squares in all.

    Puzzle #154 after step 6: 5 of 12 queens placed
    The board after step 6 — 5 of 12 queens placed.

  7. Step 7. Row 4 has only mint squares left (4 open squares). The row needs a queen and only mint can provide one, which pins that colour to this row and kills its squares elsewhere: 2 squares.

  8. Step 8. Every open square left in row 8 (4 open squares) belongs to the khaki region. Since that row must contain a queen, khaki is the colour that supplies it — so khaki squares anywhere else on the board are out, 7 squares in all.

  9. Step 9. 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: row 9 is down to one square, putting a queen on row 9, column 10; row 10 is down to one square, putting a queen on row 10, column 2; pale yellow has one square left, so its queen takes row 7, column 4; khaki has one square left, so its queen takes row 8, column 6; teal has one square left, so its queen takes row 11, column 5; blue has one square left, so its queen takes row 3, column 3; mint has one square left, so its queen takes row 4, column 8. 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 4, column 8.

    Puzzle #154 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 #154

Board #154 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, #154 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 #154 are: red (1 square), rose (1 square), slate (4 squares), indigo (7 squares), amber (8 squares), sea green (8 squares), teal (13 squares), pale yellow (14 squares), orange (18 squares), khaki (22 squares), mint (23 squares), blue (25 squares). An even split would hand every color 12 squares, so the red region is running 11 squares under that average while the blue region is the roomiest area on the grid with 25 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 red, with 1 square, is under far more pressure than blue with 25. A 24-square gap like this one rewards players who start where the choices are fewest.

A region's outline can constrain it more than its size does. Here red is the most solid, filling 100% of its 1×1 box, and amber the most diffuse at 53% of its 3×5 box. Solid blocks give clean eliminations; diffuse ones spread across the board and stay open longer.

Region by region

Below is every color on #154 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.

Red covers 1 square, spanning 1 row and 1 column (rows 6–6, columns 7–7). It never leaves row 6, so its queen is locked to that row.

Rose occupies 1 square within rows 12–12, columns 1–1. It never leaves row 12, so its queen is locked to that row.

Slate: 4 squares across rows 5–6, columns 10–12.

Indigo covers 7 squares, spanning 5 rows and 2 columns (rows 1–5, columns 11–12).

Amber occupies 8 squares within rows 1–3, columns 7–11.

Sea green: 8 squares across rows 9–12, columns 1–3.

Teal covers 13 squares, spanning 3 rows and 8 columns (rows 10–12, columns 3–10).

Pale yellow occupies 14 squares within rows 5–8, columns 1–6.

Orange: 18 squares across rows 7–12, columns 8–12.

Khaki covers 22 squares, spanning 5 rows and 7 columns (rows 7–11, columns 2–8).

Mint occupies 23 squares within rows 2–8, columns 5–10.

Blue: 25 squares across rows 1–5, columns 1–7.

Where to start on this board

Red is the natural opening on #154: it is the smallest region on the grid at 1 square, boxed into rows 6–6 and columns 7–7. Since one of those squares must hold a queen, that block of 1 row and 1 column is the most contested part of the board.

Because red never leaves row 6, its queen must be in that row — and that instantly settles row 6 for everyone else. Sweep along it and X out every square that is not red. 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. Rose and slate 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 #154

A quick way to find the next move is to count how many different colors touch each line. On this board, rows 1, 4 and 9 are the narrowest, touched by only 3 colors. Column 12 is the tightest column, 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 5 is the crowded extreme at 5 colors — worth revisiting later, not now.

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.

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 #154 is rated easy

What earns a board its rating is the shape of its opening. Here that opening offers four single-line regions, a 1-square smallest color, a tightest row touched by 3 colors, and a region-size spread of 24. 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 #154, start hunting for it near row 1.

A non-spoiling distribution check: solved, #154 carries 3 queens on the perimeter against 9 queens inside, 1 of them cornered. 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

  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 #154?

Puzzle #154 is rated easy. Its smallest color region holds 1 square, its tightest row is touched by 3 colors, and four of its regions are confined to a single row or column, which gives you a forced move early.

Does 12x12 puzzle #154 have only one solution?

Yes. Every puzzle in the 12x12 collection, including #154, 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 #154?

Start with the red region — the most constrained color on this board, with 1 square spanning rows 6–6 and columns 7–7. Narrowing the smallest region first removes the most squares elsewhere on the grid.