9x9 Queens Puzzle #62
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 #62
What follows is a complete solve of puzzle #62, 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 region shadow.
Techniques this board needs: region confined to one line, last square in a region, region shadow.
Show the full walkthrough (10 steps) — contains the solution
Step 1. Indigo cannot leave row 1 — every one of its open squares (4 open squares) sits there. That row belongs to indigo, so every square on it owned by another colour is dead: 5 squares in all.
Step 2. The amber region is down to one open square, at row 2, column 1. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 2 and column 1, the remaining amber squares, and the ring of neighbours around row 2, column 1.
Step 3. Only row 8, column 2 is still open in khaki, and since each colour must take a queen, that settles it. Everything else in row 8, in column 2, in khaki and in the ring around that square is now dead.
The board after step 3 — 2 of 9 queens placed. Step 4. Wherever blue 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 5. Red cannot leave column 9 — 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: 7 squares in all.
Step 6. All of the mint region's remaining squares (2 open squares) lie in column 8. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 5 squares come off.
Step 7. Only row 9, column 7 is still open in orange, and since each colour must take a queen, that settles it. Everything else in row 9, in column 7, in orange and in the ring around that square is now dead.
The board after step 7 — 3 of 9 queens placed. Step 8. The indigo region is down to one open square, at row 1, column 6. Every colour holds exactly one queen, so that square is forced. Row 1 and column 6 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 (3 open squares) sits there. That column belongs to pale yellow, so every square in it owned by another colour is dead: 3 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 4; mint has one square left, so its queen takes row 4, column 8; red has one square left, so its queen takes row 6, column 9; slate has one square left, so its queen takes row 5, column 3; pale yellow has one square left, so its queen takes row 7, column 5. 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 5.
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 #62
Board #62 of the 9x9 bank carries a hard 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.
There is exactly one way to finish #62, 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 #62 are: red (2 squares), indigo (4 squares), amber (5 squares), khaki (5 squares), blue (8 squares), mint (9 squares), orange (9 squares), slate (16 squares), pale yellow (23 squares). An even split would hand every color 9 squares, so the red region is running 7 squares under that average while the pale yellow region is the roomiest area on the grid with 23 squares.
That imbalance is the first thing to read, because every region takes exactly one queen regardless of how much space it owns. Red has only 2 places to put its queen; pale yellow has 23. The spread between them on this board is 21 squares, and the wider that spread runs, the more it pays to solve from the small end inward.
A region's outline can constrain it more than its size does. Here indigo is the most solid, filling 100% of its 1×4 box, and pale yellow the most diffuse at 47% of its 7×7 box. Solid blocks give clean eliminations; diffuse ones spread across the board and stay open longer.
Region by region
Below is every color on #62 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.
Red occupies 2 squares within rows 5–6, columns 9–9. It sits wholly inside column 9, so its queen must be in that column.
Indigo: 4 squares across rows 1–1, columns 6–9. It never leaves row 1, so its queen is locked to that row.
Amber covers 5 squares, spanning 2 rows and 4 columns (rows 1–2, columns 1–4).
Khaki occupies 5 squares within rows 6–9, columns 1–2.
Blue: 8 squares across rows 1–4, columns 2–5.
Mint covers 9 squares, spanning 3 rows and 4 columns (rows 2–4, columns 6–9).
Orange occupies 9 squares within rows 6–9, columns 7–9.
Slate: 16 squares across rows 3–7, columns 1–4.
Pale yellow covers 23 squares, spanning 7 rows and 7 columns (rows 3–9, columns 2–8).
Where to start on this board
Open on the tightest color. Here that is red, confined to 2 squares between rows 5 and 6 and columns 9 and 9. Its queen has nowhere else to go, which means those 2 rows and 1 column carry more constraint than anywhere else on #62.
Because red stays inside column 9, its queen belongs to that column and no other region may use it. Cross out the rest of column 9 straight away. Any color that was relying on those squares now has a visibly smaller footprint, and that shrinkage is where your second deduction comes from.
Work outward to the other flat regions next. Indigo and amber 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 #62
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, 8 and 9 are the narrowest, touched by only 3 colors. Column 5 is the tightest column, with 2 colors.
The fewer colors a line touches, the sooner it surrenders its queen. A row meeting just 3 colors has to be claimed by one of them, which pushes every remaining region into the other 8 rows. Row 6, meeting 5 colors, is the opposite case — the busiest line on #62 and the last one you should expect to crack.
Working through the middle game
Once two or three queens are down, the board changes character. Each queen removes an entire row, an entire column and the ring of up to eight squares around it, so the grid shrinks faster than most people expect. The habit that pays here is marking rather than remembering: after every placement, cross out the full row, the full column and all eight neighbours before hunting for the next move.
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 #62 is rated hard
What earns a board its rating is the shape of its opening. Here that opening offers two single-line regions, a 2-square smallest color, a tightest row touched by 3 colors, and a region-size spread of 21. Lopsided grids with flat regions fall quickly; balanced ones like this take more patience.
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 #62 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.
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 #62 the place to look for one is around column 5.
Here is a shape check that gives nothing away: when #62 is solved, 4 queens sit on the outer edge of the grid and 5 sit inside it, and no queen lands 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 #62?
Puzzle #62 is rated hard. Its smallest color region holds 2 squares, its tightest row is touched by 3 colors, and two of its regions are confined to a single row or column, which gives you a forced move early.
Does 9x9 puzzle #62 have only one solution?
Yes. Every puzzle in the 9x9 collection, including #62, 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 #62?
Start with the red region — the most constrained color on this board, with 2 squares spanning rows 5–6 and columns 9–9. Narrowing the smallest region first removes the most squares elsewhere on the grid.