9x9 Queens Puzzle #222
Difficulty: medium. 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 #222
What follows is a complete solve of puzzle #222, 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 proof by contradiction.
Techniques this board needs: last square in a region, region confined to one line, region shadow, proof by contradiction.
Show the full walkthrough (10 steps) — contains the solution
Step 1. Only row 3, column 8 is still open in blue, and since each colour must take a queen, that settles it. That clears row 3, column 8, the rest of the blue region and every square adjacent to it — diagonals included.
Step 2. The slate region is down to one open square, at row 5, column 7. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 5 and column 7, the remaining slate squares, and the ring of neighbours around row 5, column 7.
Step 3. Only row 1, column 9 is still open in indigo, and since each colour must take a queen, that settles it. Everything else in row 1, in column 9, in indigo and in the ring around that square is now dead.
The board after step 3 — 3 of 9 queens placed. Step 4. All of the amber region's remaining squares (3 open squares) lie in row 2. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 3 squares come off.
Step 5. Khaki cannot leave row 8 — every one of its open squares (2 open squares) sits there. That row belongs to khaki, so every square on it owned by another colour is dead: 8 squares in all.
Step 6. The orange region is down to one open square, at row 9, column 4. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 9 and column 4, the remaining orange squares, and the ring of neighbours around row 9, column 4.
Step 7. Only row 8, column 6 is still open in khaki, and since each colour must take a queen, that settles it. Everything else in row 8, in column 6, in khaki and in the ring around that square is now dead.
The board after step 7 — 5 of 9 queens placed. Step 8. Pale yellow is down to 3 candidates in rows 6 and 7, columns 2 and 3, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about pale yellow itself.
Step 9. Test row 2, column 5 for amber: place a queen there, run the forced consequences through, and the mint region is left with nowhere to put its queen. The assumption breaks, so the square is eliminated.
Step 10. 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: amber has one square left, so its queen takes row 2, column 1; mint has one square left, so its queen takes row 4, column 2; red has one square left, so its queen takes row 6, column 5; pale yellow has one square left, so its queen takes row 7, 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 7, column 3.
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 #222
Board #222 of the 9x9 bank carries a medium rating. Its 81 squares are shared between nine colored regions, and the solution places nine queens: one per row, one per column, one per region, none of them side by side or corner to corner.
As with every puzzle in this collection, #222 has a single verified solution and needs no guesswork. Each queen follows from something already visible. What the board controls is tempo — how soon the first forced move shows up and how far apart the rest are spaced — and that is a direct consequence of how these colors are cut.
How the colors divide this board
From smallest to largest, the regions on puzzle #222 are: blue (1 square), slate (1 square), orange (5 squares), pale yellow (8 squares), amber (9 squares), mint (14 squares), red (14 squares), khaki (14 squares), indigo (15 squares). An even split would hand every color 9 squares, so the blue region is running 8 squares under that average while the indigo region is the roomiest area on the grid with 15 squares.
That imbalance is the first thing to read, because every region takes exactly one queen regardless of how much space it owns. Blue has only 1 place to put its queen; indigo has 15. The spread between them on this board is 14 squares, and the wider that spread runs, the more it pays to solve from the small end inward.
Shape matters as much as size. The blue region is the most compact color here, filling 100% of the 1×1 box that encloses it, while red is the most scattered at 58% of its 6×4 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
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.
Blue: 1 square across rows 3–3, columns 8–8. It never leaves row 3, so its queen is locked to that row.
Slate covers 1 square, spanning 1 row and 1 column (rows 5–5, columns 7–7). It never leaves row 5, so its queen is locked to that row.
Orange occupies 5 squares within rows 8–9, columns 3–6.
Pale yellow: 8 squares across rows 6–9, columns 1–3.
Amber covers 9 squares, spanning 2 rows and 6 columns (rows 1–2, columns 1–6).
Mint occupies 14 squares within rows 2–7, columns 1–4.
Red: 14 squares across rows 2–7, columns 3–6.
Khaki covers 14 squares, spanning 4 rows and 5 columns (rows 6–9, columns 5–9).
Indigo occupies 15 squares within rows 1–5, columns 5–9.
Where to start on this board
Open on the tightest color. Here that is blue, confined to 1 square between rows 3 and 3 and columns 8 and 8. Its queen has nowhere else to go, which means those 1 row and 1 column carry more constraint than anywhere else on #222.
Because blue never leaves row 3, its queen must be in that row — and that instantly settles row 3 for everyone else. Sweep along it and X out every square that is not blue. 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. Slate, amber and orange 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 #222
A quick way to find the next move is to count how many different colors touch each line. On this board, row 1 is the narrowest, touched by only 2 colors. Column 9 is the tightest column, with 2 colors.
The fewer colors a line touches, the sooner it surrenders its queen. A row meeting just 2 colors has to be claimed by one of them, which pushes every remaining region into the other 8 rows. Row 7, meeting 4 colors, is the opposite case — the busiest line on #222 and the last one you should expect to crack.
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.
The whole middle game reduces to two sweeps. Sweep the nine colors looking for one with a single square left; sweep the nine rows and nine columns looking for the same. Each sweep feeds the next, and switching between them deliberately — rather than drifting — is what separates a fast 9x9 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 #222 is rated medium
Ratings track how generous the opening is. On #222 you get four regions pinned to a single row or column, a smallest color of 1 square, a tightest row crossed by 2 colors, and a 14-square gap between the largest and smallest regions. Those four numbers largely explain the medium label.
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.
A board that feels above its rating is nearly always a board with a missing X. Audit every queen on the grid: full row cleared, full column cleared, all eight touching squares cleared. Diagonals are the common omission, and missing one is far more often the cause of a stall than any genuine difficulty in the puzzle.
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.
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 #222 the place to look for one is around row 1.
Here is a shape check that gives nothing away: when #222 is solved, 3 queens sit on the outer edge of the grid and 6 sit inside it, with 1 queen in a corner. A work-in-progress board that clusters its queens in one quadrant while leaving others bare is usually carrying a mistake.
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 #222?
Puzzle #222 is rated medium. Its smallest color region holds 1 square, its tightest row is touched by 2 colors, and four of its regions are confined to a single row or column, which gives you a forced move early.
Does 9x9 puzzle #222 have only one solution?
Yes. Every puzzle in the 9x9 collection, including #222, 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 #222?
Start with the blue region — the most constrained color on this board, with 1 square spanning rows 3–3 and columns 8–8. Narrowing the smallest region first removes the most squares elsewhere on the grid.