9x9 Queens Puzzle #150
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 17-step reasoning is written out below.
Previous puzzle · All 9x9 puzzles · Next puzzle
Step-by-step solution for puzzle #150
What follows is a complete solve of puzzle #150, worked the way a person works it rather than the way a computer does. It runs to 17 deductions — 9 queen placements and 8 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 rows.
Techniques this board needs: last square in a region, region confined to one line, region shadow, line confined to one region, pairing argument on rows.
Show the full walkthrough (12 steps) — contains the solution
Step 1. Only row 2, column 9 is still open in amber, and since each colour must take a queen, that settles it. That clears row 2, column 9, the rest of the amber 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: 5 squares come off.
Step 3. The blue region has 3 squares left, spread across rows 3 and 4, columns 7 and 8. 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 4. Wherever slate ends up among its 3 squares, the same squares fall within reach of it — 1 square in total, impossible regardless of how the colour resolves.
The board after step 4 — 1 of 9 queens placed. Step 5. Row 9 has only orange squares left (8 open squares). The row needs a queen and only orange can provide one, which pins that colour to this row and kills its squares elsewhere: 9 squares.
Step 6. Here is the pairing argument. The blue and mint regions have no open squares outside rows 3 and 4 — 2 colours confined to 2 rows. Between them they must take one row each, in some order, so every other colour is shut out of all of them: 6 squares come off in one stroke.
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: 6 squares in all.
Step 8. The red region is down to one open square, at row 6, column 1. Every colour holds exactly one queen, so that square is forced. Row 6 and column 1 are now spoken for, along with the squares touching that queen.
The board after step 8 — 2 of 9 queens placed. Step 9. Only row 1, column 2 is still open in indigo, and since each colour must take a queen, that settles it. That clears row 1, column 2, the rest of the indigo region and every square adjacent to it — diagonals included.
Step 10. Wherever pale yellow 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 11. Khaki cannot leave column 8 — 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: 3 squares in all.
Step 12. From here the board cascades. Keep alternating the region sweep and the line sweep and 6 queens fall out in order without any new idea being needed: blue has one square left, so its queen takes row 3, column 7; slate has one square left, so its queen takes row 5, column 6; mint has one square left, so its queen takes row 4, column 4; pale yellow has one square left, so its queen takes row 7, column 5; khaki has one square left, so its queen takes row 8, column 8; orange has one square left, so its queen takes row 9, 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 9, column 3.
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 #150
Board #150 of the 9x9 bank carries a hard 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, #150 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 #150 are: amber (1 square), slate (5 squares), indigo (6 squares), mint (9 squares), khaki (9 squares), red (10 squares), pale yellow (10 squares), blue (14 squares), orange (17 squares). An even split would hand every color 9 squares, so the amber region is running 8 squares under that average while the orange region is the roomiest area on the grid with 17 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 amber, with 1 square, is under far more pressure than orange with 17. A 16-square gap like this one rewards players who start where the choices are fewest.
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 pale yellow the most diffuse at 50% of its 4×5 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.
Amber: 1 square across rows 2–2, columns 9–9. It never leaves row 2, so its queen is locked to that row.
Slate covers 5 squares, spanning 3 rows and 3 columns (rows 3–5, columns 6–8).
Indigo occupies 6 squares within rows 1–2, columns 1–4.
Mint: 9 squares across rows 1–4, columns 3–5.
Khaki covers 9 squares, spanning 4 rows and 3 columns (rows 6–9, columns 7–9).
Red occupies 10 squares within rows 3–6, columns 1–4.
Pale yellow: 10 squares across rows 5–8, columns 2–6.
Blue covers 14 squares, spanning 5 rows and 4 columns (rows 1–5, columns 6–9).
Orange occupies 17 squares within rows 7–9, columns 1–8.
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 9 and 9. Its queen has nowhere else to go, which means those 1 row and 1 column carry more constraint than anywhere else on #150.
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. Indigo 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 #150
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, 5 and 9 are the tightest columns, with 3 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 5 is the crowded extreme at 4 colors — worth revisiting later, not now.
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.
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 #150 is rated hard
Ratings track how generous the opening is. On #150 you get two regions pinned to a single row or column, a smallest color of 1 square, a tightest row crossed by 2 colors, and a 16-square gap between the largest and smallest regions. Those four numbers largely explain the hard label.
The scale has nothing to do with maths or luck — every puzzle here is solvable by deduction and has exactly one answer. It measures reasoning depth: how many eliminations must stack up before a placement becomes provable. That depth is what separates a hard board from the rest.
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.
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 #150, start hunting for it near row 9.
A non-spoiling distribution check: solved, #150 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.
Full rules · Strategy library · Puzzle statistics
Questions about this puzzle
How hard is 9x9 Queens puzzle #150?
Puzzle #150 is rated hard. Its smallest color region holds 1 square, 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 #150 have only one solution?
Yes. Every puzzle in the 9x9 collection, including #150, 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 #150?
Start with the amber region — the most constrained color on this board, with 1 square spanning rows 2–2 and columns 9–9. Narrowing the smallest region first removes the most squares elsewhere on the grid.