7x7 Queens Puzzle #289
Difficulty: hard. Place 7 queens on this 7x7 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 14-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 14 deductions — 7 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 pairing argument on columns.
Techniques this board needs: region shadow, pairing argument on rows, region confined to one line, pairing argument on columns, last square in a region, last square in a row.
Show the full walkthrough (8 steps) — contains the solution
Step 1. Wherever blue 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.
Step 2. Pale yellow is down to 3 candidates in rows 6 and 7, columns 6 and 7, and they overlap enough to cover 2 squares elsewhere. Cross those out without deciding anything about pale yellow itself.
Step 3. Indigo and amber are now boxed into rows 1 and 2 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 4 squares at once.
Step 4. All of the blue region's remaining squares (2 open squares) lie in row 3. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 6 squares come off.
The board after step 4 — 0 of 7 queens placed. Step 5. Mint is down to 3 candidates in rows 4 and 5, columns 6 and 7, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about mint itself.
Step 6. The red region has 4 squares left, spread across rows 4–6, columns 4 and 5. 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. Mint and pale yellow are now boxed into columns 6 and 7 and nothing else. That is 2 colours needing 2 columns, so they fill those columns between them — which locks every remaining colour out and removes 3 squares at once.
Step 8. 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: indigo has one square left, so its queen takes row 1, column 5; amber has one square left, so its queen takes row 2, column 3; blue has one square left, so its queen takes row 3, column 1; red has one square left, so its queen takes row 6, column 4; row 4 is down to one square, putting a queen on row 4, column 7; pale yellow has one square left, so its queen takes row 7, column 6; slate has one square left, so its queen takes row 5, column 2. 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 2.
The board after step 8 — 7 of 7 queens placed.
That completes the board: 7 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 7x7 Queens puzzle #289
Puzzle #289 is one of the hard-rated boards in the 7x7 set. Seven colors divide its 49 squares, and you win by placing seven 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, #289 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 #289 are: pale yellow (3 squares), indigo (4 squares), blue (4 squares), amber (6 squares), mint (6 squares), red (9 squares), slate (17 squares). An even split would hand every color 7 squares, so the pale yellow region is running 4 squares under that average while the slate region is the roomiest area on the grid with 17 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 3 squares, is under far more pressure than slate with 17. A 14-square gap like this one rewards players who start where the choices are fewest.
Shape matters as much as size. The amber region is the most compact color here, filling 100% of the 2×3 box that encloses it, while red is the most scattered at 50% of its 6×3 box. Compact regions are easy to eliminate around; straggling ones reach into more rows and columns and tend to stay unresolved until late.
Region by region
The complete breakdown of each region on this board follows, ordered from tightest to roomiest. Skimming the spans first tells you where the board is crowded and where it has slack.
Pale yellow covers 3 squares, spanning 2 rows and 2 columns (rows 6–7, columns 6–7).
Indigo occupies 4 squares within rows 1–2, columns 5–7.
Blue: 4 squares across rows 1–3, columns 1–2.
Amber covers 6 squares, spanning 2 rows and 3 columns (rows 1–2, columns 2–4).
Mint occupies 6 squares within rows 2–6, columns 6–7.
Red: 9 squares across rows 2–7, columns 4–6.
Slate covers 17 squares, spanning 5 rows and 4 columns (rows 3–7, columns 1–4).
Where to start on this board
Pale yellow is the natural opening on #289: it is the smallest region on the grid at 3 squares, boxed into rows 6–7 and columns 6–7. 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.
Pale yellow does not collapse onto a single line, so it will not hand you a queen on move one. What it does give you is a short list of 3 candidates. Take each one in turn, imagine the queen there, cross out its row, its column and the eight squares around it, and ask whether any other region is left with nowhere to go. One or two candidates usually fail that test immediately.
Work outward to the other flat regions next. Amber and indigo 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 #289
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 and 7 are the narrowest, touched by only 3 colors. Columns 1, 3 and 5 are the tightest columns, with 2 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 6 rows. By contrast row 2 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
Past the opening, treat this as an elimination exercise rather than a placement exercise. Each queen takes out a row, a column and its eight neighbours, and the value of a move is measured by how much it removes. Cross everything out as you go and let the board do the remembering.
Keep alternating between two views of the board. In the region view you ask which of the seven 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 7x7 board unwinds.
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 hard
Ratings track how generous the opening is. On #289 you get no region pinned to a single row or column, a smallest color of 3 squares, a tightest row crossed by 3 colors, and a 14-square gap between the largest and smallest regions. Those four numbers largely explain the hard label.
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 7x7
At 7x7 the whole grid stays within a single glance, which makes systematic scanning practical. Read the rows in order and count the colors in each — a row touched by two colors is far more constrained than one touched by five, and that is usually where the next forced move hides. The board is small enough that re-scanning from the top after each placement costs almost nothing.
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 #289, start hunting for it near column 1.
As a sanity check rather than a spoiler: the finished solution to #289 puts 4 queens on the outer border and 3 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 7x7 Queens puzzle #289?
Puzzle #289 is rated hard. 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 7x7 puzzle #289 have only one solution?
Yes. Every puzzle in the 7x7 collection, including #289, has been verified to have exactly one valid arrangement of seven 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 3 squares spanning rows 6–7 and columns 6–7. Narrowing the smallest region first removes the most squares elsewhere on the grid.