7x7 Queens Puzzle #105

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 #105

What follows is a complete solve of puzzle #105, 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 row.

Techniques this board needs: last square in a region, last square in a row.

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

  1. Step 1. Only row 2, column 5 is still open in amber, and since each colour must take a queen, that settles it. That clears row 2, column 5, the rest of the amber region and every square adjacent to it — diagonals included.

  2. Step 2. The indigo region is down to one open square, at row 1, column 7. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 1 and column 7, the remaining indigo squares, and the ring of neighbours around row 1, column 7.

  3. Step 3. Only row 4, column 4 is still open in mint, and since each colour must take a queen, that settles it. Everything else in row 4, in column 4, in mint and in the ring around that square is now dead.

  4. Step 4. The slate region is down to one open square, at row 5, column 1. Every colour holds exactly one queen, so that square is forced. Row 5 and column 1 are now spoken for, along with the squares touching that queen.

    Puzzle #105 after step 4: 4 of 7 queens placed
    The board after step 4 — 4 of 7 queens placed.

  5. Step 5. Look along row 3: one square survives, row 3, column 2, which belongs to blue. A row cannot be left empty, so the queen goes there. Everything else in row 3, in column 2, in blue and in the ring around that square is now dead.

  6. Step 6. The pale yellow region is down to one open square, at row 7, column 3. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 7 and column 3, the remaining pale yellow squares, and the ring of neighbours around row 7, column 3.

  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 #105 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 #105

Puzzle #105 is one of the easy-rated boards in the 7x7 set. Seven colors divide its 49 squares, and you win by placing seven queens so that each row, each column and each color holds exactly one, with no two queens adjacent in any direction.

Puzzle #105 has been checked to admit exactly one arrangement of queens, and every step toward it is deducible from what is already on the board. There is no point at which you are expected to pick a square and hope. The only thing that differs between boards is how quickly the first certainty surfaces, and that depends entirely on the shapes the colors happen to take here.

How the colors divide this board

From smallest to largest, the regions on puzzle #105 are: amber (1 square), mint (2 squares), slate (2 squares), indigo (4 squares), pale yellow (7 squares), red (14 squares), blue (19 squares). An even split would hand every color 7 squares, so the amber region is running 6 squares under that average while the blue region is the roomiest area on the grid with 19 squares.

Why does the split matter? Because a region's square count has no bearing on how many queens it gets — the answer is always one. So amber, with 1 square, is under far more pressure than blue with 19. A 18-square gap like this one rewards players who start where the choices are fewest.

Square count is only half the story — how a color is arranged counts too. Indigo is the tidiest shape on #105, packing 100% of its 2×2 bounding box, whereas blue straggles across its 6×5 box at just 63%. Tidy blocks are easy to work around; scattered ones touch more lines and resist resolution.

Region by region

Each region's exact extent on this grid is listed below, starting with the most constrained. Knowing which lines a color can and cannot reach is most of the work on a easy board.

Amber: 1 square across rows 2–2, columns 5–5. It never leaves row 2, so its queen is locked to that row.

Mint covers 2 squares, spanning 2 rows and 1 column (rows 3–4, columns 4–4). It sits wholly inside column 4, so its queen must be in that column.

Slate occupies 2 squares within rows 4–5, columns 1–1. It sits wholly inside column 1, so its queen must be in that column.

Indigo: 4 squares across rows 1–2, columns 6–7.

Pale yellow covers 7 squares, spanning 2 rows and 4 columns (rows 6–7, columns 1–4).

Red occupies 14 squares within rows 3–7, columns 5–7.

Blue: 19 squares across rows 1–6, columns 1–5.

Where to start on this board

Amber is the natural opening on #105: it is the smallest region on the grid at 1 square, boxed into rows 2–2 and columns 5–5. Since one of those squares must hold a queen, that block of 1 row and 1 column is the most contested part of the board.

Because amber never leaves row 2, its queen must be in that row — and that instantly settles row 2 for everyone else. Sweep along it and X out every square that is not amber. 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, mint, slate 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 #105

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

Count colors per line and you have a ranking of where to look. The narrowest rows here see only 2 colors, so one of that handful must take the row and the rest are squeezed into the other 6 rows. Row 4 sits at the far end with 4 colors crossing it; it will almost certainly be among the last to settle.

Working through the middle game

After the first few queens the puzzle becomes bookkeeping. A placed queen wipes its row, its column and every square it touches — as many as eight neighbours — so the space collapses quickly. Record those eliminations on the board instead of carrying them in your head, and the next forced move tends to announce itself.

Two checks, run alternately, will carry you through the 49 squares of this grid. First: has any of the seven regions been reduced to a single open square? Second: has any row or column? Either answer forces a queen. Players who stall on 7x7 boards almost always run one of those checks and forget the other.

Resist the plausible-looking queen. On #105 every correct placement has a stated reason behind it, and any move you cannot justify is a guess wearing a disguise. Backing out of a wrong guess on a single-solution board takes far longer than finding the real deduction would have.

Why puzzle #105 is rated easy

The easy label comes out of four measurable things about #105: four of its regions are locked to one row or column, its smallest color spans 1 square, its least crowded row meets 2 colors, and its largest and smallest regions differ by 18. Boards that score tight on those measures give up their first queen fast.

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.

When a board plays tougher than its label, look for a missed mark before you look for a clever deduction. Walk back over every queen you have placed and confirm the full row, the full column and all eight surrounding squares are crossed out. The diagonal neighbours are the ones players skip, and a single skipped diagonal will hide the next forced move indefinitely.

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.

Learn the pairing argument and you will use it on every board, this one included. If two colors can only sit inside the same two rows, between them they consume both rows and every other color is shut out. It generalises to any matching count — three colors across three rows, four across four. On #105, start hunting for it near row 1.

Use this as a rough check on your progress: the completed board has 3 queens around the border and 4 queens in the middle, including 1 in a corner. Solutions spread out; if yours is bunching up in one region of the grid, retrace a few moves.

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 #105?

Puzzle #105 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 #105 have only one solution?

Yes. Every puzzle in the 7x7 collection, including #105, 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 #105?

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