7x7 Queens Puzzle #41
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 15-step reasoning is written out below.
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Step-by-step solution for puzzle #41
What follows is a complete solve of puzzle #41, 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 pairing argument on columns.
Techniques this board needs: region shadow, region confined to one line, pairing argument on rows, pairing argument on columns, last square in a region.
Show the full walkthrough (12 steps) — contains the solution
Step 1. Wherever indigo ends up among its 3 squares, the same squares fall within reach of it — 2 squares in total, impossible regardless of how the colour resolves.
Step 2. Mint is down to 5 candidates in rows 3 and 4, columns 1–4, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about mint itself.
Step 3. The slate region has 5 squares left, spread across rows 5 and 6, columns 1–3. 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 4. All of the pale yellow region's remaining squares (3 open squares) lie in row 7. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 4 squares come off.
The board after step 4 — 0 of 7 queens placed. Step 5. Indigo, amber, blue, and mint are now boxed into rows 1–4 and nothing else. That is 4 colours needing 4 rows, so they fill those rows between them — which locks every remaining colour out and removes 1 square at once.
Step 6. Here is the pairing argument. The indigo, slate, and pale yellow regions have no open squares outside columns 1–3 — 3 colours confined to 3 columns. Between them they must take one column each, in some order, so every other colour is shut out of all of them: 7 squares come off in one stroke.
Step 7. Wherever amber ends up among its 3 squares, the same squares fall within reach of it — 2 squares in total, impossible regardless of how the colour resolves.
Step 8. From here the board cascades. Keep alternating the region sweep and the line sweep and 4 queens fall out in order without any new idea being needed: mint has one square left, so its queen takes row 4, column 4; amber has one square left, so its queen takes row 2, column 5; indigo has one square left, so its queen takes row 1, column 1; blue has one square left, so its queen takes row 3, 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 3, column 7.
The board after step 8 — 4 of 7 queens placed. Step 9. The slate region has 2 squares left, spread across rows 5 and 6, columns 2 and 3. 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 10. Only row 7, column 3 is still open in pale yellow, and since each colour must take a queen, that settles it. That clears row 7, column 3, the rest of the pale yellow region and every square adjacent to it — diagonals included.
Step 11. The slate region is down to one open square, at row 5, column 2. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 5 and column 2, the remaining slate squares, and the ring of neighbours around row 5, column 2.
Step 12. Only row 6, column 6 is still open in red, and since each colour must take a queen, that settles it. Everything else in row 6, in column 6, in red and in the ring around that square is now dead.
The board after step 12 — 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 #41
Puzzle #41 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, #41 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 #41 are: indigo (3 squares), pale yellow (4 squares), slate (5 squares), mint (6 squares), amber (8 squares), blue (9 squares), red (14 squares). An even split would hand every color 7 squares, so the indigo region is running 4 squares under that average while the red region is the roomiest area on the grid with 14 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 indigo, with 3 squares, is under far more pressure than red with 14. 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. Red is the tidiest shape on #41, packing 88% of its 4×4 bounding box, whereas pale yellow straggles across its 2×3 box at just 67%. 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 #41, smallest first. Reading these spans before you place anything is the quickest way to see which parts of the grid are genuinely contested.
Indigo occupies 3 squares within rows 1–2, columns 1–2.
Pale yellow: 4 squares across rows 6–7, columns 1–3.
Slate covers 5 squares, spanning 2 rows and 3 columns (rows 5–6, columns 1–3).
Mint occupies 6 squares within rows 3–4, columns 1–4.
Amber: 8 squares across rows 1–3, columns 2–5.
Blue covers 9 squares, spanning 4 rows and 3 columns (rows 1–4, columns 5–7).
Red occupies 14 squares within rows 4–7, columns 4–7.
Where to start on this board
Indigo is the natural opening on #41: it is the smallest region on the grid at 3 squares, boxed into rows 1–2 and columns 1–2. 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.
Indigo 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. Mint, slate and pale yellow 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 #41
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 5 and 7 are the narrowest, touched by only 2 colors. Columns 6 and 7 are the tightest columns, with 2 colors.
The fewer colors a line touches, the sooner it surrenders its queen. A row meeting just 2 colors has to be claimed by one of them, which pushes every remaining region into the other 6 rows. Row 6, meeting 3 colors, is the opposite case — the busiest line on #41 and the last one you should expect to crack.
Working through the middle game
The middle of #41 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.
The whole middle game reduces to two sweeps. Sweep the seven colors looking for one with a single square left; sweep the seven rows and seven columns looking for the same. Each sweep feeds the next, and switching between them deliberately — rather than drifting — is what separates a fast 7x7 solve from a stalled one.
Resist the plausible-looking queen. On #41 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 #41 is rated hard
The rating reflects how much the board concedes up front. Puzzle #41 has no region confined to a single row or column, its smallest color holds 3 squares, its tightest row meets just 2 colors, and the gap between its largest and smallest regions is 11 squares. Flat, lopsided boards open quickly; even, sprawling ones make you earn the first placement.
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 #41, start hunting for it near row 5.
Here is a shape check that gives nothing away: when #41 is solved, 3 queens sit on the outer edge of the grid and 4 sit inside it, with 1 queen in a corner. A work-in-progress board that clusters its queens in one quadrant while leaving others bare is usually carrying a mistake.
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 #41?
Puzzle #41 is rated hard. Its smallest color region holds 3 squares, its tightest row is touched by 2 colors, and no region is confined to a single row or column, so the opening move takes some hunting.
Does 7x7 puzzle #41 have only one solution?
Yes. Every puzzle in the 7x7 collection, including #41, 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 #41?
Start with the indigo region — the most constrained color on this board, with 3 squares spanning rows 1–2 and columns 1–2. Narrowing the smallest region first removes the most squares elsewhere on the grid.