12x12 Queens Puzzle #289

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 56-step reasoning is written out below.

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Step-by-step solution for puzzle #289

What follows is a complete solve of puzzle #289, worked the way a person works it rather than the way a computer does. It runs to 56 deductions — 12 queen placements and 44 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 proof by contradiction.

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

Show the full walkthrough (47 steps) — contains the solution

Step 1. Only row 7, column 8 is still open in pale yellow, and since each colour must take a queen, that settles it. That clears row 7, column 8, the rest of the pale yellow region and every square adjacent to it — diagonals included.
Step 2. Now a short proof by contradiction. Suppose the blue queen went to row 1, column 1. Follow the forced moves that would create and the slate region is left with nowhere to put its queen — impossible. So that square is ruled out for good.
Step 3. Test row 1, column 2 for blue: place a queen there, run the forced consequences through, and the slate region is left with nowhere to put its queen. The assumption breaks, so the square is eliminated.
Step 4. Now a short proof by contradiction. Suppose the blue queen went to row 2, column 1. Follow the forced moves that would create and the slate region is left with nowhere to put its queen — impossible. So that square is ruled out for good.
Step 5. Test row 2, column 2 for blue: place a queen there, run the forced consequences through, and the slate region is left with nowhere to put its queen. The assumption breaks, so the square is eliminated.
Step 6. Now a short proof by contradiction. Suppose the blue queen went to row 3, column 1. Follow the forced moves that would create and the slate region is left with nowhere to put its queen — impossible. So that square is ruled out for good.
Step 7. Test row 3, column 2 for blue: place a queen there, run the forced consequences through, and the slate region is left with nowhere to put its queen. The assumption breaks, so the square is eliminated.
Step 8. Now a short proof by contradiction. Suppose the blue queen went to row 4, column 1. Follow the forced moves that would create and the slate region is left with nowhere to put its queen — impossible. So that square is ruled out for good.
Step 9. Test row 4, column 2 for blue: place a queen there, run the forced consequences through, and the slate region is left with nowhere to put its queen. The assumption breaks, so the square is eliminated.
Step 10. Now a short proof by contradiction. Suppose the blue queen went to row 4, column 6. Follow the forced moves that would create and row 8 runs out of open squares entirely — impossible. So that square is ruled out for good.
Step 11. Test row 5, column 2 for blue: place a queen there, run the forced consequences through, and the slate region is left with nowhere to put its queen. The assumption breaks, so the square is eliminated.
Step 12. Now a short proof by contradiction. Suppose the mint queen went to row 1, column 11. Follow the forced moves that would create and the rose region is left with nowhere to put its queen — impossible. So that square is ruled out for good.
The board after step 12 — 1 of 12 queens placed.
Step 13. Test row 2, column 11 for mint: place a queen there, run the forced consequences through, and the rose region is left with nowhere to put its queen. The assumption breaks, so the square is eliminated.
Step 14. Now a short proof by contradiction. Suppose the mint queen went to row 3, column 11. Follow the forced moves that would create and the rose region is left with nowhere to put its queen — impossible. So that square is ruled out for good.
Step 15. Test row 4, column 11 for mint: place a queen there, run the forced consequences through, and the rose region is left with nowhere to put its queen. The assumption breaks, so the square is eliminated.
Step 16. Now a short proof by contradiction. Suppose the mint queen went to row 5, column 11. Follow the forced moves that would create and the rose region is left with nowhere to put its queen — impossible. So that square is ruled out for good.
Step 17. Test row 5, column 12 for mint: place a queen there, run the forced consequences through, and the rose region is left with nowhere to put its queen. The assumption breaks, so the square is eliminated.
Step 18. Now a short proof by contradiction. Suppose the mint queen went to row 6, column 12. Follow the forced moves that would create and the sea green region is left with nowhere to put its queen — impossible. So that square is ruled out for good.
Step 19. Test row 6, column 1 for slate: place a queen there, run the forced consequences through, and the sea green region is left with nowhere to put its queen. The assumption breaks, so the square is eliminated.
Step 20. Now a short proof by contradiction. Suppose the slate queen went to row 6, column 2. Follow the forced moves that would create and the sea green region is left with nowhere to put its queen — impossible. So that square is ruled out for good.
Step 21. Test row 8, column 4 for slate: place a queen there, run the forced consequences through, and the rose region is left with nowhere to put its queen. The assumption breaks, so the square is eliminated.
Step 22. Now a short proof by contradiction. Suppose the slate queen went to row 8, column 5. Follow the forced moves that would create and the rose region is left with nowhere to put its queen — impossible. So that square is ruled out for good.
Step 23. Test row 6, column 11 for red: place a queen there, run the forced consequences through, and the teal region is left with nowhere to put its queen. The assumption breaks, so the square is eliminated.
Step 24. Now a short proof by contradiction. Suppose the red queen went to row 8, column 10. Follow the forced moves that would create and the rose region is left with nowhere to put its queen — impossible. So that square is ruled out for good.
The board after step 24 — 1 of 12 queens placed.
Step 25. Test row 8, column 11 for red: place a queen there, run the forced consequences through, and the sea green region is left with nowhere to put its queen. The assumption breaks, so the square is eliminated.
Step 26. Now a short proof by contradiction. Suppose the red queen went to row 8, column 12. Follow the forced moves that would create and the rose region is left with nowhere to put its queen — impossible. So that square is ruled out for good.
Step 27. Test row 4, column 5 for amber: place a queen there, run the forced consequences through, and the orange region is left with nowhere to put its queen. The assumption breaks, so the square is eliminated.
Step 28. Now a short proof by contradiction. Suppose the blue queen went to row 1, column 3. Follow the forced moves that would create and the orange region is left with nowhere to put its queen — impossible. So that square is ruled out for good.
Step 29. Test row 2, column 3 for blue: place a queen there, run the forced consequences through, and the orange region is left with nowhere to put its queen. The assumption breaks, so the square is eliminated.
Step 30. Now a short proof by contradiction. Suppose the amber queen went to row 3, column 5. Follow the forced moves that would create and the rose region is left with nowhere to put its queen — impossible. So that square is ruled out for good.
Step 31. Test row 1, column 6 for indigo: place a queen there, run the forced consequences through, and the rose region is left with nowhere to put its queen. The assumption breaks, so the square is eliminated.
Step 32. Now a short proof by contradiction. Suppose the amber queen went to row 3, column 6. Follow the forced moves that would create and the rose region is left with nowhere to put its queen — impossible. So that square is ruled out for good.
Step 33. Test row 4, column 4 for amber: place a queen there, run the forced consequences through, and row 1 runs out of open squares entirely. The assumption breaks, so the square is eliminated.
Step 34. Now a short proof by contradiction. Suppose the blue queen went to row 3, column 3. Follow the forced moves that would create and the orange region is left with nowhere to put its queen — impossible. So that square is ruled out for good.
Step 35. Test row 1, column 7 for indigo: place a queen there, run the forced consequences through, and the rose region is left with nowhere to put its queen. The assumption breaks, so the square is eliminated.
The board after step 35 — 1 of 12 queens placed.
Step 36. Now a short proof by contradiction. Suppose the amber queen went to row 1, column 4. Follow the forced moves that would create and the rose region is left with nowhere to put its queen — impossible. So that square is ruled out for good.
Step 37. Test row 4, column 3 for blue: place a queen there, run the forced consequences through, and the orange region is left with nowhere to put its queen. The assumption breaks, so the square is eliminated.
Step 38. Now a short proof by contradiction. Suppose the indigo queen went to row 1, column 10. Follow the forced moves that would create and row 6 runs out of open squares entirely — impossible. So that square is ruled out for good.
Step 39. Test row 3, column 7 for indigo: place a queen there, run the forced consequences through, and row 2 runs out of open squares entirely. The assumption breaks, so the square is eliminated.
Step 40. Now a short proof by contradiction. Suppose the indigo queen went to row 5, column 7. Follow the forced moves that would create and row 2 runs out of open squares entirely — impossible. So that square is ruled out for good.
Step 41. Indigo is down to 2 candidates in rows 1 and 4, columns 7 and 9, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about indigo itself.
Step 42. Now a short proof by contradiction. Suppose the amber queen went to row 1, column 5. Follow the forced moves that would create and the khaki region is left with nowhere to put its queen — impossible. So that square is ruled out for good.
Step 43. Amber cannot leave row 2 — every one of its open squares (4 open squares) sits there. That row belongs to amber, so every square on it owned by another colour is dead: 3 squares in all.
Step 44. Now a short proof by contradiction. Suppose the indigo queen went to row 4, column 7. Follow the forced moves that would create and row 8 runs out of open squares entirely — impossible. So that square is ruled out for good.
Step 45. Only row 1, column 9 is still open in indigo, and since each colour must take a queen, that settles it. That clears row 1, column 9, the rest of the indigo region and every square adjacent to it — diagonals included.
Step 46. Every open square left in row 4 (2 open squares) belongs to the mint region. Since that row must contain a queen, mint is the colour that supplies it — so mint squares anywhere else on the board are out, 3 squares in all.
Step 47. From here the board cascades. Keep alternating the region sweep and the line sweep and 10 queens fall out in order without any new idea being needed: row 3 is down to one square, putting a queen on row 3, column 4; row 5 is down to one square, putting a queen on row 5, column 1; orange has one square left, so its queen takes row 9, column 2; rose has one square left, so its queen takes row 12, column 3; teal has one square left, so its queen takes row 11, column 11; red has one square left, so its queen takes row 6, column 10; mint has one square left, so its queen takes row 4, column 12; row 8 is down to one square, putting a queen on row 8, column 6; amber has one square left, so its queen takes row 2, column 7; sea green has one square left, so its queen takes row 10, 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 10, column 5.
The board after step 47 — 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 #289

Puzzle #289 is one of the easy-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.

There is exactly one way to finish #289, and it has been verified. More importantly, you can reach it without ever gambling: at every stage some square is provably right or provably wrong. Boards differ only in how deep you must dig before that proof appears, and the geometry of these twelve regions is what sets the depth.

How the colors divide this board

From smallest to largest, the regions on puzzle #289 are: pale yellow (1 square), teal (5 squares), orange (6 squares), rose (6 squares), amber (10 squares), indigo (11 squares), slate (12 squares), red (15 squares), khaki (16 squares), blue (19 squares), mint (20 squares), sea green (23 squares). An even split would hand every color 12 squares, so the pale yellow region is running 11 squares under that average while the sea green region is the roomiest area on the grid with 23 squares.

Every color takes one queen and one only, whatever its size — which is why the 22 square difference between pale yellow and sea green 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.

Square count is only half the story — how a color is arranged counts too. Pale yellow is the tidiest shape on #289, packing 100% of its 1×1 bounding box, whereas indigo straggles across its 5×5 box at just 44%. Tidy blocks are easy to work around; scattered ones touch more lines and resist resolution.

Region by region

Here is the full footprint of every color on puzzle #289, smallest first. Reading these spans before you place anything is the quickest way to see which parts of the grid are genuinely contested.

Pale yellow covers 1 square, spanning 1 row and 1 column (rows 7–7, columns 8–8). It never leaves row 7, so its queen is locked to that row.

Teal occupies 5 squares within rows 11–12, columns 9–12.

Orange: 6 squares across rows 7–10, columns 1–2.

Rose covers 6 squares, spanning 3 rows and 3 columns (rows 10–12, columns 1–3).

Amber occupies 10 squares within rows 1–4, columns 4–7.

Indigo: 11 squares across rows 1–5, columns 6–10.

Slate covers 12 squares, spanning 4 rows and 6 columns (rows 5–8, columns 1–6).

Red occupies 15 squares within rows 6–11, columns 8–12.

Khaki: 16 squares across rows 6–10, columns 6–11.

Blue covers 19 squares, spanning 5 rows and 6 columns (rows 1–5, columns 1–6).

Mint occupies 20 squares within rows 1–6, columns 8–12.

Sea green: 23 squares across rows 8–12, columns 2–10.

Where to start on this board

Open on the tightest color. Here that is pale yellow, confined to 1 square between rows 7 and 7 and columns 8 and 8. Its queen has nowhere else to go, which means those 1 row and 1 column carry more constraint than anywhere else on #289.

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 is no more than two rows tall, so its queen is 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 #289

A quick way to find the next move is to count how many different colors touch each line. On this board, row 12 is the narrowest, touched by only 3 colors. Column 12 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 10 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

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.

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 #289 is rated easy

The rating reflects how much the board concedes up front. Puzzle #289 has two 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 22 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.

Stuck on #289 despite the easy rating? The odds strongly favour a bookkeeping error over a hard chain of logic. Re-check each placed queen for its complete set of eliminations, paying particular attention to the four diagonal squares — those are the ones that get overlooked, and one of them is usually sitting on the answer.

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 #289 is row 12.

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

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 #289?

Puzzle #289 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 #289 have only one solution?

Yes. Every puzzle in the 12x12 collection, including #289, 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 #289?

Start with the pale yellow region — the most constrained color on this board, with 1 square spanning rows 7–7 and columns 8–8. Narrowing the smallest region first removes the most squares elsewhere on the grid.