11x11 Queens Puzzle #26
Difficulty: hard. 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 21-step reasoning is written out below.
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Step-by-step solution for puzzle #26
What follows is a complete solve of puzzle #26, worked the way a person works it rather than the way a computer does. It runs to 21 deductions — 11 queen placements and 10 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 pairing argument on columns.
Techniques this board needs: last square in a region, region shadow, pairing argument on columns, region confined to one line, pairing argument on rows.
Show the full walkthrough (14 steps) — contains the solution
Step 1. Only row 11, column 11 is still open in teal, and since each colour must take a queen, that settles it. That clears row 11, column 11, the rest of the teal region and every square adjacent to it — diagonals included.
Step 2. Indigo is down to 4 candidates in rows 1–3, columns 9 and 10, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about indigo itself.
Step 3. The slate region has 5 squares left, spread across rows 2–5, columns 1 and 2. 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 4. 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 5. Indigo and khaki are now boxed into columns 9 and 10 and nothing else. That is 2 colours needing 2 columns, so they fill those columns between them — which locks every remaining colour out and removes 8 squares at once.
The board after step 5 — 1 of 11 queens placed. Step 6. All of the orange region's remaining squares (4 open squares) lie in column 8. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 6 squares come off.
Step 7. Only row 4, column 7 is still open in mint, and since each colour must take a queen, that settles it. Everything else in row 4, in column 7, in mint and in the ring around that square is now dead.
Step 8. Blue is down to 3 candidates in rows 1 and 3, columns 5 and 6, and they overlap enough to cover 2 squares elsewhere. Cross those out without deciding anything about blue itself.
Step 9. Indigo, amber, and blue are now boxed into rows 1–3 and nothing else. That is 3 colours needing 3 rows, so they fill those rows between them — which locks every remaining colour out and removes 3 squares at once.
The board after step 9 — 2 of 11 queens placed. Step 10. The slate region is down to one open square, at row 5, column 1. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 5 and column 1, the remaining slate squares, and the ring of neighbours around row 5, column 1.
Step 11. Red cannot leave row 6 — every one of its open squares (3 open squares) sits there. That row belongs to red, so every square on it owned by another colour is dead: 4 squares in all.
Step 12. All of the khaki region's remaining squares (2 open squares) lie in row 8. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 6 squares come off.
Step 13. Orange cannot leave column 8 — every one of its open squares (2 open squares) sits there. That column belongs to orange, so every square in it owned by another colour is dead: 1 square in all.
Step 14. From here the board cascades. Keep alternating the region sweep and the line sweep and 8 queens fall out in order without any new idea being needed: khaki has one square left, so its queen takes row 8, column 10; indigo has one square left, so its queen takes row 1, column 9; blue has one square left, so its queen takes row 3, column 5; amber has one square left, so its queen takes row 2, column 3; red has one square left, so its queen takes row 6, column 4; pale yellow has one square left, so its queen takes row 7, column 6; orange has one square left, so its queen takes row 9, column 8; sea green has one square left, so its queen takes row 10, column 2. 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 10, column 2.
The board after step 14 — 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 #26
Board #26 of the 11x11 bank carries a hard 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, #26 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 #26 are: teal (1 square), slate (5 squares), indigo (7 squares), khaki (9 squares), blue (11 squares), mint (11 squares), red (11 squares), amber (12 squares), orange (15 squares), pale yellow (16 squares), sea green (23 squares). An even split would hand every color 11 squares, so the teal region is running 10 squares under that average while the sea green region is the roomiest area on the grid with 23 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 teal, with 1 square, is under far more pressure than sea green with 23. A 22-square gap like this one rewards players who start where the choices are fewest.
Look at arrangement as well as area. Teal is the densest region on this grid at 100% of a 1×1 frame; amber is the loosest, occupying only 50% of its 4×6 frame. The loose one reaches into more rows and columns, which is exactly why it usually settles last.
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.
Teal occupies 1 square within rows 11–11, columns 11–11. It never leaves row 11, so its queen is locked to that row.
Slate: 5 squares across rows 2–5, columns 1–2.
Indigo covers 7 squares, spanning 3 rows and 3 columns (rows 1–3, columns 9–11).
Khaki occupies 9 squares within rows 4–8, columns 9–11.
Blue: 11 squares across rows 1–5, columns 5–7.
Mint covers 11 squares, spanning 5 rows and 4 columns (rows 1–5, columns 7–10).
Red occupies 11 squares within rows 4–6, columns 1–5.
Amber: 12 squares across rows 1–4, columns 1–6.
Orange covers 15 squares, spanning 6 rows and 4 columns (rows 6–11, columns 8–11).
Pale yellow occupies 16 squares within rows 6–10, columns 4–8.
Sea green: 23 squares across rows 7–11, columns 1–8.
Where to start on this board
Begin where the choices are fewest. On this board that means teal, which owns just 1 square inside a 1×1 window running from row 11 to row 11 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 teal never leaves row 11, its queen must be in that row — and that instantly settles row 11 for everyone else. Sweep along it and X out every square that is not teal. 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.
No region here is pinned to a shallow band of rows, so turn the same idea sideways: slate spans only two columns. Two narrow regions sharing the same two columns take one column each and lock everyone else out of both, which is usually enough to crack a board that offers no free opening.
The tightest lines on puzzle #26
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 9, 10 and 11 are the narrowest, touched by only 3 colors. Column 3 is the tightest column, 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 4, meeting 6 colors, is the opposite case — the busiest line on #26 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.
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 #26 is rated hard
Ratings track how generous the opening is. On #26 you get two regions pinned to a single row or column, a smallest color of 1 square, a tightest row crossed by 3 colors, and a 22-square gap between the largest and smallest regions. Those four numbers largely explain the hard 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 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 #26, start hunting for it near row 9.
Here is a shape check that gives nothing away: when #26 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 #26?
Puzzle #26 is rated hard. Its smallest color region holds 1 square, 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 11x11 puzzle #26 have only one solution?
Yes. Every puzzle in the 11x11 collection, including #26, 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 #26?
Start with the teal region — the most constrained color on this board, with 1 square spanning rows 11–11 and columns 11–11. Narrowing the smallest region first removes the most squares elsewhere on the grid.