9x9 Queens Puzzle #117
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 15-step reasoning is written out below.
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Step-by-step solution for puzzle #117
What follows is a complete solve of puzzle #117, worked the way a person works it rather than the way a computer does. It runs to 15 deductions — 9 queen placements and 6 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 line confined to one region.
Techniques this board needs: last square in a region, region confined to one line, region shadow, line confined to one region, last square in a column.
Show the full walkthrough (12 steps) — contains the solution
Step 1. Only row 4, column 7 is still open in mint, and since each colour must take a queen, that settles it. That clears row 4, column 7, the rest of the mint region and every square adjacent to it — diagonals included.
Step 2. 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: 6 squares come off.
Step 3. Only row 2, column 9 is still open in amber, and since each colour must take a queen, that settles it. Everything else in row 2, in column 9, in amber and in the ring around that square is now dead.
Step 4. The red region is down to one open square, at row 6, column 8. Every colour holds exactly one queen, so that square is forced. Row 6 and column 8 are now spoken for, along with the squares touching that queen.
The board after step 4 — 3 of 9 queens placed. Step 5. Only row 9, column 6 is still open in orange, and since each colour must take a queen, that settles it. That clears row 9, column 6, the rest of the orange region and every square adjacent to it — diagonals included.
Step 6. All of the blue region's remaining squares (2 open squares) lie in row 3. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 3 squares come off.
Step 7. Wherever khaki ends up among its 5 squares, the same squares fall within reach of it — 1 square in total, impossible regardless of how the colour resolves.
Step 8. Every open square left in column 1 (3 open squares) belongs to the slate region. Since that column must contain a queen, slate is the colour that supplies it — so slate squares anywhere else on the board are out, 2 squares in all.
The board after step 8 — 4 of 9 queens placed. Step 9. Column 2 has only khaki squares left (2 open squares). The column needs a queen and only khaki can provide one, which pins that colour to this column and kills its squares elsewhere: 3 squares.
Step 10. Column 3 now has exactly one open square, row 1, column 3, in the indigo region. Columns must each hold a queen, so that placement is forced. That clears row 1, column 3, the rest of the indigo region and every square adjacent to it — diagonals included.
Step 11. Khaki cannot leave column 2 — 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: 2 squares in all.
Step 12. 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 1; pale yellow has one square left, so its queen takes row 7, column 5; blue has one square left, so its queen takes row 3, column 4; khaki has one square left, so its queen takes row 8, column 2. 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 2.
The board after step 12 — 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 #117
Puzzle #117 is one of the hard-rated boards in the 9x9 set. Nine colors divide its 81 squares, and you win by placing nine queens so that each row, each column and each color holds exactly one, with no two queens adjacent in any direction.
Like every board on this site, #117 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 #117 are: mint (1 square), indigo (3 squares), amber (5 squares), orange (8 squares), pale yellow (10 squares), blue (11 squares), khaki (12 squares), red (15 squares), slate (16 squares). An even split would hand every color 9 squares, so the mint region is running 8 squares under that average while the slate 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 mint, with 1 square, is under far more pressure than slate with 16. A 15-square gap like this one rewards players who start where the choices are fewest.
Look at arrangement as well as area. Indigo is the densest region on this grid at 100% of a 1×3 frame; khaki is the loosest, occupying only 60% of its 4×5 frame. The loose one reaches into more rows and columns, which is exactly why it usually settles last.
Region by region
Below is every color on #117 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.
Mint: 1 square across rows 4–4, columns 7–7. It never leaves row 4, so its queen is locked to that row.
Indigo covers 3 squares, spanning 1 row and 3 columns (rows 1–1, columns 3–5). It never leaves row 1, so its queen is locked to that row.
Amber occupies 5 squares within rows 1–2, columns 7–9.
Orange: 8 squares across rows 7–9, columns 6–9.
Pale yellow covers 10 squares, spanning 4 rows and 4 columns (rows 5–8, columns 3–6).
Blue occupies 11 squares within rows 1–4, columns 3–6.
Khaki: 12 squares across rows 6–9, columns 1–5.
Red covers 15 squares, spanning 6 rows and 4 columns (rows 2–7, columns 6–9).
Slate occupies 16 squares within rows 1–8, columns 1–3.
Where to start on this board
The most constrained color is where a solve should begin, and on #117 that is mint with 1 square. It reaches from row 4 to row 4 and from column 7 to column 7 — 1 row by 1 column. One queen has to live inside that footprint no matter what else happens, which makes those lines the busiest real estate on the board.
Because mint never leaves row 4, its queen must be in that row — and that instantly settles row 4 for everyone else. Sweep along it and X out every square that is not mint. 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 amber 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 #117
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 and 2 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 7 is the crowded extreme at 5 colors — worth revisiting later, not now.
Working through the middle game
The middle of #117 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 #117 is rated hard
What earns a board its rating is the shape of its opening. Here that opening offers three single-line regions, a 1-square smallest color, a tightest row touched by 2 colors, and a region-size spread of 15. Lopsided grids with flat regions fall quickly; balanced ones like this take more patience.
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 #117 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.
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 #117, start hunting for it near row 9.
A non-spoiling distribution check: solved, #117 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 #117?
Puzzle #117 is rated hard. Its smallest color region holds 1 square, its tightest row is touched by 2 colors, and three of its regions are confined to a single row or column, which gives you a forced move early.
Does 9x9 puzzle #117 have only one solution?
Yes. Every puzzle in the 9x9 collection, including #117, 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 #117?
Start with the mint region — the most constrained color on this board, with 1 square spanning rows 4–4 and columns 7–7. Narrowing the smallest region first removes the most squares elsewhere on the grid.