7x7 Queens Puzzle #71

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 7-step reasoning is written out below.

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Step-by-step solution for puzzle #71

What follows is a complete solve of puzzle #71, 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 7, column 2 is still open in pale yellow, and since each colour must take a queen, that settles it. That clears row 7, column 2, the rest of the pale yellow 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 3. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 5 and column 3, the remaining slate squares, and the ring of neighbours around row 5, column 3.

  3. Step 3. Only row 3, column 4 is still open in blue, and since each colour must take a queen, that settles it. Everything else in row 3, in column 4, in blue 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 7. Every colour holds exactly one queen, so that square is forced. Row 2 and column 7 are now spoken for, along with the squares touching that queen.

    Puzzle #71 after step 4: 4 of 7 queens placed
    The board after step 4 — 4 of 7 queens placed.

  5. Step 5. Only row 4, column 1 is still open in mint, and since each colour must take a queen, that settles it. That clears row 4, column 1, the rest of the mint region and every square adjacent to it — diagonals included.

  6. Step 6. The indigo region is down to one open square, at row 1, column 5. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 1 and column 5, the remaining indigo squares, and the ring of neighbours around row 1, column 5.

  7. Step 7. Only row 6, column 6 is still open in red, and since each colour must take a queen, that settles it. Everything else in row 6, in column 6, in red and in the ring around that square is now dead.

    Puzzle #71 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 #71

7x7 puzzle #71 is rated hard. 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.

As with every puzzle in this collection, #71 has a single verified solution and needs no guesswork. Each queen follows from something already visible. What the board controls is tempo — how soon the first forced move shows up and how far apart the rest are spaced — and that is a direct consequence of how these colors are cut.

How the colors divide this board

From smallest to largest, the regions on puzzle #71 are: pale yellow (1 square), amber (3 squares), blue (4 squares), mint (7 squares), slate (7 squares), indigo (12 squares), red (15 squares). An even split would hand every color 7 squares, so the pale yellow region is running 6 squares under that average while the red 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. Pale yellow is working with 1 square while red has 15 to spare, a gap of 14. Attack the cramped end and the roomy regions tend to resolve themselves.

Look at arrangement as well as area. Blue is the densest region on this grid at 100% of a 2×2 frame; indigo is the loosest, occupying only 57% of its 3×7 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 #71 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 2–2. It never leaves row 7, so its queen is locked to that row.

Amber: 3 squares across rows 2–3, columns 6–7.

Blue covers 4 squares, spanning 2 rows and 2 columns (rows 3–4, columns 3–4).

Mint occupies 7 squares within rows 2–5, columns 1–2.

Slate: 7 squares across rows 5–7, columns 1–3.

Indigo covers 12 squares, spanning 3 rows and 7 columns (rows 1–3, columns 1–7).

Red occupies 15 squares within rows 4–7, columns 4–7.

Where to start on this board

The most constrained color is where a solve should begin, and on #71 that is pale yellow with 1 square. It reaches from row 7 to row 7 and from column 2 to column 2 — 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 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. Amber and blue 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 #71

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 1 color. Column 5 is the tightest column, with 2 colors.

Those lines matter because a row touched by few colors gives its queen away sooner. If a row meets only 1 color, 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

Past the opening, treat this as an elimination exercise rather than a placement exercise. Each queen takes out a row, a column and its eight neighbours, and the value of a move is measured by how much it removes. Cross everything out as you go and let the board do the remembering.

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.

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 #71 is rated hard

What earns a board its rating is the shape of its opening. Here that opening offers two single-line regions, a 1-square smallest color, a tightest row touched by 1 color, and a region-size spread of 14. Lopsided grids with flat regions fall quickly; balanced ones like this take more patience.

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.

A board that feels above its rating is nearly always a board with a missing X. Audit every queen on the grid: full row cleared, full column cleared, all eight touching squares cleared. Diagonals are the common omission, and missing one is far more often the cause of a stall than any genuine difficulty in the puzzle.

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 #71 puts 4 queens on the outer border and 3 queens in the interior, with none in a 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 #71?

Puzzle #71 is rated hard. Its smallest color region holds 1 square, its tightest row is touched by 1 color, and two of its regions are confined to a single row or column, which gives you a forced move early.

Does 7x7 puzzle #71 have only one solution?

Yes. Every puzzle in the 7x7 collection, including #71, 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 #71?

Start with the pale yellow region — the most constrained color on this board, with 1 square spanning rows 7–7 and columns 2–2. Narrowing the smallest region first removes the most squares elsewhere on the grid.