9x9 Queens Puzzle #177
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 9-step reasoning is written out below.
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Step-by-step solution for puzzle #177
What follows is a complete solve of puzzle #177, worked the way a person works it rather than the way a computer does. It runs to 9 deductions, every one of them a forced placement. Each step names the rule that forces it, so nothing below is a guess, and the hardest idea required is the last square in a region.
Techniques this board needs: last square in a region.
Show the full walkthrough (9 steps) — contains the solution
Step 1. Only row 1, column 5 is still open in indigo, and since each colour must take a queen, that settles it. That clears row 1, column 5, the rest of the indigo region and every square adjacent to it — diagonals included.
Step 2. The mint region is down to one open square, at row 4, column 4. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 4 and column 4, the remaining mint squares, and the ring of neighbours around row 4, column 4.
Step 3. Only row 2, column 3 is still open in amber, and since each colour must take a queen, that settles it. Everything else in row 2, in column 3, in amber and in the ring around that square is now dead.
The board after step 3 — 3 of 9 queens placed. Step 4. The orange region is down to one open square, at row 9, column 9. Every colour holds exactly one queen, so that square is forced. Row 9 and column 9 are now spoken for, along with the squares touching that queen.
Step 5. Only row 8, column 6 is still open in khaki, and since each colour must take a queen, that settles it. That clears row 8, column 6, the rest of the khaki region and every square adjacent to it — diagonals included.
Step 6. The pale yellow region is down to one open square, at row 7, column 1. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 7 and column 1, the remaining pale yellow squares, and the ring of neighbours around row 7, column 1.
The board after step 6 — 6 of 9 queens placed. Step 7. Only row 5, column 2 is still open in slate, and since each colour must take a queen, that settles it. Everything else in row 5, in column 2, in slate and in the ring around that square is now dead.
Step 8. 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.
Step 9. Only row 3, column 7 is still open in blue, and since each colour must take a queen, that settles it. That clears row 3, column 7, the rest of the blue region and every square adjacent to it — diagonals included.
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 #177
Puzzle #177 is one of the easy-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.
There is exactly one way to finish #177, and it has been verified. More importantly, you can reach it without ever gambling: at every stage some square is provably right or provably wrong. Boards differ only in how deep you must dig before that proof appears, and the geometry of these nine regions is what sets the depth.
How the colors divide this board
From smallest to largest, the regions on puzzle #177 are: indigo (1 square), orange (1 square), mint (3 squares), khaki (6 squares), pale yellow (10 squares), slate (12 squares), amber (13 squares), red (16 squares), blue (19 squares). An even split would hand every color 9 squares, so the indigo region is running 8 squares under that average while the blue region is the roomiest area on the grid with 19 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 1 square, is under far more pressure than blue with 19. A 18-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 1×1 box, and amber the most diffuse at 52% of its 5×5 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.
Indigo: 1 square across rows 1–1, columns 5–5. It never leaves row 1, so its queen is locked to that row.
Orange covers 1 square, spanning 1 row and 1 column (rows 9–9, columns 9–9). It never leaves row 9, so its queen is locked to that row.
Mint occupies 3 squares within rows 4–5, columns 4–5.
Khaki: 6 squares across rows 7–9, columns 4–6.
Pale yellow covers 10 squares, spanning 4 rows and 4 columns (rows 6–9, columns 1–4).
Slate occupies 12 squares within rows 2–8, columns 1–3.
Amber: 13 squares across rows 1–5, columns 1–5.
Red covers 16 squares, spanning 5 rows and 5 columns (rows 5–9, columns 5–9).
Blue occupies 19 squares within rows 1–6, columns 5–9.
Where to start on this board
The most constrained color is where a solve should begin, and on #177 that is indigo with 1 square. It reaches from row 1 to row 1 and from column 5 to column 5 — 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 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 and mint 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 #177
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 1, 2 and 3 are the narrowest, touched by only 3 colors. Columns 7 and 8 are the tightest columns, with 2 colors.
Count colors per line and you have a ranking of where to look. The narrowest rows here see only 3 colors, so one of that handful must take the row and the rest are squeezed into the other 8 rows. Row 5 sits at the far end with 5 colors crossing it; it will almost certainly be among the last to settle.
Working through the middle game
Once two or three queens are down, the board changes character. Each queen removes an entire row, an entire column and the ring of up to eight squares around it, so the grid shrinks faster than most people expect. The habit that pays here is marking rather than remembering: after every placement, cross out the full row, the full column and all eight neighbours before hunting for the next move.
Two checks, run alternately, will carry you through the 81 squares of this grid. First: has any of the nine regions been reduced to a single open square? Second: has any row or column? Either answer forces a queen. Players who stall on 9x9 boards almost always run one of those checks and forget the other.
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 #177 is rated easy
The easy label comes out of four measurable things about #177: four of its regions are locked to one row or column, its smallest color spans 1 square, its least crowded row meets 3 colors, and its largest and smallest regions differ by 18. Boards that score tight on those measures give up their first queen fast.
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.
Stuck on #177 despite the easy rating? The odds strongly favour a bookkeeping error over a hard chain of logic. Re-check each placed queen for its complete set of eliminations, paying particular attention to the four diagonal squares — those are the ones that get overlooked, and one of them is usually sitting on the answer.
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 #177, start hunting for it near column 7.
Use this as a rough check on your progress: the completed board has 3 queens around the border and 6 queens in the middle, including 1 in a corner. Solutions spread out; if yours is bunching up in one region of the grid, retrace a few moves.
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 #177?
Puzzle #177 is rated easy. 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 #177 have only one solution?
Yes. Every puzzle in the 9x9 collection, including #177, 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 #177?
Start with the indigo region — the most constrained color on this board, with 1 square spanning rows 1–1 and columns 5–5. Narrowing the smallest region first removes the most squares elsewhere on the grid.