7x7 Queens Puzzle #29
Difficulty: hard. 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 12-step reasoning is written out below.
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Step-by-step solution for puzzle #29
What follows is a complete solve of puzzle #29, worked the way a person works it rather than the way a computer does. It runs to 12 deductions — 7 queen placements and 5 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 line confined to one region.
Techniques this board needs: last square in a region, region confined to one line, region shadow, line confined to one region, last square in a row.
Show the full walkthrough (7 steps) — contains the solution
Step 1. Only row 6, column 7 is still open in red, and since each colour must take a queen, that settles it. That clears row 6, column 7, the rest of the red region and every square adjacent to it — diagonals included.
Step 2. All of the amber region's remaining squares (2 open squares) lie in column 6. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 4 squares come off.
Step 3. The blue region has 6 squares left, spread across rows 2–5, columns 2–4. 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.
Step 4. All of the slate region's remaining squares (2 open squares) lie in column 2. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 8 squares come off.
The board after step 4 — 1 of 7 queens placed. Step 5. Blue is down to 3 candidates in rows 2 and 3, columns 3 and 4, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about blue itself.
Step 6. Every open square left in row 7 (4 open squares) belongs to the pale yellow region. Since that row must contain a queen, pale yellow is the colour that supplies it — so pale yellow squares anywhere else on the board are out, 2 squares in all.
Step 7. From here the board cascades. Keep alternating the region sweep and the line sweep and 6 queens fall out in order without any new idea being needed: row 5 is down to one square, putting a queen on row 5, column 2; row 4 is down to one square, putting a queen on row 4, column 5; amber has one square left, so its queen takes row 2, column 6; blue has one square left, so its queen takes row 3, column 3; indigo has one square left, so its queen takes row 1, column 1; pale yellow has one square left, so its queen takes row 7, 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 7, column 4.
The board after step 7 — 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 #29
Puzzle #29 is one of the hard-rated boards in the 7x7 set. Seven colors divide its 49 squares, and you win by placing seven queens so that each row, each column and each color holds exactly one, with no two queens adjacent in any direction.
Like every board on this site, #29 has been verified to have exactly one valid solution, and that solution is reachable by deduction alone. You never have to guess and then unwind; every queen can be justified by something already visible on the grid. What changes from puzzle to puzzle is where the first certainty appears and how long the chain of reasoning runs before the next one — and that is entirely a product of how these particular colors are shaped.
How the colors divide this board
From smallest to largest, the regions on puzzle #29 are: red (1 square), slate (3 squares), blue (6 squares), indigo (7 squares), amber (7 squares), mint (9 squares), pale yellow (16 squares). An even split would hand every color 7 squares, so the red region is running 6 squares under that average while the pale yellow region is the roomiest area on the grid with 16 squares.
Why does the split matter? Because a region's square count has no bearing on how many queens it gets — the answer is always one. So red, with 1 square, is under far more pressure than pale yellow with 16. A 15-square gap like this one rewards players who start where the choices are fewest.
Square count is only half the story — how a color is arranged counts too. Slate is the tidiest shape on #29, packing 100% of its 3×1 bounding box, whereas blue straggles across its 4×3 box at just 50%. Tidy blocks are easy to work around; scattered ones touch more lines and resist resolution.
Region by region
Below is every color on #29 with its exact reach, smallest region first. It is worth a slow read: the spans reveal which rows and columns several regions are fighting over.
Red occupies 1 square within rows 6–6, columns 7–7. It never leaves row 6, so its queen is locked to that row.
Slate: 3 squares across rows 4–6, columns 2–2. It sits wholly inside column 2, so its queen must be in that column.
Blue covers 6 squares, spanning 4 rows and 3 columns (rows 2–5, columns 2–4).
Indigo occupies 7 squares within rows 1–3, columns 1–3.
Amber: 7 squares across rows 1–5, columns 6–7.
Mint covers 9 squares, spanning 5 rows and 3 columns (rows 1–5, columns 4–6).
Pale yellow occupies 16 squares within rows 4–7, columns 1–7.
Where to start on this board
Red is the natural opening on #29: it is the smallest region on the grid at 1 square, boxed into rows 6–6 and columns 7–7. Since one of those squares must hold a queen, that block of 1 row and 1 column is the most contested part of 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.
No region here is pinned to a shallow band of rows, so turn the same idea sideways: amber spans only two columns. Two narrow regions sharing the same two columns take one column each and lock everyone else out of both, which is usually enough to crack a board that offers no free opening.
The tightest lines on puzzle #29
A quick way to find the next move is to count how many different colors touch each line. On this board, row 7 is the narrowest, touched by only 1 color. Columns 1 and 5 are the tightest columns, with 2 colors.
A line with few colors is a line close to resolving. Where only 1 color 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 5 colors — worth revisiting later, not now.
Working through the middle game
The middle of #29 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.
Two checks, run alternately, will carry you through the 49 squares of this grid. First: has any of the seven regions been reduced to a single open square? Second: has any row or column? Either answer forces a queen. Players who stall on 7x7 boards almost always run one of those checks and forget the other.
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 #29 is rated hard
What earns a board its rating is the shape of its opening. Here that opening offers three single-line regions, a 1-square smallest color, a tightest row touched by 1 color, and a region-size spread of 15. Lopsided grids with flat regions fall quickly; balanced ones like this take more patience.
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.
If #29 feels harder than its rating suggests, the usual culprit is incomplete marking rather than a difficult deduction. Check that every queen already on the grid has its full cross of eliminations recorded — including the diagonal neighbours, which are by far the easiest to miss. More stalled solves come from one forgotten diagonal X than from any genuinely deep chain of logic.
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.
Learn the pairing argument and you will use it on every board, this one included. If two colors can only sit inside the same two rows, between them they consume both rows and every other color is shut out. It generalises to any matching count — three colors across three rows, four across four. On #29, start hunting for it near row 7.
A non-spoiling distribution check: solved, #29 carries 3 queens on the perimeter against 4 queens inside, 1 of them cornered. 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 #29?
Puzzle #29 is rated hard. Its smallest color region holds 1 square, its tightest row is touched by 1 color, and three of its regions are confined to a single row or column, which gives you a forced move early.
Does 7x7 puzzle #29 have only one solution?
Yes. Every puzzle in the 7x7 collection, including #29, 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 #29?
Start with the red region — the most constrained color on this board, with 1 square spanning rows 6–6 and columns 7–7. Narrowing the smallest region first removes the most squares elsewhere on the grid.