7x7 Queens Puzzle #199

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 8-step reasoning is written out below.

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Step-by-step solution for puzzle #199

What follows is a complete solve of puzzle #199, worked the way a person works it rather than the way a computer does. It runs to 8 deductions — 7 queen placements and 1 elimination step 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 confined to one line.

Techniques this board needs: last square in a region, region confined to one line, last square in a column.

Show the full walkthrough (5 steps) — contains the solution

  1. Step 1. Only row 6, column 6 is still open in red, and since each colour must take a queen, that settles it. That clears row 6, column 6, the rest of the red 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 7. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 2 and column 7, the remaining amber squares, and the ring of neighbours around row 2, column 7.

  3. Step 3. Only row 4, column 5 is still open in mint, and since each colour must take a queen, that settles it. Everything else in row 4, in column 5, in mint and in the ring around that square is now dead.

    Puzzle #199 after step 3: 3 of 7 queens placed
    The board after step 3 — 3 of 7 queens placed.

  4. Step 4. 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: 2 squares come off.

  5. Step 5. 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: column 4 is down to one square, putting a queen on row 7, column 4; slate has one square left, so its queen takes row 5, column 1; indigo has one square left, so its queen takes row 1, column 2; blue has one square left, so its queen takes row 3, column 3. 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 3, column 3.

    Puzzle #199 after step 5: 7 of 7 queens placed
    The board after step 5 — 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 #199

7x7 puzzle #199 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.

As with every puzzle in this collection, #199 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 #199 are: red (1 square), amber (2 squares), slate (3 squares), indigo (4 squares), mint (8 squares), pale yellow (14 squares), blue (17 squares). An even split would hand every color 7 squares, so the red region is running 6 squares under that average while the blue region is the roomiest area on the grid with 17 squares.

One queen per color, regardless of acreage: that is what turns this uneven split into a solving order. Red is working with 1 square while blue has 17 to spare, a gap of 16. 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 2×2 frame; blue is the loosest, occupying only 61% of its 4×7 frame. The loose one reaches into more rows and columns, which is exactly why it usually settles last.

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.

Red covers 1 square, spanning 1 row and 1 column (rows 6–6, columns 6–6). It never leaves row 6, so its queen is locked to that row.

Amber occupies 2 squares within rows 2–2, columns 6–7. It never leaves row 2, so its queen is locked to that row.

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

Indigo covers 4 squares, spanning 2 rows and 2 columns (rows 1–2, columns 1–2).

Mint occupies 8 squares within rows 3–5, columns 5–7.

Pale yellow: 14 squares across rows 5–7, columns 2–7.

Blue covers 17 squares, spanning 4 rows and 7 columns (rows 1–4, columns 1–7).

Where to start on this board

The most constrained color is where a solve should begin, and on #199 that is red with 1 square. It reaches from row 6 to row 6 and from column 6 to column 6 — 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 red never leaves row 6, its queen must be in that row — and that instantly settles row 6 for everyone else. Sweep along it and X out every square that is not red. 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 indigo 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 #199

A quick way to find the next move is to count how many different colors touch each line. On this board, rows 1, 3, 4 and 7 are the narrowest, touched by only 2 colors. Columns 3 and 4 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 6 sits at the far end with 3 colors crossing it; it will almost certainly be among the last to settle.

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.

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 #199 is rated easy

The easy label comes out of four measurable things about #199: 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 16. 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.

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.

Use this as a rough check on your progress: the completed board has 4 queens around the border and 3 queens in the middle, and nothing in the corners. 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 #199?

Puzzle #199 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 #199 have only one solution?

Yes. Every puzzle in the 7x7 collection, including #199, 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 #199?

Start with the red region — the most constrained color on this board, with 1 square spanning rows 6–6 and columns 6–6. Narrowing the smallest region first removes the most squares elsewhere on the grid.