7x7 Queens Puzzle #118
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 9-step reasoning is written out below.
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Step-by-step solution for puzzle #118
What follows is a complete solve of puzzle #118, worked the way a person works it rather than the way a computer does. It runs to 9 deductions — 7 queen placements and 2 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 (9 steps) — contains the solution
Step 1. Only row 4, column 5 is still open in mint, and since each colour must take a queen, that settles it. That clears row 4, column 5, the rest of the mint region and every square adjacent to it — diagonals included.
Step 2. The pale yellow region is down to one open square, at row 7, column 4. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 7 and column 4, the remaining pale yellow squares, and the ring of neighbours around row 7, column 4.
Step 3. Only row 1, column 6 is still open in indigo, and since each colour must take a queen, that settles it. Everything else in row 1, in column 6, in indigo and in the ring around that square is now dead.
The board after step 3 — 3 of 7 queens placed. Step 4. All of the blue region's remaining squares (2 open squares) lie in column 7. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 1 square come off.
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.
Step 6. The amber region has 3 squares left, spread across rows 2 and 3, 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.
The board after step 6 — 4 of 7 queens placed. Step 7. Only row 5, column 3 is still open in slate, and since each colour must take a queen, that settles it. Everything else in row 5, in column 3, in slate and in the ring around that square is now dead.
Step 8. The blue region is down to one open square, at row 3, column 7. Every colour holds exactly one queen, so that square is forced. Row 3 and column 7 are now spoken for, along with the squares touching that queen.
Step 9. Only row 2, column 2 is still open in amber, and since each colour must take a queen, that settles it. That clears row 2, column 2, the rest of the amber region and every square adjacent to it — diagonals included.
The board after step 9 — 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 #118
Board #118 of the 7x7 bank carries a medium rating. Its 49 squares are shared between seven colored regions, and the solution places seven queens: one per row, one per column, one per region, none of them side by side or corner to corner.
Puzzle #118 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 #118 are: mint (1 square), pale yellow (2 squares), indigo (3 squares), amber (8 squares), red (11 squares), blue (12 squares), slate (12 squares). An even split would hand every color 7 squares, so the mint region is running 6 squares under that average while the slate region is the roomiest area on the grid with 12 squares.
That imbalance is the first thing to read, because every region takes exactly one queen regardless of how much space it owns. Mint has only 1 place to put its queen; slate has 12. The spread between them on this board is 11 squares, and the wider that spread runs, the more it pays to solve from the small end inward.
Square count is only half the story — how a color is arranged counts too. Indigo is the tidiest shape on #118, packing 100% of its 1×3 bounding box, whereas slate straggles across its 4×5 box at just 60%. Tidy blocks are easy to work around; scattered ones touch more lines and resist resolution.
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.
Mint covers 1 square, spanning 1 row and 1 column (rows 4–4, columns 5–5). It never leaves row 4, so its queen is locked to that row.
Pale yellow occupies 2 squares within rows 7–7, columns 4–5. It never leaves row 7, so its queen is locked to that row.
Indigo: 3 squares across rows 1–1, columns 4–6. It never leaves row 1, so its queen is locked to that row.
Amber covers 8 squares, spanning 3 rows and 3 columns (rows 1–3, columns 1–3).
Red occupies 11 squares within rows 6–7, columns 1–7.
Blue: 12 squares across rows 1–5, columns 4–7.
Slate covers 12 squares, spanning 4 rows and 5 columns (rows 3–6, columns 1–5).
Where to start on this board
Begin where the choices are fewest. On this board that means mint, which owns just 1 square inside a 1×1 window running from row 4 to row 4 and column 5 to column 5. A queen is guaranteed somewhere in there, so every line that window crosses is under pressure from the very first move.
Because mint never leaves row 4, its queen must be in that row — and that instantly settles row 4 for everyone else. Sweep along it and X out every square that is not mint. 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, pale yellow 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 #118
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 2, 5, 6 and 7 are the narrowest, touched by only 2 colors. Column 7 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 3 colors crossing it; it will almost certainly be among the last to settle.
Working through the middle game
The middle of #118 is where careless play costs time. Every queen you place kills a row, a column and the eight surrounding squares; if you do not mark all of that immediately, you will later "discover" a move that was available several turns ago. Mark first, then look.
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 #118 is rated medium
Ratings track how generous the opening is. On #118 you get four regions pinned to a single row or column, a smallest color of 1 square, a tightest row crossed by 2 colors, and a 11-square gap between the largest and smallest regions. Those four numbers largely explain the medium label.
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.
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.
One pattern is worth learning at every size, and it is available here. When two regions can only fit inside the same two rows, they must take one row each — which locks every other region out of both. The same argument works for columns, and for any matching count: three regions sharing three rows, four sharing four. Spotting these pairings turns a slow grind into a quick cascade, and on #118 the place to look for one is around row 2.
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
- 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.
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Questions about this puzzle
How hard is 7x7 Queens puzzle #118?
Puzzle #118 is rated medium. 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 #118 have only one solution?
Yes. Every puzzle in the 7x7 collection, including #118, 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 #118?
Start with the mint region — the most constrained color on this board, with 1 square spanning rows 4–4 and columns 5–5. Narrowing the smallest region first removes the most squares elsewhere on the grid.