7x7 Queens Puzzle #159

Difficulty: easy. 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 7-step reasoning is written out below.

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Step-by-step solution for puzzle #159

What follows is a complete solve of puzzle #159, worked the way a person works it rather than the way a computer does. It runs to 7 deductions, every one of them a forced placement. Each step names the rule that forces it, so nothing below is a guess, and the hardest idea required is the last square in a region.

Techniques this board needs: last square in a region.

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

  1. Step 1. Only row 3, column 5 is still open in blue, and since each colour must take a queen, that settles it. That clears row 3, column 5, the rest of the blue region and every square adjacent to it — diagonals included.

  2. Step 2. The slate region is down to one open square, at row 5, column 7. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 5 and column 7, the remaining slate squares, and the ring of neighbours around row 5, column 7.

  3. Step 3. Only row 1, column 6 is still open in indigo, and since each colour must take a queen, that settles it. Everything else in row 1, in column 6, in indigo and in the ring around that square is now dead.

  4. Step 4. The amber region is down to one open square, at row 2, column 3. Every colour holds exactly one queen, so that square is forced. Row 2 and column 3 are now spoken for, along with the squares touching that queen.

    Puzzle #159 after step 4: 4 of 7 queens placed
    The board after step 4 — 4 of 7 queens placed.

  5. Step 5. Only row 6, column 1 is still open in red, and since each colour must take a queen, that settles it. That clears row 6, column 1, the rest of the red region and every square adjacent to it — diagonals included.

  6. Step 6. The mint region is down to one open square, at row 4, column 2. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 4 and column 2, the remaining mint squares, and the ring of neighbours around row 4, column 2.

  7. Step 7. Only row 7, column 4 is still open in pale yellow, and since each colour must take a queen, that settles it. Everything else in row 7, in column 4, in pale yellow and in the ring around that square is now dead.

    Puzzle #159 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 #159

7x7 puzzle #159 is rated easy. Seven colored regions cover its 49 squares, and your job is to seat seven queens so that every row, column and color contains exactly one — with no queen touching another, including diagonally.

Like every board on this site, #159 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 #159 are: blue (1 square), slate (1 square), red (2 squares), amber (6 squares), pale yellow (11 squares), indigo (12 squares), mint (16 squares). An even split would hand every color 7 squares, so the blue region is running 6 squares under that average while the mint region is the roomiest area on the grid with 16 squares.

Every color takes one queen and one only, whatever its size — which is why the 15 square difference between blue and mint is worth noting before you touch the grid. The cramped colors resolve first and hand you information; the roomy ones absorb whatever is left over at the end.

Look at arrangement as well as area. Blue is the densest region on this grid at 100% of a 1×1 frame; mint is the loosest, occupying only 57% of its 7×4 frame. The loose one reaches into more rows and columns, which is exactly why it usually settles last.

Region by region

Below is every color on #159 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.

Blue: 1 square across rows 3–3, columns 5–5. It never leaves row 3, so its queen is locked to that row.

Slate covers 1 square, spanning 1 row and 1 column (rows 5–5, columns 7–7). It never leaves row 5, so its queen is locked to that row.

Red occupies 2 squares within rows 5–6, columns 1–1. It sits wholly inside column 1, so its queen must be in that column.

Amber: 6 squares across rows 1–3, columns 3–5.

Pale yellow covers 11 squares, spanning 3 rows and 5 columns (rows 5–7, columns 3–7).

Indigo occupies 12 squares within rows 1–5, columns 5–7.

Mint: 16 squares across rows 1–7, columns 1–4.

Where to start on this board

The most constrained color is where a solve should begin, and on #159 that is blue with 1 square. It reaches from row 3 to row 3 and from column 5 to column 5 — 1 row by 1 column. One queen has to live inside that footprint no matter what else happens, which makes those lines the busiest real estate on the board.

Because blue never leaves row 3, its queen must be in that row — and that instantly settles row 3 for everyone else. Sweep along it and X out every square that is not blue. 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. Slate 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 #159

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

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 5, meeting 5 colors, is the opposite case — the busiest line on #159 and the last one you should expect to crack.

Working through the middle game

The middle of #159 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.

With seven queens to seat and seven regions competing over 49 squares, keep two questions in rotation. Does any region now have exactly one open square left? That queen is forced. Does any row or column now have exactly one open square left? That queen is forced too. Alternating between the region view and the row-and-column view is what keeps a solve moving, and it is the clearest difference between players who finish 7x7 boards quickly and players who stall halfway.

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 #159 is rated easy

What earns a board its rating is the shape of its opening. Here that opening offers five single-line regions, a 1-square smallest color, a tightest row touched by 2 colors, and a region-size spread of 15. 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 easy board from the rest.

If #159 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.

There is one technique that repays study at every grid size. Two regions restricted to the same two rows must occupy one row apiece, which excludes all other regions from those rows entirely; the identical logic applies to columns and to larger matched sets. It converts slow boards into fast ones, and the likeliest place to find it on #159 is column 2.

Here is a shape check that gives nothing away: when #159 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 #159?

Puzzle #159 is rated easy. Its smallest color region holds 1 square, its tightest row is touched by 2 colors, and five of its regions are confined to a single row or column, which gives you a forced move early.

Does 7x7 puzzle #159 have only one solution?

Yes. Every puzzle in the 7x7 collection, including #159, 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 #159?

Start with the blue region — the most constrained color on this board, with 1 square spanning rows 3–3 and columns 5–5. Narrowing the smallest region first removes the most squares elsewhere on the grid.