7x7 Queens Puzzle #49
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 10-step reasoning is written out below.
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Step-by-step solution for puzzle #49
What follows is a complete solve of puzzle #49, worked the way a person works it rather than the way a computer does. It runs to 10 deductions — 7 queen placements and 3 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: region confined to one line, last square in a region.
Show the full walkthrough (5 steps) — contains the solution
Step 1. Blue cannot leave column 7 — every one of its open squares (3 open squares) sits there. That column belongs to blue, so every square in it owned by another colour is dead: 5 squares in all.
Step 2. All of the red region's remaining squares (2 open squares) lie in column 6. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 6 squares come off.
Step 3. Only row 2, column 5 is still open in amber, and since each colour must take a queen, that settles it. Everything else in row 2, in column 5, in amber and in the ring around that square is now dead.
The board after step 3 — 1 of 7 queens placed. Step 4. All of the mint region's remaining squares (2 open squares) lie in column 4. Its queen therefore has to be somewhere in that column, 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 6 queens fall out in order without any new idea being needed: pale yellow has one square left, so its queen takes row 7, column 3; red has one square left, so its queen takes row 6, column 6; slate has one square left, so its queen takes row 5, column 2; mint has one square left, so its queen takes row 4, column 4; blue has one square left, so its queen takes row 3, column 7; indigo has one square left, so its queen takes row 1, column 1. 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 1.
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 #49
Puzzle #49 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.
Like every board on this site, #49 has been verified to have exactly one valid solution, and that solution is reachable by deduction alone. You never have to guess and then unwind; every queen can be justified by something already visible on the grid. What changes from puzzle to puzzle is where the first certainty appears and how long the chain of reasoning runs before the next one — and that is entirely a product of how these particular colors are shaped.
How the colors divide this board
From smallest to largest, the regions on puzzle #49 are: blue (3 squares), red (4 squares), pale yellow (4 squares), amber (6 squares), mint (7 squares), indigo (9 squares), slate (16 squares). An even split would hand every color 7 squares, so the blue region is running 4 squares under that average while the slate region is the roomiest area on the grid with 16 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 blue, with 3 squares, is under far more pressure than slate with 16. A 13-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 #49, packing 100% of its 3×1 bounding box, whereas slate straggles across its 7×5 box at just 46%. 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 #49, smallest first. Reading these spans before you place anything is the quickest way to see which parts of the grid are genuinely contested.
Blue covers 3 squares, spanning 3 rows and 1 column (rows 2–4, columns 7–7). It sits wholly inside column 7, so its queen must be in that column.
Red occupies 4 squares within rows 6–7, columns 6–7.
Pale yellow: 4 squares across rows 6–7, columns 3–5.
Amber covers 6 squares, spanning 4 rows and 3 columns (rows 1–4, columns 5–7).
Mint occupies 7 squares within rows 4–6, columns 4–7.
Indigo: 9 squares across rows 1–5, columns 1–2.
Slate covers 16 squares, spanning 7 rows and 5 columns (rows 1–7, columns 1–5).
Where to start on this board
Blue is the natural opening on #49: it is the smallest region on the grid at 3 squares, boxed into rows 2–4 and columns 7–7. Since one of those squares must hold a queen, that block of 3 rows and 1 column is the most contested part of the board.
Because blue stays inside column 7, its queen belongs to that column and no other region may use it. Cross out the rest of column 7 straight away. Any color that was relying on those squares now has a visibly smaller footprint, and that shrinkage is where your second deduction comes from.
Work outward to the other flat regions next. Pale yellow and red 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 #49
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 1, 5 and 7 are the narrowest, touched by only 3 colors. Columns 1, 2 and 3 are the tightest columns, with 2 colors.
A line with few colors is a line close to resolving. Where only 3 colors appear, one of them owns the row outright and the others must fit into the remaining 6 rows. Row 4 is the crowded extreme at 5 colors — worth revisiting later, not now.
Working through the middle game
The middle of #49 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.
A placement without a reason is a guess. Because this board has exactly one solution, a guess that happens to be wrong will not announce itself for several moves — and unwinding it is slower than simply finishing the eliminations first.
Why puzzle #49 is rated hard
The rating reflects how much the board concedes up front. Puzzle #49 has one region confined to a single row or column, its smallest color holds 3 squares, its tightest row meets just 3 colors, and the gap between its largest and smallest regions is 13 squares. Flat, lopsided boards open quickly; even, sprawling ones make you earn the first placement.
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.
If #49 feels harder than its rating suggests, the usual culprit is incomplete marking rather than a difficult deduction. Check that every queen already on the grid has its full cross of eliminations recorded — including the diagonal neighbours, which are by far the easiest to miss. More stalled solves come from one forgotten diagonal X than from any genuinely deep chain of logic.
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 #49, start hunting for it near column 1.
A non-spoiling distribution check: solved, #49 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 #49?
Puzzle #49 is rated hard. Its smallest color region holds 3 squares, its tightest row is touched by 3 colors, and one of its regions is confined to a single row or column, which gives you a forced move early.
Does 7x7 puzzle #49 have only one solution?
Yes. Every puzzle in the 7x7 collection, including #49, 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 #49?
Start with the blue region — the most constrained color on this board, with 3 squares spanning rows 2–4 and columns 7–7. Narrowing the smallest region first removes the most squares elsewhere on the grid.