9x9 Queens Puzzle #216
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 13-step reasoning is written out below.
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Step-by-step solution for puzzle #216
What follows is a complete solve of puzzle #216, worked the way a person works it rather than the way a computer does. It runs to 13 deductions — 9 queen placements and 4 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, last square in a region, region confined to one line.
Show the full walkthrough (10 steps) — contains the solution
Step 1. Wherever amber 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. Khaki is down to 3 candidates in rows 8 and 9, columns 3 and 4, and they overlap enough to cover 2 squares elsewhere. Cross those out without deciding anything about khaki itself.
Step 3. Only row 9, column 1 is still open in orange, and since each colour must take a queen, that settles it. Everything else in row 9, in column 1, in orange and in the ring around that square is now dead.
The board after step 3 — 1 of 9 queens placed. Step 4. The khaki region is down to one open square, at row 8, column 3. Every colour holds exactly one queen, so that square is forced. Row 8 and column 3 are now spoken for, along with the squares touching that queen.
Step 5. Red cannot leave column 2 — every one of its open squares (3 open squares) sits there. That column belongs to red, so every square in it owned by another colour is dead: 3 squares in all.
Step 6. From here the board cascades. Keep alternating the region sweep and the line sweep and 4 queens fall out in order without any new idea being needed: indigo has one square left, so its queen takes row 1, column 4; amber has one square left, so its queen takes row 2, column 9; blue has one square left, so its queen takes row 3, column 5; mint has one square left, so its queen takes row 4, column 8. 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 4, column 8.
Step 7. 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.
The board after step 7 — 6 of 9 queens placed. Step 8. Only row 7, column 7 is still open in pale yellow, and since each colour must take a queen, that settles it. Everything else in row 7, in column 7, in pale yellow and in the ring around that square is now dead.
Step 9. The slate region is down to one open square, at row 5, column 6. Every colour holds exactly one queen, so that square is forced. Row 5 and column 6 are now spoken for, along with the squares touching that queen.
Step 10. Only row 6, column 2 is still open in red, and since each colour must take a queen, that settles it. That clears row 6, column 2, the rest of the red region and every square adjacent to it — diagonals included.
The board after step 10 — 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 #216
This is puzzle number 216 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 #216, 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 #216 are: orange (2 squares), khaki (3 squares), amber (4 squares), mint (6 squares), blue (9 squares), indigo (11 squares), red (14 squares), slate (16 squares), pale yellow (16 squares). An even split would hand every color 9 squares, so the orange region is running 7 squares under that average while the pale yellow region is the roomiest area on the grid with 16 squares.
One queen per color, regardless of acreage: that is what turns this uneven split into a solving order. Orange is working with 2 squares while pale yellow has 16 to spare, a gap of 14. Attack the cramped end and the roomy regions tend to resolve themselves.
Look at arrangement as well as area. Orange is the densest region on this grid at 100% of a 1×2 frame; blue is the loosest, occupying only 56% of its 4×4 frame. The loose one reaches into more rows and columns, which is exactly why it usually settles last.
Region by region
Below is every color on #216 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.
Orange: 2 squares across rows 9–9, columns 1–2. It never leaves row 9, so its queen is locked to that row.
Khaki covers 3 squares, spanning 2 rows and 2 columns (rows 8–9, columns 3–4).
Amber occupies 4 squares within rows 1–2, columns 7–9.
Mint: 6 squares across rows 2–4, columns 7–9.
Blue covers 9 squares, spanning 4 rows and 4 columns (rows 1–4, columns 4–7).
Indigo occupies 11 squares within rows 1–4, columns 1–4.
Red: 14 squares across rows 4–8, columns 1–4.
Slate covers 16 squares, spanning 4 rows and 6 columns (rows 3–6, columns 4–9).
Pale yellow occupies 16 squares within rows 7–9, columns 4–9.
Where to start on this board
Begin where the choices are fewest. On this board that means orange, which owns just 2 squares inside a 1×2 window running from row 9 to row 9 and column 1 to column 2. A queen is guaranteed somewhere in there, so every line that window crosses is under pressure from the very first move.
Because orange never leaves row 9, its queen must be in that row — and that instantly settles row 9 for everyone else. Sweep along it and X out every square that is not orange. 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 #216
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 5, 6 and 7 are the narrowest, touched by only 2 colors. Columns 1, 2, 3, 5 and 6 are the tightest columns, with 3 colors.
Those lines matter because a row touched by few colors gives its queen away sooner. If a row meets only 2 colors, then one of those regions has to own it, and every other region is competing for the remaining 8 rows. By contrast row 4 meets 5 colors — the most crowded line here, and the one least likely to resolve early. Spend your attention accordingly.
Working through the middle game
After the first few queens the puzzle becomes bookkeeping. A placed queen wipes its row, its column and every square it touches — as many as eight neighbours — so the space collapses quickly. Record those eliminations on the board instead of carrying them in your head, and the next forced move tends to announce itself.
With nine queens to seat and nine regions competing over 81 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 9x9 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 #216 is rated hard
What earns a board its rating is the shape of its opening. Here that opening offers one single-line region, a 2-square smallest color, a tightest row touched by 2 colors, and a region-size spread of 14. Lopsided grids with flat regions fall quickly; balanced ones like this take more patience.
The scale has nothing to do with maths or luck — every puzzle here is solvable by deduction and has exactly one answer. It measures reasoning depth: how many eliminations must stack up before a placement becomes provable. That depth is what separates a hard board from the rest.
Stuck on #216 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.
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 5 on this board.
As a sanity check rather than a spoiler: the finished solution to #216 puts 3 queens on the outer border and 6 queens in the interior, 1 of them in an actual 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 #216?
Puzzle #216 is rated hard. Its smallest color region holds 2 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 9x9 puzzle #216 have only one solution?
Yes. Every puzzle in the 9x9 collection, including #216, 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 #216?
Start with the orange region — the most constrained color on this board, with 2 squares spanning rows 9–9 and columns 1–2. Narrowing the smallest region first removes the most squares elsewhere on the grid.