7x7 Queens Puzzle #237
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 9-step reasoning is written out below.
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Step-by-step solution for puzzle #237
What follows is a complete solve of puzzle #237, worked the way a person works it rather than the way a computer does. It runs to 9 deductions — 7 queen placements and 2 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 region confined to one line.
Techniques this board needs: last square in a region, region confined to one line.
Show the full walkthrough (5 steps) — contains the solution
Step 1. Only row 5, column 6 is still open in slate, and since each colour must take a queen, that settles it. That clears row 5, column 6, the rest of the slate region and every square adjacent to it — diagonals included.
Step 2. The amber region is down to one open square, at row 2, column 5. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 2 and column 5, the remaining amber squares, and the ring of neighbours around row 2, column 5.
Step 3. Indigo cannot leave column 7 — every one of its open squares (2 open squares) sits there. That column belongs to indigo, so every square in it owned by another colour is dead: 1 square in all.
The board after step 3 — 2 of 7 queens placed. 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: 4 squares come off.
Step 5. From here the board cascades. Keep alternating the region sweep and the line sweep and 5 queens fall out in order without any new idea being needed: indigo has one square left, so its queen takes row 1, column 7; mint has one square left, so its queen takes row 4, column 1; blue has one square left, so its queen takes row 3, column 3; red has one square left, so its queen takes row 6, column 2; pale yellow has one square left, so its queen takes row 7, column 4. 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 7, column 4.
The board after step 5 — 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 #237
Puzzle #237 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, #237 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 #237 are: slate (1 square), indigo (5 squares), amber (5 squares), blue (6 squares), mint (10 squares), red (10 squares), pale yellow (12 squares). An even split would hand every color 7 squares, so the slate region is running 6 squares under that average while the pale yellow region is the roomiest area on the grid with 12 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 slate, with 1 square, is under far more pressure than pale yellow with 12. A 11-square gap like this one rewards players who start where the choices are fewest.
Square count is only half the story — how a color is arranged counts too. Blue is the tidiest shape on #237, packing 100% of its 2×3 bounding box, whereas mint straggles across its 5×4 box at just 50%. Tidy blocks are easy to work around; scattered ones touch more lines and resist resolution.
Region by region
Below is every color on #237 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.
Slate: 1 square across rows 5–5, columns 6–6. It never leaves row 5, so its queen is locked to that row.
Indigo covers 5 squares, spanning 3 rows and 3 columns (rows 1–3, columns 5–7).
Amber occupies 5 squares within rows 2–4, columns 5–7.
Blue: 6 squares across rows 2–3, columns 2–4.
Mint covers 10 squares, spanning 5 rows and 4 columns (rows 1–5, columns 1–4).
Red occupies 10 squares within rows 3–6, columns 2–5.
Pale yellow: 12 squares across rows 5–7, columns 1–7.
Where to start on this board
Slate is the natural opening on #237: it is the smallest region on the grid at 1 square, boxed into rows 5–5 and columns 6–6. 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 slate never leaves row 5, its queen must be in that row — and that instantly settles row 5 for everyone else. Sweep along it and X out every square that is not slate. 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. Blue 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 #237
A quick way to find the next move is to count how many different colors touch each line. On this board, row 7 is the narrowest, touched by only 1 color. Column 1 is the tightest column, with 2 colors.
A line with few colors is a line close to resolving. Where only 1 color appear, one of them owns the row outright and the others must fit into the remaining 6 rows. Row 3 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.
Two checks, run alternately, will carry you through the 49 squares of this grid. First: has any of the seven regions been reduced to a single open square? Second: has any row or column? Either answer forces a queen. Players who stall on 7x7 boards almost always run one of those checks and forget the other.
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 #237 is rated hard
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 1 color, and a region-size spread of 11. Lopsided grids with flat regions fall quickly; balanced ones like this take more patience.
Difficulty in Queens is never arithmetic and never luck. Every board has one solution and none require guessing. What varies is the length of the chain you must follow before the next queen becomes certain — one or two steps on an easy board, five or six on a hard one, sometimes with several partial eliminations held in play at once.
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 #237, start hunting for it near row 7.
A non-spoiling distribution check: solved, #237 carries 3 queens on the perimeter against 4 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
- 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 #237?
Puzzle #237 is rated hard. Its smallest color region holds 1 square, its tightest row is touched by 1 color, and two of its regions are confined to a single row or column, which gives you a forced move early.
Does 7x7 puzzle #237 have only one solution?
Yes. Every puzzle in the 7x7 collection, including #237, 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 #237?
Start with the slate region — the most constrained color on this board, with 1 square spanning rows 5–5 and columns 6–6. Narrowing the smallest region first removes the most squares elsewhere on the grid.