9x9 Queens Puzzle #110
Difficulty: easy. 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.
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Step-by-step solution for puzzle #110
What follows is a complete solve of puzzle #110, 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 region shadow.
Techniques this board needs: last square in a region, region shadow, region confined to one line.
Show the full walkthrough (9 steps) — contains the solution
Step 1. Only row 2, column 1 is still open in amber, and since each colour must take a queen, that settles it. That clears row 2, column 1, the rest of the amber region and every square adjacent to it — diagonals included.
Step 2. The orange region is down to one open square, at row 9, column 8. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 9 and column 8, the remaining orange squares, and the ring of neighbours around row 9, column 8.
Step 3. Only row 7, column 7 is still open in pale yellow, and since each colour must take a queen, that settles it. Everything else in row 7, in column 7, in pale yellow and in the ring around that square is now dead.
The board after step 3 — 3 of 9 queens placed. Step 4. Wherever blue ends up among its 5 squares, the same squares fall within reach of it — 2 squares in total, impossible regardless of how the colour resolves.
Step 5. Slate is down to 5 candidates in rows 1, 3, 4, and 5, columns 5, 6, and 9, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about slate itself.
Step 6. The red region is down to one open square, at row 6, column 9. Every colour holds exactly one queen, so that square 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.
The board after step 6 — 4 of 9 queens placed. Step 7. Slate cannot leave row 5 — every one of its open squares (2 open squares) sits there. That row belongs to slate, so every square on it owned by another colour is dead: 5 squares in all.
Step 8. All of the khaki region's remaining squares (2 open squares) lie in row 8. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 2 squares come off.
Step 9. 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: mint has one square left, so its queen takes row 4, column 2; 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 5; slate has one square left, so its queen takes row 5, column 6; indigo has one square left, so its queen takes row 1, 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 1, column 3.
The board after step 9 — 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 #110
Board #110 of the 9x9 bank carries a easy 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, #110 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 #110 are: amber (1 square), orange (1 square), pale yellow (3 squares), red (7 squares), blue (8 squares), indigo (12 squares), khaki (12 squares), slate (18 squares), mint (19 squares). An even split would hand every color 9 squares, so the amber region is running 8 squares under that average while the mint region is the roomiest area on the grid with 19 squares.
That imbalance is the first thing to read, because every region takes exactly one queen regardless of how much space it owns. Amber has only 1 place to put its queen; mint has 19. The spread between them on this board is 18 squares, and the wider that spread runs, the more it pays to solve from the small end inward.
A region's outline can constrain it more than its size does. Here amber is the most solid, filling 100% of its 1×1 box, and blue the most diffuse at 44% of its 3×6 box. Solid blocks give clean eliminations; diffuse ones spread across the board and stay open longer.
Region by region
Each region's exact extent on this grid is listed below, starting with the most constrained. Knowing which lines a color can and cannot reach is most of the work on a easy board.
Amber occupies 1 square within rows 2–2, columns 1–1. It never leaves row 2, so its queen is locked to that row.
Orange: 1 square across rows 9–9, columns 8–8. It never leaves row 9, so its queen is locked to that row.
Pale yellow covers 3 squares, spanning 3 rows and 1 column (rows 7–9, columns 7–7). It sits wholly inside column 7, so its queen must be in that column.
Red occupies 7 squares within rows 5–9, columns 8–9.
Blue: 8 squares across rows 2–4, columns 1–6.
Indigo covers 12 squares, spanning 3 rows and 6 columns (rows 1–3, columns 1–6).
Khaki occupies 12 squares within rows 6–9, columns 2–6.
Slate: 18 squares across rows 1–6, columns 5–9.
Mint covers 19 squares, spanning 6 rows and 5 columns (rows 4–9, 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 1 and 1. Its queen has nowhere else to go, which means those 1 row and 1 column carry more constraint than anywhere else on #110.
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 is no more than two rows tall, so its queen is 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 #110
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 7 and 9 are the tightest columns, with 2 colors.
The fewer colors a line touches, the sooner it surrenders its queen. A row meeting just 2 colors has to be claimed by one of them, which pushes every remaining region into the other 8 rows. Row 9, meeting 5 colors, is the opposite case — the busiest line on #110 and the last one you should expect to crack.
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.
Keep alternating between two views of the board. In the region view you ask which of the nine colors is down to one open square. In the line view you ask the same of each row and column. Both produce forced queens, and each placement refreshes the other view, so cycling between them deliberately is how a 9x9 board unwinds.
The trap on a board like this is placing a queen that is merely plausible. Every placement should be traceable to an elimination you can point at. If you cannot name the rule that forced it, you are guessing — and on a single-solution grid a guess costs more to unwind than the deduction would have taken to find.
Why puzzle #110 is rated easy
The easy label comes out of four measurable things about #110: five of its regions are locked to one row or column, its smallest color spans 1 square, its least crowded row meets 2 colors, and its largest and smallest regions differ by 18. Boards that score tight on those measures give up their first queen fast.
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.
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.
One pattern is worth learning at every size, and it is available here. When two regions can only fit inside the same two rows, they must take one row each — which locks every other region out of both. The same argument works for columns, and for any matching count: three regions sharing three rows, four sharing four. Spotting these pairings turns a slow grind into a quick cascade, and on #110 the place to look for one is around row 1.
Here is a shape check that gives nothing away: when #110 is solved, 4 queens sit on the outer edge of the grid and 5 sit inside it, and no queen lands in a corner. A work-in-progress board that clusters its queens in one quadrant while leaving others bare is usually carrying a mistake.
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 #110?
Puzzle #110 is rated easy. Its smallest color region holds 1 square, its tightest row is touched by 2 colors, and five of its regions are confined to a single row or column, which gives you a forced move early.
Does 9x9 puzzle #110 have only one solution?
Yes. Every puzzle in the 9x9 collection, including #110, 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 #110?
Start with the amber region — the most constrained color on this board, with 1 square spanning rows 2–2 and columns 1–1. Narrowing the smallest region first removes the most squares elsewhere on the grid.