9x9 Queens Puzzle #63
Difficulty: hard. 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 24-step reasoning is written out below.
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Step-by-step solution for puzzle #63
What follows is a complete solve of puzzle #63, worked the way a person works it rather than the way a computer does. It runs to 24 deductions — 9 queen placements and 15 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 columns.
Techniques this board needs: region confined to one line, region shadow, line confined to one region, pairing argument on rows, pairing argument on columns, last square in a region, last square in a row.
Show the full walkthrough (18 steps) — contains the solution
Step 1. Indigo cannot leave row 1 — every one of its open squares (4 open squares) sits there. That row belongs to indigo, so every square on it owned by another colour is dead: 5 squares in all.
Step 2. Mint is down to 4 candidates in rows 3 and 4, columns 5–7, and they overlap enough to cover 2 squares elsewhere. Cross those out without deciding anything about mint itself.
Step 3. The khaki region has 4 squares left, spread across rows 7–9, columns 1 and 2. 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 orange region's remaining squares (2 open squares) lie in row 9. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 9 squares come off.
Step 5. Khaki cannot leave column 1 — every one of its open squares (2 open squares) sits there. That column belongs to khaki, so every square in it owned by another colour is dead: 7 squares in all.
The board after step 5 — 0 of 9 queens placed. Step 6. All of the indigo region's remaining squares (3 open squares) lie in row 1. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 1 square come off.
Step 7. Blue cannot leave column 2 — every one of its open squares (3 open squares) sits there. That column belongs to blue, so every square in it owned by another colour is dead: 4 squares in all.
Step 8. All of the indigo region's remaining squares (2 open squares) lie in row 1. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 1 square come off.
Step 9. Column 9 has only red squares left (7 open squares). The column needs a queen and only red can provide one, which pins that colour to this column and kills its squares elsewhere: 8 squares.
The board after step 9 — 0 of 9 queens placed. Step 10. Every open square left in column 8 (3 open squares) belongs to the amber region. Since that column must contain a queen, amber is the colour that supplies it — so amber squares anywhere else on the board are out, 4 squares in all.
Step 11. Amber cannot leave column 8 — every one of its open squares (3 open squares) sits there. That column belongs to amber, so every square in it owned by another colour is dead: 1 square in all.
Step 12. Here is the pairing argument. The amber, blue, and mint regions have no open squares outside rows 2–4 — 3 colours confined to 3 rows. Between them they must take one row each, in some order, so every other colour is shut out of all of them: 4 squares come off in one stroke.
Step 13. Wherever slate ends up among its 4 squares, the same squares fall within reach of it — 1 square in total, impossible regardless of how the colour resolves.
Step 14. Here is the pairing argument. The indigo and slate regions have no open squares outside columns 3 and 4 — 2 colours confined to 2 columns. Between them they must take one column each, in some order, so every other colour is shut out of all of them: 3 squares come off in one stroke.
The board after step 14 — 0 of 9 queens placed. Step 15. Only row 9, column 5 is still open in orange, and since each colour must take a queen, that settles it. Everything else in row 9, in column 5, in orange and in the ring around that square is now dead.
Step 16. Row 6 has a single open square left, at column 9 in the red region. Every row needs a queen, so this one is forced. Cross out the whole of row 6 and column 9, the remaining red squares, and the ring of neighbours around row 6, column 9.
Step 17. 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 18. 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: pale yellow has one square left, so its queen takes row 7, column 6; mint has one square left, so its queen takes row 4, column 7; amber has one square left, so its queen takes row 2, column 8; blue has one square left, so its queen takes row 3, column 2; khaki has one square left, so its queen takes row 8, column 1; slate has one square left, so its queen takes row 5, column 3; indigo has one square left, so its queen takes row 1, 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 1, column 4.
The board after step 18 — 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 #63
9x9 puzzle #63 is rated hard. 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.
As with every puzzle in this collection, #63 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 #63 are: orange (2 squares), indigo (4 squares), mint (4 squares), khaki (4 squares), blue (7 squares), pale yellow (12 squares), amber (13 squares), slate (17 squares), red (18 squares). An even split would hand every color 9 squares, so the orange region is running 7 squares under that average while the red 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. Orange is working with 2 squares while red has 18 to spare, a gap of 16. Attack the cramped end and the roomy regions tend to resolve themselves.
Shape matters as much as size. The indigo region is the most compact color here, filling 100% of the 1×4 box that encloses it, while pale yellow is the most scattered at 48% of its 5×5 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 #63, smallest first. Reading these spans before you place anything is the quickest way to see which parts of the grid are genuinely contested.
Orange: 2 squares across rows 9–9, columns 4–5. It never leaves row 9, so its queen is locked to that row.
Indigo covers 4 squares, spanning 1 row and 4 columns (rows 1–1, columns 1–4). It never leaves row 1, so its queen is locked to that row.
Mint occupies 4 squares within rows 3–4, columns 5–7.
Khaki: 4 squares across rows 7–9, columns 1–2.
Blue covers 7 squares, spanning 3 rows and 3 columns (rows 2–4, columns 1–3).
Pale yellow occupies 12 squares within rows 5–9, columns 3–7.
Amber: 13 squares across rows 1–4, columns 5–9.
Slate covers 17 squares, spanning 8 rows and 4 columns (rows 2–9, columns 1–4).
Red occupies 18 squares within rows 2–9, columns 6–9.
Where to start on this board
Orange is the natural opening on #63: it is the smallest region on the grid at 2 squares, boxed into rows 9–9 and columns 4–5. Since one of those squares must hold a queen, that block of 1 row and 2 columns is the most contested part of the board.
Because orange never leaves row 9, its queen must be in that row — and that instantly settles row 9 for everyone else. Sweep along it and X out every square that is not orange. 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 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 #63
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. Columns 8 and 9 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 8 rows. Row 9 is the crowded extreme at 5 colors — worth revisiting later, not now.
Working through the middle game
Once two or three queens are down, the board changes character. Each queen removes an entire row, an entire column and the ring of up to eight squares around it, so the grid shrinks faster than most people expect. The habit that pays here is marking rather than remembering: after every placement, cross out the full row, the full column and all eight neighbours before hunting for the next move.
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 #63 is rated hard
The rating reflects how much the board concedes up front. Puzzle #63 has two regions 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 16 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 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, #63 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.
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Questions about this puzzle
How hard is 9x9 Queens puzzle #63?
Puzzle #63 is rated hard. Its smallest color region holds 2 squares, its tightest row is touched by 2 colors, and two of its regions are confined to a single row or column, which gives you a forced move early.
Does 9x9 puzzle #63 have only one solution?
Yes. Every puzzle in the 9x9 collection, including #63, 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 #63?
Start with the orange region — the most constrained color on this board, with 2 squares spanning rows 9–9 and columns 4–5. Narrowing the smallest region first removes the most squares elsewhere on the grid.