11x11 Queens Puzzle #34
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 19-step reasoning is written out below.
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Step-by-step solution for puzzle #34
What follows is a complete solve of puzzle #34, worked the way a person works it rather than the way a computer does. It runs to 19 deductions — 11 queen placements and 8 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: last square in a region, region shadow, region confined to one line, last square in a row.
Show the full walkthrough (15 steps) — contains the solution
Step 1. Only row 1, column 1 is still open in indigo, and since each colour must take a queen, that settles it. That clears row 1, column 1, the rest of the indigo region and every square adjacent to it — diagonals included.
Step 2. The amber region is down to one open square, at row 2, column 9. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 2 and column 9, the remaining amber squares, and the ring of neighbours around row 2, column 9.
Step 3. The blue region has 3 squares left, spread across rows 3 and 4, columns 3 and 4. You do not need to know which of them takes the queen: every one of those options attacks the same 2 squares, so they can be crossed out now.
Step 4. All of the mint region's remaining squares (3 open squares) lie in column 11. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 7 squares come off.
Step 5. Red cannot leave column 10 — 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: 4 squares in all.
The board after step 5 — 2 of 11 queens placed. Step 6. The teal region is down to one open square, at row 11, column 8. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 11 and column 8, the remaining teal squares, and the ring of neighbours around row 11, column 8.
Step 7. Wherever khaki ends up among its 4 squares, the same squares fall within reach of it — 2 squares in total, impossible regardless of how the colour resolves.
Step 8. All of the orange region's remaining squares (2 open squares) lie in row 9. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 7 squares come off.
Step 9. The khaki region has 2 squares left, spread across rows 8 and 10, columns 2 and 3. You do not need to know which of them takes the queen: every one of those options attacks the same 1 square, so they can be crossed out now.
Step 10. All of the sea green region's remaining squares (2 open squares) lie in row 10. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 1 square come off.
The board after step 10 — 3 of 11 queens placed. Step 11. 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: khaki has one square left, so its queen takes row 8, column 3; blue has one square left, so its queen takes row 3, column 4; sea green has one square left, so its queen takes row 10, column 5; orange has one square left, so its queen takes row 9, column 7; row 7 is down to one square, putting a queen on row 7, column 6. 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 6.
Step 12. All of the mint region's remaining squares (2 open squares) lie in column 11. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 1 square come off.
Step 13. Only row 6, column 10 is still open in red, and since each colour must take a queen, that settles it. That clears row 6, column 10, the rest of the red region and every square adjacent to it — diagonals included.
Step 14. The mint region is down to one open square, at row 4, column 11. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 4 and column 11, the remaining mint squares, and the ring of neighbours around row 4, column 11.
Step 15. Only row 5, column 2 is still open in slate, and since each colour must take a queen, that settles it. Everything else in row 5, in column 2, in slate and in the ring around that square is now dead.
The board after step 15 — 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 #34
Board #34 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, #34 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 #34 are: indigo (1 square), amber (2 squares), teal (4 squares), mint (10 squares), red (10 squares), khaki (10 squares), blue (11 squares), sea green (11 squares), orange (14 squares), slate (21 squares), pale yellow (27 squares). An even split would hand every color 11 squares, so the indigo region is running 10 squares under that average while the pale yellow region is the roomiest area on the grid with 27 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 indigo, with 1 square, is under far more pressure than pale yellow with 27. A 26-square gap like this one rewards players who start where the choices are fewest.
Look at arrangement as well as area. Indigo is the densest region on this grid at 100% of a 1×1 frame; blue is the loosest, occupying only 55% of its 4×5 frame. The loose one reaches into more rows and columns, which is exactly why it usually settles last.
Region by region
Here is the full footprint of every color on puzzle #34, smallest first. Reading these spans before you place anything is the quickest way to see which parts of the grid are genuinely contested.
Indigo covers 1 square, spanning 1 row and 1 column (rows 1–1, columns 1–1). It never leaves row 1, so its queen is locked to that row.
Amber occupies 2 squares within rows 1–2, columns 9–9. It sits wholly inside column 9, so its queen must be in that column.
Teal: 4 squares across rows 11–11, columns 8–11. It never leaves row 11, so its queen is locked to that row.
Mint covers 10 squares, spanning 5 rows and 3 columns (rows 1–5, columns 9–11).
Red occupies 10 squares within rows 4–9, columns 9–11.
Khaki: 10 squares across rows 7–11, columns 1–3.
Blue covers 11 squares, spanning 4 rows and 5 columns (rows 1–4, columns 2–6).
Sea green occupies 11 squares within rows 9–11, columns 3–7.
Orange: 14 squares across rows 7–10, columns 6–11.
Slate covers 21 squares, spanning 7 rows and 5 columns (rows 2–8, columns 1–5).
Pale yellow occupies 27 squares within rows 1–8, columns 5–8.
Where to start on this board
Begin where the choices are fewest. On this board that means indigo, which owns just 1 square inside a 1×1 window running from row 1 to row 1 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 indigo never leaves row 1, its queen must be in that row — and that instantly settles row 1 for everyone else. Sweep along it and X out every square that is not indigo. 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. Teal 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 #34
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 6, 10 and 11 are the narrowest, touched by only 3 colors. Columns 1, 2, 4, 7 and 8 are the tightest columns, with 3 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 10 rows. Row 8, meeting 5 colors, is the opposite case — the busiest line on #34 and the last one you should expect to crack.
Working through the middle game
The middle of #34 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.
The whole middle game reduces to two sweeps. Sweep the eleven colors looking for one with a single square left; sweep the eleven rows and eleven columns looking for the same. Each sweep feeds the next, and switching between them deliberately — rather than drifting — is what separates a fast 11x11 solve from a stalled one.
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 #34 is rated easy
The rating reflects how much the board concedes up front. Puzzle #34 has four regions confined to a single row or column, its smallest color holds 1 square, its tightest row meets just 3 colors, and the gap between its largest and smallest regions is 26 squares. Flat, lopsided boards open quickly; even, sprawling ones make you earn the first placement.
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 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 #34, start hunting for it near row 6.
Here is a shape check that gives nothing away: when #34 is solved, 3 queens sit on the outer edge of the grid and 8 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 11x11 Queens puzzle #34?
Puzzle #34 is rated easy. Its smallest color region holds 1 square, its tightest row is touched by 3 colors, and four of its regions are confined to a single row or column, which gives you a forced move early.
Does 11x11 puzzle #34 have only one solution?
Yes. Every puzzle in the 11x11 collection, including #34, 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 #34?
Start with the indigo region — the most constrained color on this board, with 1 square spanning rows 1–1 and columns 1–1. Narrowing the smallest region first removes the most squares elsewhere on the grid.