7x7 Queens Puzzle #187
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.
Previous puzzle · All 7x7 puzzles · Next puzzle
Step-by-step solution for puzzle #187
What follows is a complete solve of puzzle #187, 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
Step 1. Only row 7, column 6 is still open in pale yellow, and since each colour must take a queen, that settles it. That clears row 7, column 6, the rest of the pale yellow region and every square adjacent to it — diagonals included.
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.
Step 3. The amber region has 3 squares left, spread across rows 2 and 3, columns 2–4. You do not need to know which of them takes the queen: every one of those options attacks the same 2 squares, so they can be crossed out now.
Step 4. All of the slate region's remaining squares (2 open squares) lie in row 5. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 4 squares come off.
The board after step 4 — 1 of 7 queens placed. Step 5. Only row 6, column 4 is still open in red, and since each colour must take a queen, that settles it. That clears row 6, column 4, the rest of the red region and every square adjacent to it — diagonals included.
Step 6. The slate region is down to one open square, at row 5, column 7. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 5 and column 7, the remaining slate squares, and the ring of neighbours around row 5, column 7.
Step 7. Wherever amber ends up among its 2 squares, the same squares fall within reach of it — 2 squares in total, impossible regardless of how the colour resolves.
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: indigo has one square left, so its queen takes row 1, column 1; mint has one square left, so its queen takes row 4, column 2; amber has one square left, so its queen takes row 2, column 3; blue has one square left, so its queen takes row 3, column 5. 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 5.
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 #187
7x7 puzzle #187 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.
Puzzle #187 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 #187 are: pale yellow (1 square), indigo (2 squares), slate (6 squares), amber (7 squares), red (7 squares), mint (10 squares), blue (16 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 16 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 16 to spare, a gap of 15. Attack the cramped end and the roomy regions tend to resolve themselves.
A region's outline can constrain it more than its size does. Here indigo is the most solid, filling 100% of its 1×2 box, and amber the most diffuse at 58% of its 3×4 box. Solid blocks give clean eliminations; diffuse ones spread across the board and stay open longer.
Region by region
The complete breakdown of each region on this board follows, ordered from tightest to roomiest. Skimming the spans first tells you where the board is crowded and where it has slack.
Pale yellow covers 1 square, spanning 1 row and 1 column (rows 7–7, columns 6–6). It never leaves row 7, so its queen is locked to that row.
Indigo occupies 2 squares within rows 1–1, columns 1–2. It never leaves row 1, so its queen is locked to that row.
Slate: 6 squares across rows 5–7, columns 5–7.
Amber covers 7 squares, spanning 3 rows and 4 columns (rows 1–3, columns 1–4).
Red occupies 7 squares within rows 5–7, columns 3–5.
Mint: 10 squares across rows 3–7, columns 1–3.
Blue covers 16 squares, spanning 4 rows and 5 columns (rows 1–4, columns 3–7).
Where to start on this board
The most constrained color is where a solve should begin, and on #187 that is pale yellow with 1 square. It reaches from row 7 to row 7 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 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 is no more than two rows tall, so its queen is 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 #187
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 2 and 4 are the narrowest, touched by only 2 colors. Column 7 is the tightest column, with 2 colors.
The fewer colors a line touches, the sooner it surrenders its queen. A row meeting just 2 colors has to be claimed by one of them, which pushes every remaining region into the other 6 rows. Row 7, meeting 4 colors, is the opposite case — the busiest line on #187 and the last one you should expect to crack.
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.
Keep alternating between two views of the board. In the region view you ask which of the seven colors is down to one open square. In the line view you ask the same of each row and column. Both produce forced queens, and each placement refreshes the other view, so cycling between them deliberately is how a 7x7 board unwinds.
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 #187 is rated easy
Ratings track how generous the opening is. On #187 you get three regions pinned to a single row or column, a smallest color of 1 square, a tightest row crossed by 2 colors, and a 15-square gap between the largest and smallest regions. Those four numbers largely explain the easy label.
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.
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.
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 2 on this board.
Here is a shape check that gives nothing away: when #187 is solved, 3 queens sit on the outer edge of the grid and 4 sit inside it, with 1 queen 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
- The board is an N×N grid divided into N colored regions.
- Place exactly one queen (♛) in each row, each column, and each colored region.
- No two queens may touch each other — not horizontally, vertically, or diagonally.
- 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.
- There is always exactly one valid solution. Use logic, never guessing, to find it.
Full rules · Strategy library · Puzzle statistics
Questions about this puzzle
How hard is 7x7 Queens puzzle #187?
Puzzle #187 is rated easy. 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 #187 have only one solution?
Yes. Every puzzle in the 7x7 collection, including #187, 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 #187?
Start with the pale yellow region — the most constrained color on this board, with 1 square spanning rows 7–7 and columns 6–6. Narrowing the smallest region first removes the most squares elsewhere on the grid.