8x8 Queens Puzzle #177
Difficulty: medium. Place 8 queens on this 8x8 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 23-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 23 deductions — 8 queen placements and 15 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 proof by contradiction.
Techniques this board needs: region shadow, pairing argument on columns, region confined to one line, proof by contradiction, last square in a region, last square in a row.
Show the full walkthrough (16 steps) — contains the solution
Step 1. Wherever indigo 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 2. Slate is down to 4 candidates in rows 4–6, columns 4 and 5, and they overlap enough to cover 2 squares elsewhere. Cross those out without deciding anything about slate itself.
Step 3. The red region has 4 squares left, spread across rows 4–6, 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 khaki ends up among its 2 squares, the same squares fall within reach of it — 3 squares in total, impossible regardless of how the colour resolves.
Step 5. Red is down to 3 candidates in rows 4–6, columns 7 and 8, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about red itself.
The board after step 5 — 0 of 8 queens placed. Step 6. Here is the pairing argument. The red and khaki regions have no open squares outside columns 7 and 8 — 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: 6 squares come off in one stroke.
Step 7. Wherever mint ends up among its 6 squares, the same squares fall within reach of it — 1 square in total, impossible regardless of how the colour resolves.
Step 8. Here is the pairing argument. The amber, mint, and slate regions have no open squares outside columns 4–6 — 3 colours confined to 3 columns. Between them they must take one column each, in some order, so every other colour is shut out of all of them: 6 squares come off in one stroke.
Step 9. Pale yellow cannot leave column 3 — every one of its open squares (2 open squares) sits there. That column belongs to pale yellow, so every square in it owned by another colour is dead: 9 squares in all.
Step 10. 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.
Step 11. Mint cannot leave column 6 — every one of its open squares (5 open squares) sits there. That column belongs to mint, so every square in it owned by another colour is dead: 1 square in all.
The board after step 11 — 0 of 8 queens placed. Step 12. Now a short proof by contradiction. Suppose the indigo queen went to row 1, column 2. Follow the forced moves that would create and row 3 runs out of open squares entirely — impossible. So that square is ruled out for good.
Step 13. Indigo cannot leave column 1 — every one of its open squares (3 open squares) sits there. That column belongs to indigo, so every square in it owned by another colour is dead: 5 squares in all.
Step 14. Now a short proof by contradiction. Suppose the indigo queen went to row 2, column 1. Follow the forced moves that would create and row 3 runs out of open squares entirely — impossible. So that square is ruled out for good.
Step 15. Test row 3, column 1 for indigo: place a queen there, run the forced consequences through, and column 7 runs out of open squares entirely. The assumption breaks, so the square is eliminated.
Step 16. From here the board cascades. Keep alternating the region sweep and the line sweep and 8 queens fall out in order without any new idea being needed: indigo has one square left, so its queen takes row 1, column 1; amber has one square left, so its queen takes row 2, column 5; row 3 is down to one square, putting a queen on row 3, column 2; row 8 is down to one square, putting a queen on row 8, column 8; red has one square left, so its queen takes row 6, column 7; mint has one square left, so its queen takes row 4, column 6; slate has one square left, so its queen takes row 5, column 4; pale yellow has one square left, so its queen takes row 7, 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 7, column 3.
The board after step 16 — 8 of 8 queens placed.
That completes the board: 8 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 8x8 Queens puzzle #177
Puzzle #177 is one of the medium-rated boards in the 8x8 set. Eight colors divide its 64 squares, and you win by placing eight queens so that each row, each column and each color holds exactly one, with no two queens adjacent in any direction.
Like every board on this site, #177 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 #177 are: khaki (3 squares), indigo (4 squares), amber (4 squares), slate (4 squares), red (4 squares), pale yellow (6 squares), mint (17 squares), blue (22 squares). An even split would hand every color 8 squares, so the khaki region is running 5 squares under that average while the blue region is the roomiest area on the grid with 22 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 khaki, with 3 squares, is under far more pressure than blue with 22. A 19-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 khaki is the most solid, filling 75% of its 2×2 box, and blue the most diffuse at 46% of its 8×6 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 medium board.
Khaki: 3 squares across rows 7–8, columns 7–8.
Indigo covers 4 squares, spanning 3 rows and 2 columns (rows 1–3, columns 1–2).
Amber occupies 4 squares within rows 1–2, columns 4–6.
Slate: 4 squares across rows 4–6, columns 4–5.
Red covers 4 squares, spanning 3 rows and 2 columns (rows 4–6, columns 7–8).
Pale yellow occupies 6 squares within rows 6–8, columns 3–5.
Mint: 17 squares across rows 1–8, columns 5–8.
Blue covers 22 squares, spanning 8 rows and 6 columns (rows 1–8, columns 1–6).
Where to start on this board
Open on the tightest color. Here that is khaki, confined to 3 squares between rows 7 and 8 and columns 7 and 8. Its queen has nowhere else to go, which means those 2 rows and 2 columns carry more constraint than anywhere else on #177.
Khaki does not collapse onto a single line, so it will not hand you a queen on move one. What it does give you is a short list of 3 candidates. Take each one in turn, imagine the queen there, cross out its row, its column and the eight squares around it, and ask whether any other region is left with nowhere to go. One or two candidates usually fail that test immediately.
Work outward to the other flat regions next. Amber 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 #177
A quick way to find the next move is to count how many different colors touch each line. On this board, row 3 is the narrowest, touched by only 3 colors. Columns 1, 2 and 3 are the tightest columns, with 2 colors.
The fewer colors a line touches, the sooner it surrenders its queen. A row meeting just 3 colors has to be claimed by one of them, which pushes every remaining region into the other 7 rows. Row 6, meeting 5 colors, is the opposite case — the busiest line on #177 and the last one you should expect to crack.
Working through the middle game
The middle of #177 is where careless play costs time. Every queen you place kills a row, a column and the eight surrounding squares; if you do not mark all of that immediately, you will later "discover" a move that was available several turns ago. Mark first, then look.
Two checks, run alternately, will carry you through the 64 squares of this grid. First: has any of the eight regions been reduced to a single open square? Second: has any row or column? Either answer forces a queen. Players who stall on 8x8 boards almost always run one of those checks and forget the other.
Resist the plausible-looking queen. On #177 every correct placement has a stated reason behind it, and any move you cannot justify is a guess wearing a disguise. Backing out of a wrong guess on a single-solution board takes far longer than finding the real deduction would have.
Why puzzle #177 is rated medium
The medium label comes out of four measurable things about #177: it has no region locked to one row or column, its smallest color spans 3 squares, its least crowded row meets 3 colors, and its largest and smallest regions differ by 19. 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.
If #177 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 8x8
At 8x8 the whole grid stays within a single glance, which makes systematic scanning practical. Read the rows in order and count the colors in each — a row touched by two colors is far more constrained than one touched by five, and that is usually where the next forced move hides. The board is small enough that re-scanning from the top after each placement costs almost nothing.
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 1.
Here is a shape check that gives nothing away: when #177 is solved, 2 queens sit on the outer edge of the grid and 6 sit inside it, with 2 queens 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 8x8 Queens puzzle #177?
Puzzle #177 is rated medium. Its smallest color region holds 3 squares, its tightest row is touched by 3 colors, and no region is confined to a single row or column, so the opening move takes some hunting.
Does 8x8 puzzle #177 have only one solution?
Yes. Every puzzle in the 8x8 collection, including #177, has been verified to have exactly one valid arrangement of eight 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 khaki region — the most constrained color on this board, with 3 squares spanning rows 7–8 and columns 7–8. Narrowing the smallest region first removes the most squares elsewhere on the grid.