11x11 Queens Puzzle #62
Difficulty: easy. Place 11 queens on this 11x11 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 17-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 17 deductions — 11 queen placements and 6 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 line confined to one region.
Techniques this board needs: last square in a region, region confined to one line, region shadow, line confined to one region, last square in a row.
Show the full walkthrough (9 steps) — contains the solution
Step 1. The board opens by cascading. Each of these placements is forced the moment the one before it is marked, so the whole run is really a single sweep repeated: slate has one square left, so its queen takes row 5, column 11; pale yellow has one square left, so its queen takes row 7, column 3; teal has one square left, so its queen takes row 11, column 10; sea green has one square left, so its queen takes row 10, column 8; khaki has one square left, so its queen takes row 8, column 9. 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 8, column 9.
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: 6 squares come off.
Step 3. 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.
The board after step 3 — 5 of 11 queens placed. Step 4. Blue is down to 3 candidates in rows 2 and 3, columns 1 and 2, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about blue itself.
Step 5. Mint cannot leave column 7 — every one of its open squares (2 open squares) sits there. That column belongs to mint, so every square in it owned by another colour is dead: 4 squares in all.
Step 6. 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. Cross out the whole of row 1 and column 6, the remaining indigo squares, and the ring of neighbours around row 1, column 6.
The board after step 6 — 6 of 11 queens placed. Step 7. Amber is down to 2 candidates in rows 2 and 3, columns 4 and 5, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about amber itself.
Step 8. Every open square left in row 9 (4 open squares) belongs to the orange region. Since that row must contain a queen, orange is the colour that supplies it — so orange squares anywhere else on the board are out, 1 square in all.
Step 9. 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: row 6 is down to one square, putting a queen on row 6, column 5; amber has one square left, so its queen takes row 2, column 4; blue has one square left, so its queen takes row 3, column 2; mint has one square left, so its queen takes row 4, column 7; orange has one square left, so its queen takes row 9, 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 9, column 1.
The board after step 9 — 11 of 11 queens placed.
That completes the board: 11 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 11x11 Queens puzzle #62
Board #62 of the 11x11 bank carries a easy rating. Its 121 squares are shared between eleven colored regions, and the solution places eleven 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, #62 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 #62 are: slate (1 square), pale yellow (1 square), indigo (5 squares), teal (5 squares), amber (6 squares), blue (8 squares), khaki (11 squares), sea green (11 squares), orange (16 squares), red (27 squares), mint (30 squares). An even split would hand every color 11 squares, so the slate region is running 10 squares under that average while the mint region is the roomiest area on the grid with 30 squares.
Why does the split matter? Because a region's square count has no bearing on how many queens it gets — the answer is always one. So slate, with 1 square, is under far more pressure than mint with 30. A 29-square gap like this one rewards players who start where the choices are fewest.
Square count is only half the story — how a color is arranged counts too. Slate is the tidiest shape on #62, packing 100% of its 1×1 bounding box, whereas red straggles across its 8×7 box at just 48%. Tidy blocks are easy to work around; scattered ones touch more lines and resist resolution.
Region by region
Here is the full footprint of every color on puzzle #62, smallest first. Reading these spans before you place anything is the quickest way to see which parts of the grid are genuinely contested.
Slate occupies 1 square within rows 5–5, columns 11–11. It never leaves row 5, so its queen is locked to that row.
Pale yellow: 1 square across rows 7–7, columns 3–3. It never leaves row 7, so its queen is locked to that row.
Indigo covers 5 squares, spanning 3 rows and 3 columns (rows 1–3, columns 6–8).
Teal occupies 5 squares within rows 8–11, columns 10–11.
Amber: 6 squares across rows 1–3, columns 4–6.
Blue covers 8 squares, spanning 3 rows and 3 columns (rows 1–3, columns 1–3).
Khaki occupies 11 squares within rows 7–10, columns 7–11.
Sea green: 11 squares across rows 10–11, columns 2–9.
Orange covers 16 squares, spanning 6 rows and 5 columns (rows 6–11, columns 1–5).
Red occupies 27 squares within rows 3–10, columns 1–7.
Mint: 30 squares across rows 1–8, columns 6–11.
Where to start on this board
Begin where the choices are fewest. On this board that means slate, which owns just 1 square inside a 1×1 window running from row 5 to row 5 and column 11 to column 11. A queen is guaranteed somewhere in there, so every line that window crosses is under pressure from the very first move.
Because slate never leaves row 5, its queen must be in that row — and that instantly settles row 5 for everyone else. Sweep along it and X out every square that is not slate. 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. Pale yellow and sea green 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, row 4 is the narrowest, touched by only 2 colors. Columns 1, 9 and 10 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 10 rows. By contrast row 10 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
Past the opening, treat this as an elimination exercise rather than a placement exercise. Each queen takes out a row, a column and its eight neighbours, and the value of a move is measured by how much it removes. Cross everything out as you go and let the board do the remembering.
Keep alternating between two views of the board. In the region view you ask which of the eleven colors is down to one open square. In the line view you ask the same of each row and column. Both produce forced queens, and each placement refreshes the other view, so cycling between them deliberately is how a 11x11 board unwinds.
The trap on a board like this is placing a queen that is merely plausible. Every placement should be traceable to an elimination you can point at. If you cannot name the rule that forced it, you are guessing — and on a single-solution grid a guess costs more to unwind than the deduction would have taken to find.
Why puzzle #62 is rated easy
The rating reflects how much the board concedes up front. Puzzle #62 has four regions confined to a single row or column, its smallest color holds 1 square, its tightest row meets just 2 colors, and the gap between its largest and smallest regions is 29 squares. Flat, lopsided boards open quickly; even, sprawling ones make you earn the first placement.
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.
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 11x11
At 11x11 you are managing 121 squares, and holding the whole board in your head will not work. Split it into quadrants and solve locally. Most useful deductions on a grid this large are regional — a color pinched between two placed queens, or a band of rows that two regions must share. Trust the marks on the board over your memory.
Learn the pairing argument and you will use it on every board, this one included. If two colors can only sit inside the same two rows, between them they consume both rows and every other color is shut out. It generalises to any matching count — three colors across three rows, four across four. On #62, start hunting for it near row 4.
As a sanity check rather than a spoiler: the finished solution to #62 puts 4 queens on the outer border and 7 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 11x11 Queens puzzle #62?
Puzzle #62 is rated easy. 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 11x11 puzzle #62 have only one solution?
Yes. Every puzzle in the 11x11 collection, including #62, has been verified to have exactly one valid arrangement of eleven 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 slate region — the most constrained color on this board, with 1 square spanning rows 5–5 and columns 11–11. Narrowing the smallest region first removes the most squares elsewhere on the grid.