9x9 Queens Puzzle #208
Difficulty: hard. 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 14-step reasoning is written out below.
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Step-by-step solution for puzzle #208
What follows is a complete solve of puzzle #208, worked the way a person works it rather than the way a computer does. It runs to 14 deductions — 9 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 pairing argument on columns.
Techniques this board needs: last square in a region, region confined to one line, region shadow, pairing argument on columns.
Show the full walkthrough (9 steps) — contains the solution
Step 1. Only row 8, column 1 is still open in khaki, and since each colour must take a queen, that settles it. That clears row 8, column 1, the rest of the khaki region and every square adjacent to it — diagonals included.
Step 2. All of the indigo region's remaining squares (2 open squares) lie in row 1. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 8 squares come off.
Step 3. The orange region has 2 squares left, spread across rows 7 and 9, columns 6 and 7. 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 — 1 of 9 queens placed. Step 4. Here is the pairing argument. The indigo and mint regions have no open squares outside columns 8 and 9 — 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: 3 squares come off in one stroke.
Step 5. Slate cannot leave column 6 — 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.
Step 6. The orange region is down to one open square, at row 9, column 7. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 9 and column 7, the remaining orange squares, and the ring of neighbours around row 9, column 7.
The board after step 6 — 2 of 9 queens placed. Step 7. Only row 3, column 5 is still open in blue, and since each colour must take a queen, that settles it. Everything else in row 3, in column 5, in blue and in the ring around that square is now dead.
Step 8. All of the red region's remaining squares (3 open squares) lie in row 6. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 4 squares come off.
Step 9. From here the board cascades. Keep alternating the region sweep and the line sweep and 6 queens fall out in order without any new idea being needed: slate has one square left, so its queen takes row 5, column 6; pale yellow has one square left, so its queen takes row 7, column 4; mint has one square left, so its queen takes row 4, column 9; indigo has one square left, so its queen takes row 1, column 8; red has one square left, so its queen takes row 6, column 2; amber has one square left, so its queen takes row 2, 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 2, column 3.
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 #208
This is puzzle number 208 in the 9x9 collection, rated hard. The grid holds 81 squares split between nine colored regions, and a finished board carries nine 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 #208, 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 #208 are: khaki (1 square), indigo (2 squares), orange (5 squares), slate (6 squares), blue (11 squares), amber (12 squares), mint (12 squares), red (12 squares), pale yellow (20 squares). An even split would hand every color 9 squares, so the khaki region is running 8 squares under that average while the pale yellow region is the roomiest area on the grid with 20 squares.
Every color takes one queen and one only, whatever its size — which is why the 19 square difference between khaki and pale yellow 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.
Square count is only half the story — how a color is arranged counts too. Indigo is the tidiest shape on #208, packing 100% of its 1×2 bounding box, whereas red straggles across its 7×4 box at just 43%. Tidy blocks are easy to work around; scattered ones touch more lines and resist resolution.
Region by region
The complete breakdown of each region on this board follows, ordered from tightest to roomiest. Skimming the spans first tells you where the board is crowded and where it has slack.
Khaki covers 1 square, spanning 1 row and 1 column (rows 8–8, columns 1–1). It never leaves row 8, so its queen is locked to that row.
Indigo occupies 2 squares within rows 1–1, columns 8–9. It never leaves row 1, so its queen is locked to that row.
Orange: 5 squares across rows 7–9, columns 6–8.
Slate covers 6 squares, spanning 3 rows and 3 columns (rows 5–7, columns 6–8).
Blue occupies 11 squares within rows 1–5, columns 5–8.
Amber: 12 squares across rows 1–5, columns 2–5.
Mint covers 12 squares, spanning 8 rows and 2 columns (rows 2–9, columns 8–9).
Red occupies 12 squares within rows 1–7, columns 1–4.
Pale yellow: 20 squares across rows 4–9, columns 1–6.
Where to start on this board
Begin where the choices are fewest. On this board that means khaki, which owns just 1 square inside a 1×1 window running from row 8 to row 8 and column 1 to column 1. A queen is guaranteed somewhere in there, so every line that window crosses is under pressure from the very first move.
Because khaki never leaves row 8, its queen must be in that row — and that instantly settles row 8 for everyone else. Sweep along it and X out every square that is not khaki. 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. Indigo 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 #208
A quick way to find the next move is to count how many different colors touch each line. On this board, row 9 is the narrowest, touched by only 3 colors. Column 9 is the tightest column, with 2 colors.
Those lines matter because a row touched by few colors gives its queen away sooner. If a row meets only 3 colors, then one of those regions has to own it, and every other region is competing for the remaining 8 rows. By contrast row 5 meets 6 colors — the most crowded line here, and the one least likely to resolve early. Spend your attention accordingly.
Working through the middle game
The middle of #208 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 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 #208 is rated hard
Ratings track how generous the opening is. On #208 you get three regions pinned to a single row or column, a smallest color of 1 square, a tightest row crossed by 3 colors, and a 19-square gap between the largest and smallest regions. Those four numbers largely explain the hard label.
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 #208 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 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.
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 #208 is column 9.
As a sanity check rather than a spoiler: the finished solution to #208 puts 4 queens on the outer border and 5 queens in the interior, with none in a corner. If your part-finished grid has queens bunched into one area while whole stretches sit empty, something probably went wrong a few moves back.
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 #208?
Puzzle #208 is rated hard. Its smallest color region holds 1 square, its tightest row is touched by 3 colors, and three of its regions are confined to a single row or column, which gives you a forced move early.
Does 9x9 puzzle #208 have only one solution?
Yes. Every puzzle in the 9x9 collection, including #208, 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 #208?
Start with the khaki region — the most constrained color on this board, with 1 square spanning rows 8–8 and columns 1–1. Narrowing the smallest region first removes the most squares elsewhere on the grid.