9x9 Queens Puzzle #86
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 11-step reasoning is written out below.
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Step-by-step solution for puzzle #86
What follows is a complete solve of puzzle #86, worked the way a person works it rather than the way a computer does. It runs to 11 deductions — 9 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 shadow, last square in a column.
Show the full walkthrough (8 steps) — contains the solution
Step 1. Only row 2, column 6 is still open in amber, and since each colour must take a queen, that settles it. That clears row 2, column 6, the rest of the amber 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 8. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 7 and column 8, the remaining pale yellow squares, and the ring of neighbours around row 7, column 8.
Step 3. The mint region has 3 squares left, spread across rows 1, 3, and 4, columns 7 and 9. 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. 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: slate has one square left, so its queen takes row 5, column 9; mint has one square left, so its queen takes row 4, column 7; red has one square left, so its queen takes row 6, column 5; khaki has one square left, so its queen takes row 8, 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 8, column 4.
The board after step 4 — 6 of 9 queens placed. Step 5. Indigo is down to 2 candidates in rows 1 and 3, columns 1 and 3, and they overlap enough to cover 2 squares elsewhere. Cross those out without deciding anything about indigo itself.
Step 6. Scan column 3 and only row 1, column 3 remains — a indigo square. Every column takes a queen, so it takes this one. Row 1 and column 3 are now spoken for, along with the squares touching that queen.
Step 7. The blue region is down to one open square, at row 3, column 2. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 3 and column 2, the remaining blue squares, and the ring of neighbours around row 3, column 2.
Step 8. Only row 9, column 1 is still open in orange, and since each colour must take a queen, that settles it. Everything else in row 9, in column 1, in orange and in the ring around that square is now dead.
The board after step 8 — 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 #86
Board #86 of the 9x9 bank carries a medium rating. Its 81 squares are shared between nine colored regions, and the solution places nine queens: one per row, one per column, one per region, none of them side by side or corner to corner.
As with every puzzle in this collection, #86 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 #86 are: amber (1 square), pale yellow (1 square), blue (7 squares), khaki (9 squares), slate (10 squares), mint (11 squares), red (12 squares), orange (13 squares), indigo (17 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 17 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 amber, with 1 square, is under far more pressure than indigo with 17. A 16-square gap like this one rewards players who start where the choices are fewest.
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 indigo is the most scattered at 57% of its 6×5 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 #86, smallest first. Reading these spans before you place anything is the quickest way to see which parts of the grid are genuinely contested.
Amber occupies 1 square within rows 2–2, columns 6–6. It never leaves row 2, so its queen is locked to that row.
Pale yellow: 1 square across rows 7–7, columns 8–8. It never leaves row 7, so its queen is locked to that row.
Blue covers 7 squares, spanning 4 rows and 3 columns (rows 1–4, columns 1–3).
Khaki occupies 9 squares within rows 8–9, columns 4–9.
Slate: 10 squares across rows 4–8, columns 7–9.
Mint covers 11 squares, spanning 4 rows and 4 columns (rows 1–4, columns 6–9).
Red occupies 12 squares within rows 3–7, columns 4–7.
Orange: 13 squares across rows 5–9, columns 1–4.
Indigo covers 17 squares, spanning 6 rows and 5 columns (rows 1–6, columns 1–5).
Where to start on this board
Open on the tightest color. Here that is amber, confined to 1 square between rows 2 and 2 and columns 6 and 6. Its queen has nowhere else to go, which means those 1 row and 1 column carry more constraint than anywhere else on #86.
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. Pale yellow and khaki 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 #86
A quick way to find the next move is to count how many different colors touch each line. On this board, row 9 is the narrowest, touched by only 2 colors. Columns 1, 2, 3, 5 and 9 are the tightest columns, with 3 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 4 is the crowded extreme at 5 colors — worth revisiting later, not now.
Working through the middle game
The middle of #86 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.
The whole middle game reduces to two sweeps. Sweep the nine colors looking for one with a single square left; sweep the nine rows and nine columns looking for the same. Each sweep feeds the next, and switching between them deliberately — rather than drifting — is what separates a fast 9x9 solve from a stalled one.
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 #86 is rated medium
The rating reflects how much the board concedes up front. Puzzle #86 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 16 squares. Flat, lopsided boards open quickly; even, sprawling ones make you earn the first placement.
The scale has nothing to do with maths or luck — every puzzle here is solvable by deduction and has exactly one answer. It measures reasoning depth: how many eliminations must stack up before a placement becomes provable. That depth is what separates a medium board from the rest.
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 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.
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 #86, start hunting for it near row 9.
A non-spoiling distribution check: solved, #86 carries 3 queens on the perimeter against 6 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 9x9 Queens puzzle #86?
Puzzle #86 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 #86 have only one solution?
Yes. Every puzzle in the 9x9 collection, including #86, 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 #86?
Start with the amber region — the most constrained color on this board, with 1 square spanning rows 2–2 and columns 6–6. Narrowing the smallest region first removes the most squares elsewhere on the grid.