9x9 Queens Puzzle #142
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 21-step reasoning is written out below.
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Step-by-step solution for puzzle #142
What follows is a complete solve of puzzle #142, worked the way a person works it rather than the way a computer does. It runs to 21 deductions — 9 queen placements and 12 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 columns.
Techniques this board needs: region confined to one line, region shadow, last square in a region, pairing argument on rows, line confined to one region, pairing argument on columns, last square in a row.
Show the full walkthrough (15 steps) — contains the solution
Step 1. 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: 9 squares in all.
Step 2. All of the blue region's remaining squares (2 open squares) lie in column 1. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 8 squares come off.
Step 3. The red region has 5 squares left, spread across rows 5–8, columns 3 and 4. You do not need to know which of them takes the queen: every one of those options attacks the same 1 square, so they can be crossed out now.
Step 4. All of the orange region's remaining squares (2 open squares) lie in row 9. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 8 squares come off.
Step 5. Pale yellow cannot leave row 7 — every one of its open squares (2 open squares) sits there. That row belongs to pale yellow, so every square on it owned by another colour is dead: 8 squares in all.
The board after step 5 — 0 of 9 queens placed. Step 6. 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: 4 squares come off.
Step 7. Only row 1, column 8 is still open in indigo, and since each colour must take a queen, that settles it. Everything else in row 1, in column 8, in indigo and in the ring around that square is now dead.
Step 8. Here is the pairing argument. The amber and blue regions have no open squares outside rows 2 and 3 — 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: 5 squares come off in one stroke.
Step 9. Column 4 has only red squares left (3 open squares). The column needs a queen and only red can provide one, which pins that colour to this column and kills its squares elsewhere: 1 square.
Step 10. Here is the pairing argument. The pale yellow and orange regions have no open squares outside columns 2 and 3 — 2 colours confined to 2 columns. Between them they must take one column each, in some order, so every other colour is shut out of all of them: 4 squares come off in one stroke.
The board after step 10 — 1 of 9 queens placed. Step 11. Amber is down to 3 candidates in rows 2 and 3, columns 6 and 7, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about amber itself.
Step 12. The mint region has 2 squares left, spread across rows 4 and 5, columns 5 and 6. You do not need to know which of them takes the queen: every one of those options attacks the same 5 squares, so they can be crossed out now.
Step 13. 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: row 4 is down to one square, putting a queen on row 4, column 5; row 5 is down to one square, putting a queen on row 5, column 7; amber has one square left, so its queen takes row 2, column 6; blue has one square left, so its queen takes row 3, column 1. 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 3, column 1.
Step 14. Red cannot leave column 4 — every one of its open squares (2 open squares) sits there. That column belongs to red, so every square in it owned by another colour is dead: 1 square in all.
Step 15. 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: pale yellow has one square left, so its queen takes row 7, column 2; orange has one square left, so its queen takes row 9, column 3; red has one square left, so its queen takes row 6, column 4; khaki has one square left, so its queen takes row 8, column 9. 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 9.
The board after step 15 — 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 #142
Board #142 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.
Like every board on this site, #142 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 #142 are: indigo (2 squares), orange (3 squares), blue (4 squares), red (5 squares), pale yellow (9 squares), khaki (10 squares), amber (15 squares), mint (16 squares), slate (17 squares). An even split would hand every color 9 squares, so the indigo region is running 7 squares under that average while the slate 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 indigo, with 2 squares, is under far more pressure than slate with 17. A 15-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 indigo is the most solid, filling 100% of its 1×2 box, and khaki the most diffuse at 42% of its 4×6 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.
Indigo covers 2 squares, spanning 1 row and 2 columns (rows 1–1, columns 8–9). It never leaves row 1, so its queen is locked to that row.
Orange occupies 3 squares within rows 9–9, columns 1–3. It never leaves row 9, so its queen is locked to that row.
Blue: 4 squares across rows 1–3, columns 1–2.
Red covers 5 squares, spanning 4 rows and 2 columns (rows 5–8, columns 3–4).
Pale yellow occupies 9 squares within rows 4–8, columns 1–3.
Khaki: 10 squares across rows 6–9, columns 4–9.
Amber covers 15 squares, spanning 4 rows and 7 columns (rows 1–4, columns 3–9).
Mint occupies 16 squares within rows 2–6, columns 2–6.
Slate: 17 squares across rows 4–8, columns 5–9.
Where to start on this board
Open on the tightest color. Here that is indigo, confined to 2 squares between rows 1 and 1 and columns 8 and 9. Its queen has nowhere else to go, which means those 1 row and 2 columns carry more constraint than anywhere else on #142.
Because indigo never leaves row 1, its queen must be in that row — and that instantly settles row 1 for everyone else. Sweep along it and X out every square that is not indigo. 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 #142
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 7 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 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.
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 #142 is rated medium
Ratings track how generous the opening is. On #142 you get two regions pinned to a single row or column, a smallest color of 2 squares, a tightest row crossed by 2 colors, and a 15-square gap between the largest and smallest regions. Those four numbers largely explain the medium label.
Nothing about the rating involves computation or chance. Each grid has a single solution reachable by pure logic; the rating simply measures how far ahead you have to reason. Easy boards resolve a queen every step or two, while hard ones can ask you to carry three unfinished lines of thought before any of them pays off.
If #142 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 #142, start hunting for it near row 9.
A non-spoiling distribution check: solved, #142 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 #142?
Puzzle #142 is rated medium. Its smallest color region holds 2 squares, 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 #142 have only one solution?
Yes. Every puzzle in the 9x9 collection, including #142, 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 #142?
Start with the indigo region — the most constrained color on this board, with 2 squares spanning rows 1–1 and columns 8–9. Narrowing the smallest region first removes the most squares elsewhere on the grid.