8x8 Queens Puzzle #180
Difficulty: hard. 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 13-step reasoning is written out below.
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Step-by-step solution for puzzle #180
What follows is a complete solve of puzzle #180, worked the way a person works it rather than the way a computer does. It runs to 13 deductions — 8 queen placements and 5 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 region shadow.
Techniques this board needs: region confined to one line, region shadow, last square in a region, last square in a column, last square in a row.
Show the full walkthrough (9 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: 8 squares in all.
Step 2. All of the amber region's remaining squares (2 open squares) lie in row 2. 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 mint region has 3 squares left, spread across rows 3 and 4, columns 5 and 6. You do not need to know which of them takes the queen: every one of those options attacks the same 3 squares, so they can be crossed out now.
The board after step 3 — 0 of 8 queens placed. Step 4. All of the khaki 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: 7 squares come off.
Step 5. Only row 2, column 3 is still open in amber, and since each colour must take a queen, that settles it. That clears row 2, column 3, the rest of the amber region and every square adjacent to it — diagonals included.
Step 6. The red region is down to one open square, at row 6, column 2. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 6 and column 2, the remaining red squares, and the ring of neighbours around row 6, column 2.
The board after step 6 — 2 of 8 queens placed. Step 7. Only row 8, column 1 is still open in khaki, and since each colour must take a queen, that settles it. Everything else in row 8, in column 1, in khaki and in the ring around that square is now dead.
Step 8. Slate is down to 2 candidates in rows 5 and 7, columns 4 and 6, and they overlap enough to cover 2 squares elsewhere. Cross those out without deciding anything about slate itself.
Step 9. 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 4 is down to one square, putting a queen on row 5, column 4; column 6 is down to one square, putting a queen on row 4, column 6; row 3 is down to one square, putting a queen on row 3, column 8; indigo has one square left, so its queen takes row 1, column 7; pale yellow has one square left, so its queen takes row 7, 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 7, column 5.
The board after step 9 — 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 #180
This is puzzle number 180 in the 8x8 collection, rated hard. The grid holds 64 squares split between eight colored regions, and a finished board carries eight queens — one in every row, one in every column, one in every color, and never two of them touching, diagonals included.
There is exactly one way to finish #180, 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 eight regions is what sets the depth.
How the colors divide this board
From smallest to largest, the regions on puzzle #180 are: indigo (2 squares), khaki (2 squares), amber (6 squares), mint (6 squares), red (8 squares), pale yellow (11 squares), slate (14 squares), blue (15 squares). An even split would hand every color 8 squares, so the indigo region is running 6 squares under that average while the blue region is the roomiest area on the grid with 15 squares.
One queen per color, regardless of acreage: that is what turns this uneven split into a solving order. Indigo is working with 2 squares while blue has 15 to spare, a gap of 13. Attack the cramped end and the roomy regions tend to resolve themselves.
Square count is only half the story — how a color is arranged counts too. Indigo is the tidiest shape on #180, packing 100% of its 1×2 bounding box, whereas slate straggles across its 6×6 box at just 39%. Tidy blocks are easy to work around; scattered ones touch more lines and resist resolution.
Region by region
Below is every color on #180 with its exact reach, smallest region first. It is worth a slow read: the spans reveal which rows and columns several regions are fighting over.
Indigo: 2 squares across rows 1–1, columns 7–8. It never leaves row 1, so its queen is locked to that row.
Khaki covers 2 squares, spanning 2 rows and 1 column (rows 7–8, columns 1–1). It sits wholly inside column 1, so its queen must be in that column.
Amber occupies 6 squares within rows 1–2, columns 1–4.
Mint: 6 squares across rows 1–4, columns 4–6.
Red covers 8 squares, spanning 4 rows and 3 columns (rows 4–7, columns 1–3).
Pale yellow occupies 11 squares within rows 6–8, columns 2–8.
Slate: 14 squares across rows 2–7, columns 1–6.
Blue covers 15 squares, spanning 7 rows and 3 columns (rows 1–7, columns 6–8).
Where to start on this board
The most constrained color is where a solve should begin, and on #180 that is indigo with 2 squares. It reaches from row 1 to row 1 and from column 7 to column 8 — 1 row by 2 columns. 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. Amber and khaki 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 #180
A quick way to find the next move is to count how many different colors touch each line. On this board, row 8 is the narrowest, touched by only 2 colors. Columns 5, 7 and 8 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 7 rows. Row 7 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.
With eight queens to seat and eight regions competing over 64 squares, keep two questions in rotation. Does any region now have exactly one open square left? That queen is forced. Does any row or column now have exactly one open square left? That queen is forced too. Alternating between the region view and the row-and-column view is what keeps a solve moving, and it is the clearest difference between players who finish 8x8 boards quickly and players who stall halfway.
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 #180 is rated hard
What earns a board its rating is the shape of its opening. Here that opening offers two single-line regions, a 2-square smallest color, a tightest row touched by 2 colors, and a region-size spread of 13. Lopsided grids with flat regions fall quickly; balanced ones like this take more patience.
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.
Stuck on #180 despite the hard 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 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.
Whatever the grid size, the pairing rule is the technique to internalise. When a pair of regions is boxed into the same pair of rows, they split those rows between them and nobody else may enter — and the same holds for columns, or for any n regions confined to n lines. Look for an instance of it around row 8 on this board.
A non-spoiling distribution check: solved, #180 carries 3 queens on the perimeter against 5 queens inside, 1 of them cornered. 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 8x8 Queens puzzle #180?
Puzzle #180 is rated hard. 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 8x8 puzzle #180 have only one solution?
Yes. Every puzzle in the 8x8 collection, including #180, 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 #180?
Start with the indigo region — the most constrained color on this board, with 2 squares spanning rows 1–1 and columns 7–8. Narrowing the smallest region first removes the most squares elsewhere on the grid.