7x7 Queens Puzzle #134
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 13-step reasoning is written out below.
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Step-by-step solution for puzzle #134
What follows is a complete solve of puzzle #134, worked the way a person works it rather than the way a computer does. It runs to 13 deductions — 7 queen placements and 6 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, region confined to one line, pairing argument on rows, last square in a column.
Show the full walkthrough (8 steps) — contains the solution
Step 1. 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 2. Amber is down to 5 candidates in rows 1–3, columns 1 and 2, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about amber itself.
Step 3. Blue cannot leave column 6 — every one of its open squares (2 open squares) sits there. That column belongs to blue, so every square in it owned by another colour is dead: 8 squares in all.
Step 4. Wherever slate ends up among its 2 squares, the same squares fall within reach of it — 2 squares in total, impossible regardless of how the colour resolves.
The board after step 4 — 1 of 7 queens placed. Step 5. Red cannot leave column 7 — every one of its open squares (2 open squares) sits there. That column belongs to red, so every square in it owned by another colour is dead: 2 squares in all.
Step 6. Here is the pairing argument. The slate and red regions have no open squares outside rows 5 and 6 — 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 7. Mint cannot leave row 4 — every one of its open squares (2 open squares) sits there. That row belongs to mint, so every square on it owned by another colour is dead: 1 square in all.
Step 8. 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: blue has one square left, so its queen takes row 3, column 6; column 5 is down to one square, putting a queen on row 1, column 5; amber has one square left, so its queen takes row 2, column 1; 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; red has one square left, so its queen takes row 6, 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 6, column 7.
The board after step 8 — 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 #134
Board #134 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.
Like every board on this site, #134 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 #134 are: pale yellow (1 square), blue (2 squares), amber (6 squares), slate (7 squares), indigo (9 squares), red (11 squares), mint (13 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 13 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 13. The spread between them on this board is 12 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. Blue is the tidiest shape on #134, packing 100% of its 2×1 bounding box, whereas mint straggles across its 5×5 box at just 52%. Tidy blocks are easy to work around; scattered ones touch more lines and resist resolution.
Region by region
Below is every color on #134 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 3–3. It never leaves row 7, so its queen is locked to that row.
Blue: 2 squares across rows 3–4, columns 6–6. It sits wholly inside column 6, so its queen must be in that column.
Amber covers 6 squares, spanning 3 rows and 3 columns (rows 1–3, columns 1–3).
Slate occupies 7 squares within rows 5–7, columns 1–3.
Indigo: 9 squares across rows 1–3, columns 4–7.
Red covers 11 squares, spanning 5 rows and 4 columns (rows 3–7, columns 4–7).
Mint occupies 13 squares within rows 2–6, columns 1–5.
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 3 to column 3. 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. 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 #134
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 7 is the tightest column, 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 3 is the crowded extreme at 5 colors — worth revisiting later, not now.
Working through the middle game
Once two or three queens are down, the board changes character. Each queen removes an entire row, an entire column and the ring of up to eight squares around it, so the grid shrinks faster than most people expect. The habit that pays here is marking rather than remembering: after every placement, cross out the full row, the full column and all eight neighbours before hunting for the next move.
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 #134 is rated medium
What earns a board its rating is the shape of its opening. Here that opening offers three single-line regions, a 1-square smallest color, a tightest row touched by 2 colors, and a region-size spread of 12. Lopsided grids with flat regions fall quickly; balanced ones like this take more patience.
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 medium board from the rest.
If #134 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.
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 #134 the place to look for one is around row 1.
A non-spoiling distribution check: solved, #134 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 #134?
Puzzle #134 is rated medium. Its smallest color region holds 1 square, its tightest row is touched by 2 colors, and three of its regions are confined to a single row or column, which gives you a forced move early.
Does 7x7 puzzle #134 have only one solution?
Yes. Every puzzle in the 7x7 collection, including #134, 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 #134?
Start with the pale yellow region — the most constrained color on this board, with 1 square spanning rows 7–7 and columns 3–3. Narrowing the smallest region first removes the most squares elsewhere on the grid.