7x7 Queens Puzzle #169
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 10-step reasoning is written out below.
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Step-by-step solution for puzzle #169
What follows is a complete solve of puzzle #169, worked the way a person works it rather than the way a computer does. It runs to 10 deductions — 7 queen placements and 3 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 pairing argument on rows.
Techniques this board needs: region confined to one line, region shadow, pairing argument on rows, last square in a region.
Show the full walkthrough (4 steps) — contains the solution
Step 1. Blue cannot leave column 1 — every one of its open squares (2 open squares) sits there. That column belongs to blue, so every square in it owned by another colour is dead: 7 squares in all.
Step 2. Indigo is down to 4 candidates in rows 1 and 3, columns 2–4, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about indigo itself.
The board after step 2 — 0 of 7 queens placed. Step 3. Indigo, amber, and blue are now boxed into rows 1–3 and nothing else. That is 3 colours needing 3 rows, so they fill those rows between them — which locks every remaining colour out and removes 4 squares at once.
Step 4. From here the board cascades. Keep alternating the region sweep and the line sweep and 7 queens fall out in order without any new idea being needed: mint has one square left, so its queen takes row 4, column 5; slate has one square left, so its queen takes row 5, column 7; pale yellow has one square left, so its queen takes row 7, column 6; amber has one square left, so its queen takes row 2, column 4; indigo has one square left, so its queen takes row 1, column 2; blue has one square left, so its queen takes row 3, column 1; red has one square left, so its queen takes row 6, column 3. 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 6, column 3.
The board after step 4 — 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 #169
Puzzle #169 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.
As with every puzzle in this collection, #169 has a single verified solution and needs no guesswork. Each queen follows from something already visible. What the board controls is tempo — how soon the first forced move shows up and how far apart the rest are spaced — and that is a direct consequence of how these colors are cut.
How the colors divide this board
From smallest to largest, the regions on puzzle #169 are: blue (2 squares), slate (4 squares), mint (5 squares), indigo (7 squares), pale yellow (7 squares), amber (8 squares), red (16 squares). An even split would hand every color 7 squares, so the blue region is running 5 squares under that average while the red 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 blue, with 2 squares, is under far more pressure than red with 16. A 14-square gap like this one rewards players who start where the choices are fewest.
Shape matters as much as size. The blue region is the most compact color here, filling 100% of the 2×1 box that encloses it, while amber is the most scattered at 53% of its 3×5 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
Here is the full footprint of every color on puzzle #169, smallest first. Reading these spans before you place anything is the quickest way to see which parts of the grid are genuinely contested.
Blue covers 2 squares, spanning 2 rows and 1 column (rows 2–3, columns 1–1). It sits wholly inside column 1, so its queen must be in that column.
Slate occupies 4 squares within rows 4–5, columns 6–7.
Mint: 5 squares across rows 2–4, columns 5–7.
Indigo covers 7 squares, spanning 3 rows and 4 columns (rows 1–3, columns 1–4).
Pale yellow occupies 7 squares within rows 5–7, columns 5–7.
Amber: 8 squares across rows 1–3, columns 3–7.
Red covers 16 squares, spanning 4 rows and 4 columns (rows 4–7, columns 1–4).
Where to start on this board
Blue is the natural opening on #169: it is the smallest region on the grid at 2 squares, boxed into rows 2–3 and columns 1–1. Since one of those squares must hold a queen, that block of 2 rows and 1 column is the most contested part of the board.
Because blue stays inside column 1, its queen belongs to that column and no other region may use it. Cross out the rest of column 1 straight away. Any color that was relying on those squares now has a visibly smaller footprint, and that shrinkage is where your second deduction comes from.
Work outward to the other flat regions next. Slate 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 #169
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 1, 6 and 7 are the narrowest, touched by only 2 colors. Column 2 is the tightest column, 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 3 is the crowded extreme at 4 colors — worth revisiting later, not now.
Working through the middle game
The middle of #169 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.
A placement without a reason is a guess. Because this board has exactly one solution, a guess that happens to be wrong will not announce itself for several moves — and unwinding it is slower than simply finishing the eliminations first.
Why puzzle #169 is rated hard
The rating reflects how much the board concedes up front. Puzzle #169 has one region confined to a single row or column, its smallest color holds 2 squares, its tightest row meets just 2 colors, and the gap between its largest and smallest regions is 14 squares. Flat, lopsided boards open quickly; even, sprawling ones make you earn the first placement.
Rating is a measure of chain length, not of chance. With one guaranteed solution and no guessing required, the only thing that changes across the collection is how many eliminations you must link together before a queen is provably forced.
A board that feels above its rating is nearly always a board with a missing X. Audit every queen on the grid: full row cleared, full column cleared, all eight touching squares cleared. Diagonals are the common omission, and missing one is far more often the cause of a stall than any genuine difficulty in the puzzle.
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 #169, start hunting for it near row 1.
A non-spoiling distribution check: solved, #169 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 #169?
Puzzle #169 is rated hard. Its smallest color region holds 2 squares, its tightest row is touched by 2 colors, and one of its regions is confined to a single row or column, which gives you a forced move early.
Does 7x7 puzzle #169 have only one solution?
Yes. Every puzzle in the 7x7 collection, including #169, 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 #169?
Start with the blue region — the most constrained color on this board, with 2 squares spanning rows 2–3 and columns 1–1. Narrowing the smallest region first removes the most squares elsewhere on the grid.