7x7 Queens Puzzle #188

Difficulty: medium. 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 #188

What follows is a complete solve of puzzle #188, 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 7 is still open in pale yellow, and since each colour must take a queen, that settles it. That clears row 7, column 7, the rest of the pale yellow region and every square adjacent to it — diagonals included.

  2. Step 2. The red region is down to one open square, at row 6, column 1. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 6 and column 1, the remaining red squares, and the ring of neighbours around row 6, column 1.

  3. Step 3. Indigo cannot leave row 1 — every one of its open squares (2 open squares) sits there. That row belongs to indigo, so every square on it owned by another colour is dead: 5 squares in all.

  4. Step 4. Wherever blue ends up among its 3 squares, the same squares fall within reach of it — 3 squares in total, impossible regardless of how the colour resolves.

    Puzzle #188 after step 4: 2 of 7 queens placed
    The board after step 4 — 2 of 7 queens placed.

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

  6. Step 6. All of the mint region's remaining squares (2 open squares) lie in column 3. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 2 squares come off.

  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: 2 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 3; amber has one square left, so its queen takes row 2, column 2; 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 #188 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 #188

This is puzzle number 188 in the 7x7 collection, rated medium. The grid holds 49 squares split between seven colored regions, and a finished board carries seven queens — one in every row, one in every column, one in every color, and never two of them touching, diagonals included.

There is exactly one way to finish #188, 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 #188 are: pale yellow (1 square), indigo (2 squares), red (6 squares), blue (8 squares), mint (8 squares), amber (10 squares), slate (14 squares). An even split would hand every color 7 squares, so the pale yellow region is running 6 squares under that average while the slate region is the roomiest area on the grid with 14 squares.

Every color takes one queen and one only, whatever its size — which is why the 13 square difference between pale yellow and slate is worth noting before you touch the grid. The cramped colors resolve first and hand you information; the roomy ones absorb whatever is left over at the end.

Shape matters as much as size. The indigo region is the most compact color here, filling 100% of the 1×2 box that encloses it, while blue is the most scattered at 50% of its 4×4 box. Compact regions are easy to eliminate around; straggling ones reach into more rows and columns and tend to stay unresolved until late.

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 medium board.

Pale yellow occupies 1 square within rows 7–7, columns 7–7. It never leaves row 7, so its queen is locked to that row.

Indigo: 2 squares across rows 1–1, columns 4–5. It never leaves row 1, so its queen is locked to that row.

Red covers 6 squares, spanning 2 rows and 5 columns (rows 6–7, columns 1–5).

Blue occupies 8 squares within rows 1–4, columns 4–7.

Mint: 8 squares across rows 3–6, columns 1–3.

Amber covers 10 squares, spanning 4 rows and 4 columns (rows 1–4, columns 1–4).

Slate occupies 14 squares within rows 3–7, columns 4–7.

Where to start on this board

Open on the tightest color. Here that is pale yellow, confined to 1 square between rows 7 and 7 and columns 7 and 7. Its queen has nowhere else to go, which means those 1 row and 1 column carry more constraint than anywhere else on #188.

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 and red 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 #188

A quick way to find the next move is to count how many different colors touch each line. On this board, rows 2 and 5 are the narrowest, touched by only 2 colors. Column 6 is the tightest column, 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

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.

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 #188 is rated medium

The medium label comes out of four measurable things about #188: three 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 13. Boards that score tight on those measures give up their first queen fast.

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.

Stuck on #188 despite the medium 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.

There is one technique that repays study at every grid size. Two regions restricted to the same two rows must occupy one row apiece, which excludes all other regions from those rows entirely; the identical logic applies to columns and to larger matched sets. It converts slow boards into fast ones, and the likeliest place to find it on #188 is row 2.

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 #188?

Puzzle #188 is rated medium. Its smallest color region holds 1 square, its tightest row is touched by 2 colors, and three of its regions are confined to a single row or column, which gives you a forced move early.

Does 7x7 puzzle #188 have only one solution?

Yes. Every puzzle in the 7x7 collection, including #188, 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 #188?

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