9x9 Queens Puzzle #170
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 16-step reasoning is written out below.
Previous puzzle · All 9x9 puzzles · Next puzzle
Step-by-step solution for puzzle #170
What follows is a complete solve of puzzle #170, worked the way a person works it rather than the way a computer does. It runs to 16 deductions — 9 queen placements and 7 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 7, column 3 is still open in pale yellow, and since each colour must take a queen, that settles it. That clears row 7, column 3, the rest of the pale yellow region and every square adjacent to it — diagonals included.
Step 2. 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: 8 squares come off.
Step 3. Only row 2, column 6 is still open in amber, and since each colour must take a queen, that settles it. Everything else in row 2, in column 6, in amber and in the ring around that square is now dead.
Step 4. The indigo region is down to one open square, at row 1, column 4. Every colour holds exactly one queen, so that square is forced. Row 1 and column 4 are now spoken for, along with the squares touching that queen.
The board after step 4 — 3 of 9 queens placed. Step 5. Blue is down to 4 candidates in rows 3–5, columns 1 and 2, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about blue itself.
Step 6. The slate region has 4 squares left, spread across rows 5, 6, 8, and 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 2 squares, so they can be crossed out now.
Step 7. Blue cannot leave row 3 — every one of its open squares (2 open squares) sits there. That row belongs to blue, so every square on it owned by another colour is dead: 2 squares in all.
Step 8. All of the khaki 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: 5 squares come off.
The board after step 8 — 3 of 9 queens placed. Step 9. Orange cannot leave row 9 — every one of its open squares (2 open squares) sits there. That row belongs to orange, so every square on it owned by another colour is dead: 3 squares in all.
Step 10. The khaki region is down to one open square, at row 8, column 9. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 8 and column 9, the remaining khaki squares, and the ring of neighbours around row 8, column 9.
Step 11. Column 8 has only mint squares left (3 open squares). The column needs a queen and only mint can provide one, which pins that colour to this column and kills its squares elsewhere: 2 squares.
Step 12. 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: column 7 is down to one square, putting a queen on row 6, column 7; mint has one square left, so its queen takes row 4, column 8; slate has one square left, so its queen takes row 5, column 2; blue has one square left, so its queen takes row 3, column 1; orange has one square left, so its queen takes row 9, column 5. 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 9, column 5.
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 #170
Board #170 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.
Puzzle #170 has been checked to admit exactly one arrangement of queens, and every step toward it is deducible from what is already on the board. There is no point at which you are expected to pick a square and hope. The only thing that differs between boards is how quickly the first certainty surfaces, and that depends entirely on the shapes the colors happen to take here.
How the colors divide this board
From smallest to largest, the regions on puzzle #170 are: pale yellow (1 square), indigo (3 squares), khaki (3 squares), amber (4 squares), orange (6 squares), blue (11 squares), slate (15 squares), mint (16 squares), red (22 squares). An even split would hand every color 9 squares, so the pale yellow region is running 8 squares under that average while the red region is the roomiest area on the grid with 22 squares.
That imbalance is the first thing to read, because every region takes exactly one queen regardless of how much space it owns. Pale yellow has only 1 place to put its queen; red has 22. The spread between them on this board is 21 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 indigo is the most solid, filling 100% of its 1×3 box, and red the most diffuse at 55% of its 8×5 box. Solid blocks give clean eliminations; diffuse ones spread across the board and stay open longer.
Region by region
The complete breakdown of each region on this board follows, ordered from tightest to roomiest. Skimming the spans first tells you where the board is crowded and where it has slack.
Pale yellow occupies 1 square within rows 7–7, columns 3–3. It never leaves row 7, so its queen is locked to that row.
Indigo: 3 squares across rows 1–1, columns 3–5. It never leaves row 1, so its queen is locked to that row.
Khaki covers 3 squares, spanning 3 rows and 1 column (rows 7–9, columns 9–9). It sits wholly inside column 9, so its queen must be in that column.
Amber occupies 4 squares within rows 1–2, columns 6–8.
Orange: 6 squares across rows 8–9, columns 2–5.
Blue covers 11 squares, spanning 5 rows and 4 columns (rows 1–5, columns 1–4).
Slate occupies 15 squares within rows 4–9, columns 1–4.
Mint: 16 squares across rows 1–6, columns 6–9.
Red covers 22 squares, spanning 8 rows and 5 columns (rows 2–9, columns 4–8).
Where to start on this board
Open on the tightest color. Here that is pale yellow, confined to 1 square between rows 7 and 7 and columns 3 and 3. Its queen has nowhere else to go, which means those 1 row and 1 column carry more constraint than anywhere else on #170.
Because pale yellow never leaves row 7, its queen must be in that row — and that instantly settles row 7 for everyone else. Sweep along it and X out every square that is not pale yellow. 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, amber and orange 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 #170
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 3 and 6 are the narrowest, touched by only 3 colors. Columns 1 and 9 are the tightest columns, with 2 colors.
Those lines matter because a row touched by few colors gives its queen away sooner. If a row meets only 3 colors, then one of those regions has to own it, and every other region is competing for the remaining 8 rows. By contrast row 9 meets 4 colors — the most crowded line here, and the one least likely to resolve early. Spend your attention accordingly.
Working through the middle game
After the first few queens the puzzle becomes bookkeeping. A placed queen wipes its row, its column and every square it touches — as many as eight neighbours — so the space collapses quickly. Record those eliminations on the board instead of carrying them in your head, and the next forced move tends to announce itself.
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.
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 #170 is rated medium
Ratings track how generous the opening is. On #170 you get four regions pinned to a single row or column, a smallest color of 1 square, a tightest row crossed by 3 colors, and a 21-square gap between the largest and smallest regions. Those four numbers largely explain the medium label.
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.
When a board plays tougher than its label, look for a missed mark before you look for a clever deduction. Walk back over every queen you have placed and confirm the full row, the full column and all eight surrounding squares are crossed out. The diagonal neighbours are the ones players skip, and a single skipped diagonal will hide the next forced move indefinitely.
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 #170 the place to look for one is around column 1.
As a sanity check rather than a spoiler: the finished solution to #170 puts 4 queens on the outer border and 5 queens in the interior, with none in a corner. If your part-finished grid has queens bunched into one area while whole stretches sit empty, something probably went wrong a few moves back.
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.
Full rules · Strategy library · Puzzle statistics
Questions about this puzzle
How hard is 9x9 Queens puzzle #170?
Puzzle #170 is rated medium. Its smallest color region holds 1 square, its tightest row is touched by 3 colors, and four of its regions are confined to a single row or column, which gives you a forced move early.
Does 9x9 puzzle #170 have only one solution?
Yes. Every puzzle in the 9x9 collection, including #170, 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 #170?
Start with the pale yellow region — the most constrained color on this board, with 1 square spanning rows 7–7 and columns 3–3. Narrowing the smallest region first removes the most squares elsewhere on the grid.