9x9 Queens Puzzle #47
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 18-step reasoning is written out below.
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Step-by-step solution for puzzle #47
What follows is a complete solve of puzzle #47, worked the way a person works it rather than the way a computer does. It runs to 18 deductions — 9 queen placements and 9 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: region confined to one line, region shadow, last square in a region.
Show the full walkthrough (18 steps) — contains the solution
Step 1. Indigo cannot leave row 1 — every one of its open squares (3 open squares) sits there. That row belongs to indigo, so every square on it owned by another colour is dead: 7 squares in all.
Step 2. Blue is down to 4 candidates in rows 2–4, columns 1 and 2, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about blue itself.
Step 3. The mint region has 3 squares left, spread across rows 4 and 5, columns 6 and 7. 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.
Step 4. All of the pale yellow region's remaining squares (2 open squares) lie in column 9. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 9 squares come off.
Step 5. 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: 1 square in all.
The board after step 5 — 0 of 9 queens placed. Step 6. All of the slate region's remaining squares (2 open squares) lie in column 8. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 4 squares come off.
Step 7. Only row 1, column 7 is still open in indigo, and since each colour must take a queen, that settles it. Everything else in row 1, in column 7, in indigo and in the ring around that square is now dead.
Step 8. The mint region is down to one open square, at row 4, column 6. Every colour holds exactly one queen, so that square is forced. Row 4 and column 6 are now spoken for, along with the squares touching that queen.
Step 9. Amber cannot leave row 2 — every one of its open squares (2 open squares) sits there. That row belongs to amber, so every square on it owned by another colour is dead: 4 squares in all.
The board after step 9 — 2 of 9 queens placed. Step 10. The blue region is down to one open square, at row 3, column 1. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 3 and column 1, the remaining blue squares, and the ring of neighbours around row 3, column 1.
Step 11. Only row 5, column 8 is still open in slate, and since each colour must take a queen, that settles it. Everything else in row 5, in column 8, in slate and in the ring around that square is now dead.
Step 12. The pale yellow region is down to one open square, at row 7, column 9. Every colour holds exactly one queen, so that square is forced. Row 7 and column 9 are now spoken for, along with the squares touching that queen.
Step 13. Khaki cannot leave column 5 — 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: 4 squares in all.
Step 14. The amber region is down to one open square, at row 2, column 4. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 2 and column 4, the remaining amber squares, and the ring of neighbours around row 2, column 4.
The board after step 14 — 6 of 9 queens placed. Step 15. The red region has 2 squares left, spread across rows 6 and 8, columns 2 and 3. 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.
Step 16. The orange region is down to one open square, at row 9, column 2. Every colour holds exactly one queen, so that square is forced. Row 9 and column 2 are now spoken for, along with the squares touching that queen.
Step 17. Only row 6, column 3 is still open in red, and since each colour must take a queen, that settles it. That clears row 6, column 3, the rest of the red region and every square adjacent to it — diagonals included.
Step 18. The khaki region is down to one open square, at row 8, column 5. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 8 and column 5, the remaining khaki squares, and the ring of neighbours around row 8, column 5.
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 #47
9x9 puzzle #47 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.
There is exactly one way to finish #47, and it has been verified. More importantly, you can reach it without ever gambling: at every stage some square is provably right or provably wrong. Boards differ only in how deep you must dig before that proof appears, and the geometry of these nine regions is what sets the depth.
How the colors divide this board
From smallest to largest, the regions on puzzle #47 are: pale yellow (2 squares), indigo (3 squares), mint (3 squares), blue (6 squares), slate (9 squares), orange (9 squares), amber (12 squares), khaki (15 squares), red (22 squares). An even split would hand every color 9 squares, so the pale yellow region is running 7 squares under that average while the red region is the roomiest area on the grid with 22 squares.
One queen per color, regardless of acreage: that is what turns this uneven split into a solving order. Pale yellow is working with 2 squares while red has 22 to spare, a gap of 20. 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 1×3 box that encloses it, while red is the most scattered at 55% of its 8×5 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
Below is every color on #47 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.
Pale yellow occupies 2 squares within rows 6–7, columns 9–9. It sits wholly inside column 9, so its queen must be in that column.
Indigo: 3 squares across rows 1–1, columns 7–9. It never leaves row 1, so its queen is locked to that row.
Mint covers 3 squares, spanning 2 rows and 2 columns (rows 4–5, columns 6–7).
Blue occupies 6 squares within rows 1–4, columns 1–2.
Slate: 9 squares across rows 2–6, columns 8–9.
Orange covers 9 squares, spanning 5 rows and 3 columns (rows 5–9, columns 1–3).
Amber occupies 12 squares within rows 1–4, columns 3–7.
Khaki: 15 squares across rows 6–9, columns 5–9.
Red covers 22 squares, spanning 8 rows and 5 columns (rows 2–9, columns 2–6).
Where to start on this board
Pale yellow is the natural opening on #47: it is the smallest region on the grid at 2 squares, boxed into rows 6–7 and columns 9–9. 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 pale yellow stays inside column 9, its queen belongs to that column and no other region may use it. Cross out the rest of column 9 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. 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 #47
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 1, 8 and 9 are the narrowest, touched by only 3 colors. Columns 1 and 4 are the tightest columns, with 2 colors.
A line with few colors is a line close to resolving. Where only 3 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
Past the opening, treat this as an elimination exercise rather than a placement exercise. Each queen takes out a row, a column and its eight neighbours, and the value of a move is measured by how much it removes. Cross everything out as you go and let the board do the remembering.
Two checks, run alternately, will carry you through the 81 squares of this grid. First: has any of the nine regions been reduced to a single open square? Second: has any row or column? Either answer forces a queen. Players who stall on 9x9 boards almost always run one of those checks and forget the other.
Resist the plausible-looking queen. On #47 every correct placement has a stated reason behind it, and any move you cannot justify is a guess wearing a disguise. Backing out of a wrong guess on a single-solution board takes far longer than finding the real deduction would have.
Why puzzle #47 is rated hard
What earns a board its rating is the shape of its opening. Here that opening offers two single-line regions, a 2-square smallest color, a tightest row touched by 3 colors, and a region-size spread of 20. Lopsided grids with flat regions fall quickly; balanced ones like this take more patience.
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.
Stuck on #47 despite the hard rating? The odds strongly favour a bookkeeping error over a hard chain of logic. Re-check each placed queen for its complete set of eliminations, paying particular attention to the four diagonal squares — those are the ones that get overlooked, and one of them is usually sitting on the answer.
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 column 1 on this board.
A non-spoiling distribution check: solved, #47 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 #47?
Puzzle #47 is rated hard. Its smallest color region holds 2 squares, its tightest row is touched by 3 colors, and two of its regions are confined to a single row or column, which gives you a forced move early.
Does 9x9 puzzle #47 have only one solution?
Yes. Every puzzle in the 9x9 collection, including #47, 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 #47?
Start with the pale yellow region — the most constrained color on this board, with 2 squares spanning rows 6–7 and columns 9–9. Narrowing the smallest region first removes the most squares elsewhere on the grid.