7x7 Queens Puzzle #123

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 #123

What follows is a complete solve of puzzle #123, 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 7 is still open in blue, and since each colour must take a queen, that settles it. That clears row 3, column 7, the rest of the blue region and every square adjacent to it — diagonals included.

  2. Step 2. 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. Cross out the whole of row 2 and column 3, the remaining amber squares, and the ring of neighbours around row 2, column 3.

  3. Step 3. Only row 7, column 1 is still open in pale yellow, and since each colour must take a queen, that settles it. Everything else in row 7, in column 1, in pale yellow and in the ring around that square is now dead.

  4. Step 4. 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. Row 4 and column 2 are now spoken for, along with the squares touching that queen.

    Puzzle #123 after step 4: 4 of 7 queens placed
    The board after step 4 — 4 of 7 queens placed.

  5. Step 5. Only row 5, column 4 is still open in slate, and since each colour must take a queen, that settles it. That clears row 5, column 4, the rest of the slate region and every square adjacent to it — diagonals included.

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

  7. Step 7. Only row 1, column 5 is still open in indigo, and since each colour must take a queen, that settles it. Everything else in row 1, in column 5, in indigo and in the ring around that square is now dead.

    Puzzle #123 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 #123

7x7 puzzle #123 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, #123 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 #123 are: blue (1 square), pale yellow (1 square), amber (3 squares), mint (7 squares), red (10 squares), slate (12 squares), indigo (15 squares). An even split would hand every color 7 squares, so the blue region is running 6 squares under that average while the indigo region is the roomiest area on the grid with 15 squares.

One queen per color, regardless of acreage: that is what turns this uneven split into a solving order. Blue is working with 1 square while indigo has 15 to spare, a gap of 14. Attack the cramped end and the roomy regions tend to resolve themselves.

A region's outline can constrain it more than its size does. Here blue is the most solid, filling 100% of its 1×1 box, and indigo the most diffuse at 63% of its 4×6 box. Solid blocks give clean eliminations; diffuse ones spread across the board and stay open longer.

Region by region

The complete breakdown of each region on this board follows, ordered from tightest to roomiest. Skimming the spans first tells you where the board is crowded and where it has slack.

Blue: 1 square across rows 3–3, columns 7–7. It never leaves row 3, so its queen is locked to that row.

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

Amber occupies 3 squares within rows 2–3, columns 3–4.

Mint: 7 squares across rows 1–4, columns 1–2.

Red covers 10 squares, spanning 3 rows and 4 columns (rows 5–7, columns 4–7).

Slate occupies 12 squares within rows 4–7, columns 1–4.

Indigo: 15 squares across rows 1–4, columns 2–7.

Where to start on this board

The most constrained color is where a solve should begin, and on #123 that is blue with 1 square. It reaches from row 3 to row 3 and from column 7 to column 7 — 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. Pale yellow and amber 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 #123

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 6 are the narrowest, touched by only 2 colors. Columns 5 and 6 are the tightest columns, with 2 colors.

Those lines matter because a row touched by few colors gives its queen away sooner. If a row meets only 2 colors, then one of those regions has to own it, and every other region is competing for the remaining 6 rows. By contrast row 3 meets 4 colors — the most crowded line here, and the one least likely to resolve early. Spend your attention accordingly.

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 #123 is rated easy

Ratings track how generous the opening is. On #123 you get four regions pinned to a single row or column, a smallest color of 1 square, a tightest row crossed by 2 colors, and a 14-square gap between the largest and smallest regions. Those four numbers largely explain the easy label.

Nothing about the rating involves computation or chance. Each grid has a single solution reachable by pure logic; the rating simply measures how far ahead you have to reason. Easy boards resolve a queen every step or two, while hard ones can ask you to carry three unfinished lines of thought before any of them pays off.

If #123 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.

Whatever the grid size, the pairing rule is the technique to internalise. When a pair of regions is boxed into the same pair of rows, they split those rows between them and nobody else may enter — and the same holds for columns, or for any n regions confined to n lines. Look for an instance of it around row 1 on this board.

As a sanity check rather than a spoiler: the finished solution to #123 puts 3 queens on the outer border and 4 queens in the interior, 1 of them in an actual corner. If your part-finished grid has queens bunched into one area while whole stretches sit empty, something probably went wrong a few moves back.

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 #123?

Puzzle #123 is rated easy. Its smallest color region holds 1 square, its tightest row is touched by 2 colors, and four of its regions are confined to a single row or column, which gives you a forced move early.

Does 7x7 puzzle #123 have only one solution?

Yes. Every puzzle in the 7x7 collection, including #123, 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 #123?

Start with the blue region — the most constrained color on this board, with 1 square spanning rows 3–3 and columns 7–7. Narrowing the smallest region first removes the most squares elsewhere on the grid.