7x7 Queens Puzzle #130

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 #130

What follows is a complete solve of puzzle #130, 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 region shadow.

Techniques this board needs: region confined to one line, region shadow, last square in a region.

Show the full walkthrough (7 steps) — contains the solution

  1. Step 1. Indigo cannot leave row 1 — every one of its open squares (2 open squares) sits there. That row belongs to indigo, so every square on it owned by another colour is dead: 7 squares in all.

  2. Step 2. All of the red region's remaining squares (2 open squares) lie in column 1. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 6 squares come off.

  3. Step 3. The amber region has 4 squares left, spread across rows 2 and 3, columns 2 and 4. You do not need to know which of them takes the queen: every one of those options attacks the same 2 squares, so they can be crossed out now.

  4. Step 4. All of the mint region's remaining squares (2 open squares) lie in column 2. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 4 squares come off.

    Puzzle #130 after step 4: 0 of 7 queens placed
    The board after step 4 — 0 of 7 queens placed.

  5. Step 5. Amber cannot leave column 4 — every one of its open squares (2 open squares) sits there. That column belongs to amber, so every square in it owned by another colour is dead: 5 squares in all.

  6. Step 6. All of the pale yellow region's remaining squares (2 open squares) lie in row 7. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 3 squares come off.

  7. Step 7. From here the board cascades. Keep alternating the region sweep and the line sweep and 7 queens fall out in order without any new idea being needed: red has one square left, so its queen takes row 6, column 1; mint has one square left, so its queen takes row 4, column 2; slate has one square left, so its queen takes row 5, column 5; indigo has one square left, so its queen takes row 1, column 6; blue has one square left, so its queen takes row 3, column 7; amber has one square left, so its queen takes row 2, column 4; pale yellow has one square left, so its queen takes row 7, column 3. 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 3.

    Puzzle #130 after step 7: 7 of 7 queens placed
    The board after step 7 — 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 #130

Board #130 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, #130 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 #130 are: indigo (2 squares), red (2 squares), mint (4 squares), pale yellow (6 squares), blue (9 squares), amber (11 squares), slate (15 squares). An even split would hand every color 7 squares, so the indigo region is running 5 squares under that average while the slate region is the roomiest area on the grid with 15 squares.

That imbalance is the first thing to read, because every region takes exactly one queen regardless of how much space it owns. Indigo has only 2 places to put its queen; slate has 15. The spread between them on this board is 13 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. Indigo is the tidiest shape on #130, packing 100% of its 1×2 bounding box, whereas slate straggles across its 6×5 box at just 50%. 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 #130, smallest first. Reading these spans before you place anything is the quickest way to see which parts of the grid are genuinely contested.

Indigo covers 2 squares, spanning 1 row and 2 columns (rows 1–1, columns 5–6). It never leaves row 1, so its queen is locked to that row.

Red occupies 2 squares within rows 6–7, columns 1–1. It sits wholly inside column 1, so its queen must be in that column.

Mint: 4 squares across rows 4–5, columns 1–2.

Pale yellow covers 6 squares, spanning 2 rows and 4 columns (rows 6–7, columns 2–5).

Blue occupies 9 squares within rows 1–5, columns 5–7.

Amber: 11 squares across rows 1–3, columns 1–5.

Slate covers 15 squares, spanning 6 rows and 5 columns (rows 2–7, columns 3–7).

Where to start on this board

Begin where the choices are fewest. On this board that means indigo, which owns just 2 squares inside a 1×2 window running from row 1 to row 1 and column 5 to column 6. A queen is guaranteed somewhere in there, so every line that window crosses is under pressure from the very first move.

Because indigo never leaves row 1, its queen must be in that row — and that instantly settles row 1 for everyone else. Sweep along it and X out every square that is not indigo. 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. Mint, red 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 #130

A quick way to find the next move is to count how many different colors touch each line. On this board, rows 1, 2, 3, 4, 5, 6 and 7 are the narrowest, touched by only 3 colors. Column 7 is the tightest column, with 2 colors.

The fewer colors a line touches, the sooner it surrenders its queen. A row meeting just 3 colors has to be claimed by one of them, which pushes every remaining region into the other 6 rows. Row 7, meeting 3 colors, is the opposite case — the busiest line on #130 and the last one you should expect to crack.

Working through the middle game

The middle of #130 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.

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 #130 is rated medium

The rating reflects how much the board concedes up front. Puzzle #130 has two regions confined to a single row or column, its smallest color holds 2 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.

Rating is a measure of chain length, not of chance. With one guaranteed solution and no guessing required, the only thing that changes across the collection is how many eliminations you must link together before a queen is provably forced.

If #130 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 #130 the place to look for one is around column 7.

Here is a shape check that gives nothing away: when #130 is solved, 4 queens sit on the outer edge of the grid and 3 sit inside it, and no queen lands 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

  1. The board is an N×N grid divided into N colored regions.
  2. Place exactly one queen (♛) in each row, each column, and each colored region.
  3. No two queens may touch each other — not horizontally, vertically, or diagonally.
  4. 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.
  5. 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 #130?

Puzzle #130 is rated medium. Its smallest color region holds 2 squares, its tightest row is touched by 3 colors, and two of its regions are confined to a single row or column, which gives you a forced move early.

Does 7x7 puzzle #130 have only one solution?

Yes. Every puzzle in the 7x7 collection, including #130, 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 #130?

Start with the indigo region — the most constrained color on this board, with 2 squares spanning rows 1–1 and columns 5–6. Narrowing the smallest region first removes the most squares elsewhere on the grid.