8x8 Queens Puzzle #200
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 21-step reasoning is written out below.
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Step-by-step solution for puzzle #200
What follows is a complete solve of puzzle #200, worked the way a person works it rather than the way a computer does. It runs to 21 deductions — 8 queen placements and 13 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 shadow, region confined to one line, pairing argument on columns, pairing argument on rows, last square in a region.
Show the full walkthrough (14 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. Blue is down to 5 candidates in rows 1–3, columns 5–7, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about blue itself.
Step 3. Amber cannot leave column 8 — every one of its open squares (2 open squares) sits there. That column belongs to amber, so every square in it owned by another colour is dead: 5 squares in all.
Step 4. Wherever pale yellow 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 5. Khaki is down to 4 candidates in rows 6–8, columns 1–3, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about khaki itself.
The board after step 5 — 0 of 8 queens placed. Step 6. Here is the pairing argument. The mint and pale yellow regions have no open squares outside columns 1 and 2 — 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: 7 squares come off in one stroke.
Step 7. Khaki cannot leave column 3 — every one of its open squares (2 open squares) sits there. That column belongs to khaki, so every square in it owned by another colour is dead: 8 squares in all.
Step 8. All of the pale yellow 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: 3 squares come off.
Step 9. Pale yellow and khaki are now boxed into rows 7 and 8 and nothing else. That is 2 colours needing 2 rows, so they fill those rows between them — which locks every remaining colour out and removes 6 squares at once.
The board after step 9 — 0 of 8 queens placed. Step 10. Wherever red 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 11. Indigo, amber, blue, and mint are now boxed into rows 1–4 and nothing else. That is 4 colours needing 4 rows, so they fill those rows between them — which locks every remaining colour out and removes 4 squares at once.
Step 12. The slate region has 3 squares left, spread across rows 5 and 6, columns 6 and 7. 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 13. 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: 4 squares in all.
Step 14. 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 5; amber has one square left, so its queen takes row 2, column 8; 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 2; slate has one square left, so its queen takes row 5, column 7; 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 3; pale yellow has one square left, so its queen takes row 7, 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 7, column 1.
The board after step 14 — 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 #200
This is puzzle number 200 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.
Puzzle #200 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 #200 are: amber (3 squares), pale yellow (3 squares), mint (5 squares), khaki (5 squares), blue (7 squares), slate (9 squares), indigo (13 squares), red (19 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 19 squares.
Every color takes one queen and one only, whatever its size — which is why the 16 square difference between amber and red is worth noting before you touch the grid. The cramped colors resolve first and hand you information; the roomy ones absorb whatever is left over at the end.
Shape matters as much as size. The mint region is the most compact color here, filling 83% of the 3×2 box that encloses it, while red is the most scattered at 45% of its 6×7 box. Compact regions are easy to eliminate around; straggling ones reach into more rows and columns and tend to stay unresolved until late.
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 occupies 3 squares within rows 1–2, columns 7–8.
Pale yellow: 3 squares across rows 7–8, columns 1–2.
Mint covers 5 squares, spanning 3 rows and 2 columns (rows 3–5, columns 1–2).
Khaki occupies 5 squares within rows 6–8, columns 1–3.
Blue: 7 squares across rows 1–3, columns 5–8.
Slate covers 9 squares, spanning 3 rows and 4 columns (rows 4–6, columns 5–8).
Indigo occupies 13 squares within rows 1–4, columns 1–5.
Red: 19 squares across rows 3–8, columns 2–8.
Where to start on this board
The most constrained color is where a solve should begin, and on #200 that is amber with 3 squares. It reaches from row 1 to row 2 and from column 7 to column 8 — 2 rows 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.
Amber 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. Pale yellow 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 #200
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 1, 2, 5, 6, 7 and 8 are the narrowest, touched by only 3 colors. Column 4 is the tightest column, with 2 colors.
A line with few colors is a line close to resolving. Where only 3 colors appear, one of them owns the row outright and the others must fit into the remaining 7 rows. Row 4 is the crowded extreme at 4 colors — worth revisiting later, not now.
Working through the middle game
The middle of #200 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.
The whole middle game reduces to two sweeps. Sweep the eight colors looking for one with a single square left; sweep the eight rows and eight columns looking for the same. Each sweep feeds the next, and switching between them deliberately — rather than drifting — is what separates a fast 8x8 solve from a stalled one.
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 #200 is rated hard
The hard label comes out of four measurable things about #200: 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 16. 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.
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.
There is one technique that repays study at every grid size. Two regions restricted to the same two rows must occupy one row apiece, which excludes all other regions from those rows entirely; the identical logic applies to columns and to larger matched sets. It converts slow boards into fast ones, and the likeliest place to find it on #200 is column 4.
A non-spoiling distribution check: solved, #200 carries 4 queens on the perimeter against 4 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 8x8 Queens puzzle #200?
Puzzle #200 is rated hard. 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 #200 have only one solution?
Yes. Every puzzle in the 8x8 collection, including #200, 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 #200?
Start with the amber region — the most constrained color on this board, with 3 squares spanning rows 1–2 and columns 7–8. Narrowing the smallest region first removes the most squares elsewhere on the grid.