7x7 Queens Puzzle #38
Difficulty: medium. 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 15-step reasoning is written out below.
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Step-by-step solution for puzzle #38
What follows is a complete solve of puzzle #38, worked the way a person works it rather than the way a computer does. It runs to 15 deductions — 7 queen placements and 8 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 line confined to one region.
Techniques this board needs: last square in a region, region shadow, region confined to one line, line confined to one region, last square in a row.
Show the full walkthrough (10 steps) — contains the solution
Step 1. Only row 7, column 1 is still open in pale yellow, and since each colour must take a queen, that settles it. That clears row 7, column 1, the rest of the pale yellow region and every square adjacent to it — diagonals included.
Step 2. Mint is down to 4 candidates in rows 4–6, columns 2 and 3, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about mint itself.
Step 3. The slate 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.
The board after step 3 — 1 of 7 queens placed. Step 4. All of the red region's remaining squares (2 open squares) lie in row 6. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 5 squares come off.
Step 5. Mint cannot leave column 2 — every one of its open squares (2 open squares) sits there. That column belongs to mint, so every square in it owned by another colour is dead: 3 squares in all.
Step 6. All of the amber region's remaining squares (2 open squares) lie in column 3. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 3 squares come off.
Step 7. Slate cannot leave column 4 — every one of its open squares (2 open squares) sits there. That column belongs to slate, so every square in it owned by another colour is dead: 2 squares in all.
The board after step 7 — 1 of 7 queens placed. Step 8. Blue is down to 4 candidates in rows 3–5, columns 5–7, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about blue itself.
Step 9. Row 1 has only indigo squares left (3 open squares). The row needs a queen and only indigo can provide one, which pins that colour to this row and kills its squares elsewhere: 4 squares.
Step 10. 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: row 2 is down to one square, putting a queen on row 2, column 3; row 3 is down to one square, putting a queen on row 3, column 5; slate has one square left, so its queen takes row 5, column 4; mint has one square left, so its queen takes row 4, column 2; red has one square left, so its queen takes row 6, column 6; indigo has one square left, so its queen takes row 1, column 7. 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 1, column 7.
The board after step 10 — 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 #38
Board #38 of the 7x7 bank carries a medium 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, #38 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 #38 are: pale yellow (1 square), slate (5 squares), red (5 squares), amber (7 squares), blue (9 squares), indigo (10 squares), mint (12 squares). An even split would hand every color 7 squares, so the pale yellow region is running 6 squares under that average while the mint region is the roomiest area on the grid with 12 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; mint has 12. The spread between them on this board is 11 squares, and the wider that spread runs, the more it pays to solve from the small end inward.
A region's outline can constrain it more than its size does. Here pale yellow is the most solid, filling 100% of its 1×1 box, and blue the most diffuse at 45% of its 5×4 box. Solid blocks give clean eliminations; diffuse ones spread across the board and stay open longer.
Region by region
Below is every color on #38 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 1–1. It never leaves row 7, so its queen is locked to that row.
Slate: 5 squares across rows 4–7, columns 4–5.
Red covers 5 squares, spanning 2 rows and 3 columns (rows 6–7, columns 5–7).
Amber occupies 7 squares within rows 1–4, columns 1–3.
Blue: 9 squares across rows 2–6, columns 4–7.
Indigo covers 10 squares, spanning 3 rows and 5 columns (rows 1–3, columns 3–7).
Mint occupies 12 squares within rows 2–7, columns 1–3.
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 1 to column 1. 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. Red 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 #38
A quick way to find the next move is to count how many different colors touch each line. On this board, row 1 is the narrowest, touched by only 2 colors. Column 2 is the tightest column, with 2 colors.
Count colors per line and you have a ranking of where to look. The narrowest rows here see only 2 colors, so one of that handful must take the row and the rest are squeezed into the other 6 rows. Row 7 sits at the far end with 4 colors crossing it; it will almost certainly be among the last to settle.
Working through the middle game
The middle of #38 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.
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.
Resist the plausible-looking queen. On #38 every correct placement has a stated reason behind it, and any move you cannot justify is a guess wearing a disguise. Backing out of a wrong guess on a single-solution board takes far longer than finding the real deduction would have.
Why puzzle #38 is rated medium
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 2 colors, and a region-size spread of 11. Lopsided grids with flat regions fall quickly; balanced ones like this take more patience.
Nothing about the rating involves computation or chance. Each grid has a single solution reachable by pure logic; the rating simply measures how far ahead you have to reason. Easy boards resolve a queen every step or two, while hard ones can ask you to carry three unfinished lines of thought before any of them pays off.
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 #38 the place to look for one is around row 1.
Use this as a rough check on your progress: the completed board has 2 queens around the border and 5 queens in the middle, including 2 in 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 7x7 Queens puzzle #38?
Puzzle #38 is rated medium. 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 #38 have only one solution?
Yes. Every puzzle in the 7x7 collection, including #38, 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 #38?
Start with the pale yellow region — the most constrained color on this board, with 1 square spanning rows 7–7 and columns 1–1. Narrowing the smallest region first removes the most squares elsewhere on the grid.