7x7 Queens Puzzle #171

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 11-step reasoning is written out below.

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Step-by-step solution for puzzle #171

What follows is a complete solve of puzzle #171, worked the way a person works it rather than the way a computer does. It runs to 11 deductions — 7 queen placements and 4 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: last square in a region, region confined to one line, region shadow.

Show the full walkthrough (8 steps) — contains the solution

  1. Step 1. Only row 7, column 4 is still open in pale yellow, and since each colour must take a queen, that settles it. That clears row 7, column 4, the rest of the pale yellow region and every square adjacent to it — diagonals included.

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

  3. Step 3. Only row 2, column 7 is still open in amber, and since each colour must take a queen, that settles it. Everything else in row 2, in column 7, in amber and in the ring around that square is now dead.

  4. Step 4. Wherever mint ends up among its 4 squares, the same squares fall within reach of it — 2 squares in total, impossible regardless of how the colour resolves.

    Puzzle #171 after step 4: 2 of 7 queens placed
    The board after step 4 — 2 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 has 2 squares left, spread across rows 4 and 5, columns 2 and 3. You do not need to know which of them takes the queen: every one of those options attacks the same 1 square, so they can be crossed out now.

  7. Step 7. Slate cannot leave row 5 — every one of its open squares (2 open squares) sits there. That row belongs to slate, so every square on it owned by another colour is dead: 3 squares in all.

  8. Step 8. From here the board cascades. Keep alternating the region sweep and the line sweep and 4 queens fall out in order without any new idea being needed: mint has one square left, so its queen takes row 4, column 2; indigo has one square left, so its queen takes row 1, column 3; blue has one square left, so its queen takes row 3, column 5; slate has one square left, so its queen takes row 5, column 6. 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 5, column 6.

    Puzzle #171 after step 8: 7 of 7 queens placed
    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 #171

7x7 puzzle #171 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.

There is exactly one way to finish #171, and it has been verified. More importantly, you can reach it without ever gambling: at every stage some square is provably right or provably wrong. Boards differ only in how deep you must dig before that proof appears, and the geometry of these seven regions is what sets the depth.

How the colors divide this board

From smallest to largest, the regions on puzzle #171 are: pale yellow (1 square), amber (2 squares), indigo (3 squares), red (3 squares), mint (4 squares), slate (16 squares), blue (20 squares). An even split would hand every color 7 squares, so the pale yellow region is running 6 squares under that average while the blue region is the roomiest area on the grid with 20 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 blue has 20 to spare, a gap of 19. Attack the cramped end and the roomy regions tend to resolve themselves.

Look at arrangement as well as area. Indigo is the densest region on this grid at 100% of a 1×3 frame; slate is the loosest, occupying only 67% of its 4×6 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 #171 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: 1 square across rows 7–7, columns 4–4. It never leaves row 7, so its queen is locked to that row.

Amber covers 2 squares, spanning 2 rows and 1 column (rows 1–2, columns 7–7). It sits wholly inside column 7, so its queen must be in that column.

Indigo occupies 3 squares within rows 1–1, columns 2–4. It never leaves row 1, so its queen is locked to that row.

Red: 3 squares across rows 5–7, columns 1–1. It sits wholly inside column 1, so its queen must be in that column.

Mint covers 4 squares, spanning 2 rows and 3 columns (rows 4–5, columns 1–3).

Slate occupies 16 squares within rows 4–7, columns 2–7.

Blue: 20 squares across rows 1–4, columns 1–7.

Where to start on this board

The most constrained color is where a solve should begin, and on #171 that is pale yellow with 1 square. It reaches from row 7 to row 7 and from column 4 to column 4 — 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. Indigo, amber and mint 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 #171

A quick way to find the next move is to count how many different colors touch each line. On this board, row 3 is the narrowest, touched by only 1 color. Columns 5 and 6 are the tightest columns, with 2 colors.

The fewer colors a line touches, the sooner it surrenders its queen. A row meeting just 1 color 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 #171 and the last one you should expect to crack.

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 #171 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 1 color, and a region-size spread of 19. 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.

Stuck on #171 despite the easy rating? The odds strongly favour a bookkeeping error over a hard chain of logic. Re-check each placed queen for its complete set of eliminations, paying particular attention to the four diagonal squares — those are the ones that get overlooked, and one of them is usually sitting on the answer.

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 3 on this board.

Here is a shape check that gives nothing away: when #171 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 #171?

Puzzle #171 is rated easy. Its smallest color region holds 1 square, its tightest row is touched by 1 color, and five of its regions are confined to a single row or column, which gives you a forced move early.

Does 7x7 puzzle #171 have only one solution?

Yes. Every puzzle in the 7x7 collection, including #171, 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 #171?

Start with the pale yellow region — the most constrained color on this board, with 1 square spanning rows 7–7 and columns 4–4. Narrowing the smallest region first removes the most squares elsewhere on the grid.