12x12 Queens Puzzle #110
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 18-step reasoning is written out below.
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Step-by-step solution for puzzle #110
What follows is a complete solve of puzzle #110, worked the way a person works it rather than the way a computer does. It runs to 18 deductions — 12 queen placements and 6 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, pairing argument on rows.
Show the full walkthrough (8 steps) — contains the solution
Step 1. Only row 7, column 9 is still open in pale yellow, and since each colour must take a queen, that settles it. That clears row 7, column 9, the rest of the pale yellow region and every square adjacent to it — diagonals included.
Step 2. Red is down to 3 candidates in rows 6 and 8, columns 1, 2, and 4, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about red itself.
Step 3. The teal region has 3 squares left, spread across rows 11 and 12, columns 1 and 2. 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.
Step 4. Wherever rose 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.
The board after step 4 — 1 of 12 queens placed. Step 5. Teal and rose are now boxed into rows 11 and 12 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 14 squares at once.
Step 6. The khaki region has 4 squares left, spread across rows 8–10, columns 11 and 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.
Step 7. Khaki, orange, and sea green are now boxed into rows 8–10 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 13 squares at once.
Step 8. From here the board cascades. Keep alternating the region sweep and the line sweep and 11 queens fall out in order without any new idea being needed: red has one square left, so its queen takes row 6, column 1; slate has one square left, so its queen takes row 5, column 7; mint has one square left, so its queen takes row 4, column 12; khaki has one square left, so its queen takes row 8, column 11; teal has one square left, so its queen takes row 11, column 2; amber has one square left, so its queen takes row 2, column 3; orange has one square left, so its queen takes row 9, column 4; sea green has one square left, so its queen takes row 10, column 6; rose has one square left, so its queen takes row 12, column 10; indigo has one square left, so its queen takes row 1, column 8; blue has one square left, so its queen takes row 3, column 5. 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 3, column 5.
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 #110
Board #110 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, #110 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 #110 are: pale yellow (1 square), teal (3 squares), rose (4 squares), red (7 squares), mint (8 squares), orange (9 squares), indigo (11 squares), amber (12 squares), khaki (12 squares), sea green (18 squares), slate (25 squares), blue (34 squares). An even split would hand every color 12 squares, so the pale yellow region is running 11 squares under that average while the blue region is the roomiest area on the grid with 34 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 pale yellow, with 1 square, is under far more pressure than blue with 34. A 33-square gap like this one rewards players who start where the choices are fewest.
Look at arrangement as well as area. Pale yellow is the densest region on this grid at 100% of a 1×1 frame; khaki is the loosest, occupying only 43% of its 7×4 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 #110 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.
Pale yellow occupies 1 square within rows 7–7, columns 9–9. It never leaves row 7, so its queen is locked to that row.
Teal: 3 squares across rows 11–12, columns 1–2.
Rose covers 4 squares, spanning 2 rows and 3 columns (rows 11–12, columns 9–11).
Red occupies 7 squares within rows 6–8, columns 1–4.
Mint: 8 squares across rows 4–6, columns 9–12.
Orange covers 9 squares, spanning 3 rows and 4 columns (rows 8–10, columns 1–4).
Indigo occupies 11 squares within rows 1–3, columns 8–12.
Amber: 12 squares across rows 1–5, columns 1–3.
Khaki covers 12 squares, spanning 7 rows and 4 columns (rows 6–12, columns 9–12).
Sea green occupies 18 squares within rows 9–12, columns 2–9.
Slate: 25 squares across rows 5–11, columns 5–11.
Blue covers 34 squares, spanning 6 rows and 10 columns (rows 1–6, columns 2–11).
Where to start on this board
Pale yellow is the natural opening on #110: it is the smallest region on the grid at 1 square, boxed into rows 7–7 and columns 9–9. 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 pale yellow never leaves row 7, its queen must be in that row — and that instantly settles row 7 for everyone else. Sweep along it and X out every square that is not pale yellow. 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. Teal 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 #110
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 1, 2, 3 and 4 are the narrowest, touched by only 3 colors. Columns 5, 6, 7 and 12 are the tightest columns, with 3 colors.
Those lines matter because a row touched by few colors gives its queen away sooner. If a row meets only 3 colors, then one of those regions has to own it, and every other region is competing for the remaining 11 rows. By contrast row 11 meets 5 colors — the most crowded line here, and the one least likely to resolve early. Spend your attention accordingly.
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.
Keep alternating between two views of the board. In the region view you ask which of the twelve colors is down to one open square. In the line view you ask the same of each row and column. Both produce forced queens, and each placement refreshes the other view, so cycling between them deliberately is how a 12x12 board unwinds.
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 #110 is rated easy
What earns a board its rating is the shape of its opening. Here that opening offers two single-line regions, a 1-square smallest color, a tightest row touched by 3 colors, and a region-size spread of 33. Lopsided grids with flat regions fall quickly; balanced ones like this take more patience.
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.
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 #110, start hunting for it near row 1.
As a sanity check rather than a spoiler: the finished solution to #110 puts 4 queens on the outer border and 8 queens in the interior, with none in a corner. If your part-finished grid has queens bunched into one area while whole stretches sit empty, something probably went wrong a few moves back.
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 #110?
Puzzle #110 is rated easy. Its smallest color region holds 1 square, its tightest row is touched by 3 colors, and two of its regions are confined to a single row or column, which gives you a forced move early.
Does 12x12 puzzle #110 have only one solution?
Yes. Every puzzle in the 12x12 collection, including #110, 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 #110?
Start with the pale yellow region — the most constrained color on this board, with 1 square spanning rows 7–7 and columns 9–9. Narrowing the smallest region first removes the most squares elsewhere on the grid.