11x11 Queens Puzzle #69
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 19-step reasoning is written out below.
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Step-by-step solution for puzzle #69
What follows is a complete solve of puzzle #69, 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 pairing argument on columns.
Techniques this board needs: region shadow, pairing argument on rows, line confined to one region, region confined to one line, pairing argument on columns, last square in a row, last square in a column, last square in a region.
Show the full walkthrough (10 steps) — contains the solution
Step 1. Wherever mint ends up among its 5 squares, the same squares fall within reach of it — 2 squares in total, impossible regardless of how the colour resolves.
Step 2. Here is the pairing argument. The indigo and amber regions have no open squares outside rows 1 and 2 — 2 colours confined to 2 rows. Between them they must take one row each, in some order, so every other colour is shut out of all of them: 10 squares come off in one stroke.
Step 3. The mint region has 3 squares left, spread across rows 3 and 4, columns 6 and 7. 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.
The board after step 3 — 0 of 11 queens placed. Step 4. Every open square left in column 1 (9 open squares) belongs to the khaki region. Since that column must contain a queen, khaki is the colour that supplies it — so khaki squares anywhere else on the board are out, 12 squares in all.
Step 5. Blue, mint, and slate are now boxed into rows 3–5 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 12 squares at once.
Step 6. All of the red region's remaining squares (4 open squares) lie in row 6. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 6 squares come off.
Step 7. Slate and orange are now boxed into columns 10 and 11 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 7 — 0 of 11 queens placed. Step 8. From here the board cascades. Keep alternating the region sweep and the line sweep and 7 queens fall out in order without any new idea being needed: row 2 is down to one square, putting a queen on row 2, column 4; column 2 is down to one square, putting a queen on row 3, column 2; mint has one square left, so its queen takes row 4, column 7; slate has one square left, so its queen takes row 5, column 11; red has one square left, so its queen takes row 6, column 9; indigo has one square left, so its queen takes row 1, column 8; orange has one square left, so its queen takes row 9, column 10. 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 10.
Step 9. The pale yellow region has 3 squares left, spread across rows 7 and 8, columns 3, 5, and 6. 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 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: sea green has one square left, so its queen takes row 10, column 6; teal has one square left, so its queen takes row 11, column 3; pale yellow has one square left, so its queen takes row 7, column 5; khaki has one square left, so its queen takes row 8, 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 8, column 1.
The board after step 10 — 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 #69
Puzzle #69 is one of the hard-rated boards in the 11x11 set. Eleven colors divide its 121 squares, and you win by placing eleven queens so that each row, each column and each color holds exactly one, with no two queens adjacent in any direction.
As with every puzzle in this collection, #69 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 #69 are: amber (5 squares), mint (5 squares), indigo (6 squares), slate (6 squares), teal (6 squares), orange (7 squares), blue (14 squares), red (15 squares), pale yellow (15 squares), khaki (21 squares), sea green (21 squares). An even split would hand every color 11 squares, so the amber region is running 6 squares under that average while the sea green region is the roomiest area on the grid with 21 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 amber, with 5 squares, is under far more pressure than sea green with 21. A 16-square gap like this one rewards players who start where the choices are fewest.
Shape matters as much as size. The slate region is the most compact color here, filling 75% of the 4×2 box that encloses it, while pale yellow is the most scattered at 50% of its 5×6 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
Each region's exact extent on this grid is listed below, starting with the most constrained. Knowing which lines a color can and cannot reach is most of the work on a hard board.
Amber: 5 squares across rows 1–2, columns 2–5.
Mint covers 5 squares, spanning 4 rows and 2 columns (rows 1–4, columns 6–7).
Indigo occupies 6 squares within rows 1–2, columns 7–11.
Slate: 6 squares across rows 2–5, columns 10–11.
Teal covers 6 squares, spanning 2 rows and 4 columns (rows 10–11, columns 3–6).
Orange occupies 7 squares within rows 7–11, columns 10–11.
Blue: 14 squares across rows 1–5, columns 1–5.
Red covers 15 squares, spanning 5 rows and 5 columns (rows 2–6, columns 7–11).
Pale yellow occupies 15 squares within rows 4–8, columns 3–8.
Khaki: 21 squares across rows 3–11, columns 1–4.
Sea green covers 21 squares, spanning 5 rows and 6 columns (rows 7–11, columns 5–10).
Where to start on this board
Amber is the natural opening on #69: it is the smallest region on the grid at 5 squares, boxed into rows 1–2 and columns 2–5. Since one of those squares must hold a queen, that block of 2 rows and 4 columns is the most contested part of the board.
Amber spans 2 rows, so it stays open for now — but it is still the shortest list on the board at 5 squares. Work through those squares first and mark the ones that would leave another region homeless. That pruning is what makes the rest of the grid legible.
Work outward to the other flat regions next. Indigo and teal 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 #69
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 6 and 9 are the narrowest, touched by only 3 colors. Column 1 is the tightest column, with 2 colors.
Those lines matter because a row touched by few colors gives its queen away sooner. If a row meets only 3 colors, then one of those regions has to own it, and every other region is competing for the remaining 10 rows. By contrast row 4 meets 6 colors — the most crowded line here, and the one least likely to resolve early. Spend your attention accordingly.
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.
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 #69 is rated hard
The hard label comes out of four measurable things about #69: it has no region locked to one row or column, its smallest color spans 5 squares, its least crowded row meets 3 colors, and its largest and smallest regions differ by 16. Boards that score tight on those measures give up their first queen fast.
Nothing about the rating involves computation or chance. Each grid has a single solution reachable by pure logic; the rating simply measures how far ahead you have to reason. Easy boards resolve a queen every step or two, while hard ones can ask you to carry three unfinished lines of thought before any of them pays off.
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 #69, start hunting for it near column 1.
As a sanity check rather than a spoiler: the finished solution to #69 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 #69?
Puzzle #69 is rated hard. Its smallest color region holds 5 squares, its tightest row is touched by 3 colors, and no region is confined to a single row or column, so the opening move takes some hunting.
Does 11x11 puzzle #69 have only one solution?
Yes. Every puzzle in the 11x11 collection, including #69, 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 #69?
Start with the amber region — the most constrained color on this board, with 5 squares spanning rows 1–2 and columns 2–5. Narrowing the smallest region first removes the most squares elsewhere on the grid.