9x9 Queens Puzzle #79
Difficulty: medium. Place 9 queens on this 9x9 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.
Previous puzzle · All 9x9 puzzles · Next puzzle
Step-by-step solution for puzzle #79
What follows is a complete solve of puzzle #79, worked the way a person works it rather than the way a computer does. It runs to 13 deductions — 9 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 proof by contradiction.
Techniques this board needs: last square in a region, region confined to one line, region shadow, pairing argument on columns, proof by contradiction.
Show the full walkthrough (6 steps) — contains the solution
Step 1. The board opens by cascading. Each of these placements is forced the moment the one before it is marked, so the whole run is really a single sweep repeated: amber has one square left, so its queen takes row 2, column 9; orange has one square left, so its queen takes row 9, column 2; mint has one square left, so its queen takes row 4, column 1; pale yellow has one square left, so its queen takes row 7, 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 7, column 3.
Step 2. Indigo cannot leave row 1 — every one of its open squares (2 open squares) sits there. That row belongs to indigo, so every square on it owned by another colour is dead: 2 squares in all.
Step 3. The slate region has 2 squares left, spread across rows 5 and 8, columns 7 and 8. You do not need to know which of them takes the queen: every one of those options attacks the same 3 squares, so they can be crossed out now.
The board after step 3 — 4 of 9 queens placed. Step 4. Indigo, red, and khaki are now boxed into columns 4–6 and nothing else. That is 3 colours needing 3 columns, so they fill those columns between them — which locks every remaining colour out and removes 1 square at once.
Step 5. Now a short proof by contradiction. Suppose the blue queen went to row 6, column 8. Follow the forced moves that would create and the khaki region is left with nowhere to put its queen — impossible. So that square is ruled out for good.
Step 6. From here the board cascades. Keep alternating the region sweep and the line sweep and 5 queens fall out in order without any new idea being needed: blue has one square left, so its queen takes row 3, column 7; slate has one square left, so its queen takes row 5, column 8; red has one square left, so its queen takes row 6, column 5; indigo has one square left, so its queen takes row 1, column 4; khaki has one square left, so its queen takes row 8, column 6. 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 8, column 6.
The board after step 6 — 9 of 9 queens placed.
That completes the board: 9 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 9x9 Queens puzzle #79
9x9 puzzle #79 is rated medium. Nine colored regions cover its 81 squares, and your job is to seat nine queens so that every row, column and color contains exactly one — with no queen touching another, including diagonally.
Like every board on this site, #79 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 #79 are: amber (1 square), orange (1 square), mint (3 squares), slate (7 squares), pale yellow (9 squares), khaki (12 squares), red (13 squares), blue (17 squares), indigo (18 squares). An even split would hand every color 9 squares, so the amber region is running 8 squares under that average while the indigo region is the roomiest area on the grid with 18 squares.
One queen per color, regardless of acreage: that is what turns this uneven split into a solving order. Amber is working with 1 square while indigo has 18 to spare, a gap of 17. Attack the cramped end and the roomy regions tend to resolve themselves.
Shape matters as much as size. The amber region is the most compact color here, filling 100% of the 1×1 box that encloses it, while khaki is the most scattered at 50% of its 4×6 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 #79, smallest first. Reading these spans before you place anything is the quickest way to see which parts of the grid are genuinely contested.
Amber covers 1 square, spanning 1 row and 1 column (rows 2–2, columns 9–9). It never leaves row 2, so its queen is locked to that row.
Orange occupies 1 square within rows 9–9, columns 2–2. It never leaves row 9, so its queen is locked to that row.
Mint: 3 squares across rows 3–4, columns 1–2.
Slate covers 7 squares, spanning 4 rows and 3 columns (rows 5–8, columns 7–9).
Pale yellow occupies 9 squares within rows 7–9, columns 1–4.
Khaki: 12 squares across rows 6–9, columns 4–9.
Red covers 13 squares, spanning 6 rows and 3 columns (rows 2–7, columns 4–6).
Blue occupies 17 squares within rows 1–6, columns 6–9.
Indigo: 18 squares across rows 1–6, columns 1–5.
Where to start on this board
Amber is the natural opening on #79: it is the smallest region on the grid at 1 square, boxed into rows 2–2 and columns 9–9. 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 amber never leaves row 2, its queen must be in that row — and that instantly settles row 2 for everyone else. Sweep along it and X out every square that is not amber. 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. Orange and mint 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 #79
A quick way to find the next move is to count how many different colors touch each line. On this board, row 1 is the narrowest, touched by only 2 colors. Column 3 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 8 rows. Row 6 is the crowded extreme at 5 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 nine queens to seat and nine regions competing over 81 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 9x9 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 #79 is rated medium
The rating reflects how much the board concedes up front. Puzzle #79 has four 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 17 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.
If #79 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 9x9
At 9x9 a full re-scan after every move starts to get slow, so work locally instead. Once a queen goes down, check only the regions, rows and columns that placement actually touched — that is where new information appeared. Fall back to a complete sweep only when the local pass turns up nothing, and your solve times will drop noticeably.
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 1 on this board.
A non-spoiling distribution check: solved, #79 carries 4 queens on the perimeter against 5 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.
Full rules · Strategy library · Puzzle statistics
Questions about this puzzle
How hard is 9x9 Queens puzzle #79?
Puzzle #79 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 9x9 puzzle #79 have only one solution?
Yes. Every puzzle in the 9x9 collection, including #79, has been verified to have exactly one valid arrangement of nine queens, and it can always be reached by logic alone — no guessing or backtracking needed.
Where should I place my first queen on puzzle #79?
Start with the amber region — the most constrained color on this board, with 1 square spanning rows 2–2 and columns 9–9. Narrowing the smallest region first removes the most squares elsewhere on the grid.