7x7 Queens Puzzle #58
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 11-step reasoning is written out below.
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Step-by-step solution for puzzle #58
What follows is a complete solve of puzzle #58, worked the way a person works it rather than the way a computer does. It runs to 11 deductions — 7 queen placements and 4 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, region confined to one line.
Show the full walkthrough (6 steps) — contains the solution
Step 1. Only row 7, column 4 is still open in pale yellow, and since each colour must take a queen, that settles it. That clears row 7, column 4, the rest of the pale yellow region and every square adjacent to it — diagonals included.
Step 2. Amber is down to 3 candidates in rows 1 and 2, columns 6 and 7, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about amber itself.
Step 3. The mint region has 3 squares left, spread across rows 3 and 4, 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.
The board after step 3 — 1 of 7 queens placed. 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: 3 squares come off in one stroke.
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: 4 squares in all.
Step 6. From here the board cascades. Keep alternating the region sweep and the line sweep and 6 queens fall out in order without any new idea being needed: mint has one square left, so its queen takes row 4, column 1; red has one square left, so its queen takes row 6, column 2; indigo has one square left, so its queen takes row 1, column 3; amber has one square left, so its queen takes row 2, column 7; blue has one square left, so its queen takes row 3, column 5; slate has one square left, so its queen takes row 5, column 6. 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 6.
The board after step 6 — 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 #58
Board #58 of the 7x7 bank carries a hard rating. Its 49 squares are shared between seven colored regions, and the solution places seven 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, #58 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 #58 are: pale yellow (1 square), amber (3 squares), mint (3 squares), indigo (6 squares), blue (8 squares), red (11 squares), slate (17 squares). An even split would hand every color 7 squares, so the pale yellow region is running 6 squares under that average while the slate region is the roomiest area on the grid with 17 squares.
That imbalance is the first thing to read, because every region takes exactly one queen regardless of how much space it owns. Pale yellow has only 1 place to put its queen; slate has 17. The spread between them on this board is 16 squares, and the wider that spread runs, the more it pays to solve from the small end inward.
Square count is only half the story — how a color is arranged counts too. Pale yellow is the tidiest shape on #58, packing 100% of its 1×1 bounding box, whereas blue straggles across its 3×4 box at just 67%. Tidy blocks are easy to work around; scattered ones touch more lines and resist resolution.
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 1 square, spanning 1 row and 1 column (rows 7–7, columns 4–4). It never leaves row 7, so its queen is locked to that row.
Amber occupies 3 squares within rows 1–2, columns 6–7.
Mint: 3 squares across rows 3–4, columns 1–2.
Indigo covers 6 squares, spanning 2 rows and 4 columns (rows 1–2, columns 1–4).
Blue occupies 8 squares within rows 1–3, columns 3–6.
Red: 11 squares across rows 4–7, columns 1–4.
Slate covers 17 squares, spanning 5 rows and 5 columns (rows 3–7, columns 3–7).
Where to start on this board
Begin where the choices are fewest. On this board that means pale yellow, which owns just 1 square inside a 1×1 window running from row 7 to row 7 and column 4 to column 4. A queen is guaranteed somewhere in there, so every line that window crosses is under pressure from the very first move.
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. Indigo, amber and mint 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 #58
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 5 and 6 are the narrowest, touched by only 2 colors. Columns 5 and 7 are the tightest columns, with 2 colors.
A line with few colors is a line close to resolving. Where only 2 colors appear, one of them owns the row outright and the others must fit into the remaining 6 rows. Row 7 is the crowded extreme at 3 colors — worth revisiting later, not now.
Working through the middle game
The middle of #58 is where careless play costs time. Every queen you place kills a row, a column and the eight surrounding squares; if you do not mark all of that immediately, you will later "discover" a move that was available several turns ago. Mark first, then look.
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 #58 is rated hard
Ratings track how generous the opening is. On #58 you get two regions pinned to a single row or column, a smallest color of 1 square, a tightest row crossed by 2 colors, and a 16-square gap between the largest and smallest regions. Those four numbers largely explain the hard label.
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 hard 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 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.
One pattern is worth learning at every size, and it is available here. When two regions can only fit inside the same two rows, they must take one row each — which locks every other region out of both. The same argument works for columns, and for any matching count: three regions sharing three rows, four sharing four. Spotting these pairings turns a slow grind into a quick cascade, and on #58 the place to look for one is around row 5.
A non-spoiling distribution check: solved, #58 carries 4 queens on the perimeter against 3 queens inside, with the corners empty. 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
- 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 #58?
Puzzle #58 is rated hard. Its smallest color region holds 1 square, its tightest row is touched by 2 colors, and two of its regions are confined to a single row or column, which gives you a forced move early.
Does 7x7 puzzle #58 have only one solution?
Yes. Every puzzle in the 7x7 collection, including #58, 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 #58?
Start with the pale yellow region — the most constrained color on this board, with 1 square spanning rows 7–7 and columns 4–4. Narrowing the smallest region first removes the most squares elsewhere on the grid.