8x8 Queens Puzzle #186
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 14-step reasoning is written out below.
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Step-by-step solution for puzzle #186
What follows is a complete solve of puzzle #186, worked the way a person works it rather than the way a computer does. It runs to 14 deductions — 8 queen placements and 6 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 shadow, region confined to one line, last square in a region.
Show the full walkthrough (10 steps) — contains the solution
Step 1. Wherever amber ends up among its 3 squares, the same squares fall within reach of it — 2 squares in total, impossible regardless of how the colour resolves.
Step 2. Mint is down to 4 candidates in rows 3 and 4, columns 6–8, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about mint itself.
Step 3. Slate cannot leave column 1 — every one of its open squares (2 open squares) sits there. That column belongs to slate, so every square in it owned by another colour is dead: 7 squares in all.
The board after step 3 — 0 of 8 queens placed. Step 4. The amber region is down to one open square, at row 2, column 2. Every colour holds exactly one queen, so that square is forced. Row 2 and column 2 are now spoken for, along with the squares touching that queen.
Step 5. Only row 1, column 4 is still open in indigo, and since each colour must take a queen, that settles it. That clears row 1, column 4, the rest of the indigo region and every square adjacent to it — diagonals included.
Step 6. All of the blue region's remaining squares (2 open squares) lie in row 3. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 3 squares come off.
Step 7. Mint cannot leave row 4 — every one of its open squares (2 open squares) sits there. That row belongs to mint, so every square on it owned by another colour is dead: 4 squares in all.
The board after step 7 — 2 of 8 queens placed. Step 8. The slate region is down to one open square, at row 5, column 1. Every colour holds exactly one queen, so that square is forced. Row 5 and column 1 are now spoken for, along with the squares touching that queen.
Step 9. Pale yellow cannot leave column 5 — 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: 4 squares in all.
Step 10. 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: blue has one square left, so its queen takes row 3, column 6; mint has one square left, so its queen takes row 4, column 8; khaki has one square left, so its queen takes row 8, column 7; pale yellow has one square left, so its queen takes row 7, column 5; red has one square left, so its queen takes row 6, 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 6, column 3.
The board after step 10 — 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 #186
Board #186 of the 8x8 bank carries a hard rating. Its 64 squares are shared between eight colored regions, and the solution places eight queens: one per row, one per column, one per region, none of them side by side or corner to corner.
Puzzle #186 has been checked to admit exactly one arrangement of queens, and every step toward it is deducible from what is already on the board. There is no point at which you are expected to pick a square and hope. The only thing that differs between boards is how quickly the first certainty surfaces, and that depends entirely on the shapes the colors happen to take here.
How the colors divide this board
From smallest to largest, the regions on puzzle #186 are: amber (3 squares), slate (3 squares), mint (4 squares), pale yellow (4 squares), indigo (5 squares), khaki (5 squares), blue (12 squares), red (28 squares). An even split would hand every color 8 squares, so the amber region is running 5 squares under that average while the red region is the roomiest area on the grid with 28 squares.
That imbalance is the first thing to read, because every region takes exactly one queen regardless of how much space it owns. Amber has only 3 places to put its queen; red has 28. The spread between them on this board is 25 squares, and the wider that spread runs, the more it pays to solve from the small end inward.
Look at arrangement as well as area. Slate is the densest region on this grid at 100% of a 3×1 frame; khaki is the loosest, occupying only 63% of its 4×2 frame. The loose one reaches into more rows and columns, which is exactly why it usually settles last.
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 hard board.
Amber: 3 squares across rows 1–2, columns 1–2.
Slate covers 3 squares, spanning 3 rows and 1 column (rows 3–5, columns 1–1). It sits wholly inside column 1, so its queen must be in that column.
Mint occupies 4 squares within rows 3–4, columns 6–8.
Pale yellow: 4 squares across rows 7–8, columns 4–5.
Indigo covers 5 squares, spanning 2 rows and 3 columns (rows 1–2, columns 2–4).
Khaki occupies 5 squares within rows 5–8, columns 7–8.
Blue: 12 squares across rows 1–3, columns 4–8.
Red covers 28 squares, spanning 6 rows and 7 columns (rows 3–8, columns 1–7).
Where to start on this board
Amber is the natural opening on #186: it is the smallest region on the grid at 3 squares, boxed into rows 1–2 and columns 1–2. Since one of those squares must hold a queen, that block of 2 rows and 2 columns is the most contested part of the board.
With 2 rows and 2 columns of room, amber needs narrowing rather than solving outright. Test its 3 squares against the neighbours: a candidate that would strand another color is dead, and eliminating even two of them tightens the whole corner of the board around rows 1–2.
Work outward to the other flat regions next. Indigo, mint and pale yellow 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 #186
A quick way to find the next move is to count how many different colors touch each line. On this board, row 6 is the narrowest, touched by only 2 colors. Column 3 is the tightest column, with 2 colors.
Count colors per line and you have a ranking of where to look. The narrowest rows here see only 2 colors, so one of that handful must take the row and the rest are squeezed into the other 7 rows. Row 3 sits at the far end with 4 colors crossing it; it will almost certainly be among the last to settle.
Working through the middle game
The middle of #186 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.
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.
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 #186 is rated hard
The hard label comes out of four measurable things about #186: one of its regions is locked to one row or column, its smallest color spans 3 squares, its least crowded row meets 2 colors, and its largest and smallest regions differ by 25. 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.
When a board plays tougher than its label, look for a missed mark before you look for a clever deduction. Walk back over every queen you have placed and confirm the full row, the full column and all eight surrounding squares are crossed out. The diagonal neighbours are the ones players skip, and a single skipped diagonal will hide the next forced move indefinitely.
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.
One pattern is worth learning at every size, and it is available here. When two regions can only fit inside the same two rows, they must take one row each — which locks every other region out of both. The same argument works for columns, and for any matching count: three regions sharing three rows, four sharing four. Spotting these pairings turns a slow grind into a quick cascade, and on #186 the place to look for one is around row 6.
Use this as a rough check on your progress: the completed board has 4 queens around the border and 4 queens in the middle, and nothing in the corners. 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 8x8 Queens puzzle #186?
Puzzle #186 is rated hard. Its smallest color region holds 3 squares, its tightest row is touched by 2 colors, and one of its regions is confined to a single row or column, which gives you a forced move early.
Does 8x8 puzzle #186 have only one solution?
Yes. Every puzzle in the 8x8 collection, including #186, 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 #186?
Start with the amber region — the most constrained color on this board, with 3 squares spanning rows 1–2 and columns 1–2. Narrowing the smallest region first removes the most squares elsewhere on the grid.