7x7 Queens Puzzle #235
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 13-step reasoning is written out below.
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Step-by-step solution for puzzle #235
What follows is a complete solve of puzzle #235, worked the way a person works it rather than the way a computer does. It runs to 13 deductions — 7 queen placements and 6 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 proof by contradiction.
Techniques this board needs: last square in a region, region confined to one line, region shadow, last square in a column, proof by contradiction.
Show the full walkthrough (10 steps) — contains the solution
Step 1. Only row 5, column 7 is still open in slate, and since each colour must take a queen, that settles it. That clears row 5, column 7, the rest of the slate 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 6. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 7 and column 6, the remaining pale yellow squares, and the ring of neighbours around row 7, column 6.
Step 3. Indigo cannot leave row 1 — every one of its open squares (3 open squares) sits there. That row belongs to indigo, so every square on it owned by another colour is dead: 3 squares in all.
The board after step 3 — 2 of 7 queens placed. Step 4. Wherever amber ends up among its 3 squares, the same squares fall within reach of it — 1 square in total, impossible regardless of how the colour resolves.
Step 5. Mint cannot leave row 4 — every one of its open squares (2 open squares) sits there. That row belongs to mint, so every square on it owned by another colour is dead: 4 squares in all.
Step 6. All of the amber region's remaining squares (2 open squares) lie in row 2. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 3 squares come off.
Step 7. Blue cannot leave row 3 — every one of its open squares (2 open squares) sits there. That row belongs to blue, so every square on it owned by another colour is dead: 1 square in all.
The board after step 7 — 2 of 7 queens placed. Step 8. Column 1 now has exactly one open square, row 6, column 1, in the red region. Columns must each hold a queen, so that placement is forced. Everything else in row 6, in column 1, in red and in the ring around that square is now dead.
Step 9. Test row 1, column 2 for indigo: place a queen there, run the forced consequences through, and column 4 runs out of open squares entirely. The assumption breaks, so the square is eliminated.
Step 10. 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 3; amber has one square left, so its queen takes row 2, column 5; blue has one square left, so its queen takes row 3, column 2; mint has one square left, so its queen takes row 4, column 4. 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 4, column 4.
The board after step 10 — 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 #235
7x7 puzzle #235 is rated medium. 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.
There is exactly one way to finish #235, 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 #235 are: slate (1 square), indigo (3 squares), pale yellow (4 squares), mint (6 squares), blue (8 squares), amber (13 squares), red (14 squares). An even split would hand every color 7 squares, so the slate region is running 6 squares under that average while the red region is the roomiest area on the grid with 14 squares.
One queen per color, regardless of acreage: that is what turns this uneven split into a solving order. Slate is working with 1 square while red has 14 to spare, a gap of 13. 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 1×3 frame; red is the loosest, occupying only 56% of its 5×5 frame. The loose one reaches into more rows and columns, which is exactly why it usually settles last.
Region by region
Here is the full footprint of every color on puzzle #235, smallest first. Reading these spans before you place anything is the quickest way to see which parts of the grid are genuinely contested.
Slate covers 1 square, spanning 1 row and 1 column (rows 5–5, columns 7–7). It never leaves row 5, so its queen is locked to that row.
Indigo occupies 3 squares within rows 1–1, columns 2–4. It never leaves row 1, so its queen is locked to that row.
Pale yellow: 4 squares across rows 6–7, columns 6–7.
Mint covers 6 squares, spanning 3 rows and 3 columns (rows 3–5, columns 3–5).
Blue occupies 8 squares within rows 1–4, columns 1–3.
Amber: 13 squares across rows 1–5, columns 4–7.
Red covers 14 squares, spanning 5 rows and 5 columns (rows 3–7, columns 1–5).
Where to start on this board
The most constrained color is where a solve should begin, and on #235 that is slate with 1 square. It reaches from row 5 to row 5 and from column 7 to column 7 — 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 slate never leaves row 5, its queen must be in that row — and that instantly settles row 5 for everyone else. Sweep along it and X out every square that is not slate. 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 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 #235
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 2, 6 and 7 are the narrowest, touched by only 2 colors. Columns 1 and 6 are the tightest columns, with 2 colors.
A line with few colors is a line close to resolving. Where only 2 colors appear, one of them owns the row outright and the others must fit into the remaining 6 rows. Row 5 is the crowded extreme at 4 colors — worth revisiting later, not now.
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.
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 #235 is rated medium
The rating reflects how much the board concedes up front. Puzzle #235 has three regions confined to a single row or column, its smallest color holds 1 square, its tightest row meets just 2 colors, and the gap between its largest and smallest regions is 13 squares. Flat, lopsided boards open quickly; even, sprawling ones make you earn the first placement.
Difficulty in Queens is never arithmetic and never luck. Every board has one solution and none require guessing. What varies is the length of the chain you must follow before the next queen becomes certain — one or two steps on an easy board, five or six on a hard one, sometimes with several partial eliminations held in play at once.
Stuck on #235 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.
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.
A non-spoiling distribution check: solved, #235 carries 4 queens on the perimeter against 3 queens inside, with the corners empty. Because no two queens may touch, real solutions always look fairly evenly spread — a lopsided board in progress is a warning sign.
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 #235?
Puzzle #235 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 #235 have only one solution?
Yes. Every puzzle in the 7x7 collection, including #235, 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 #235?
Start with the slate region — the most constrained color on this board, with 1 square spanning rows 5–5 and columns 7–7. Narrowing the smallest region first removes the most squares elsewhere on the grid.