11x11 Queens Puzzle #97
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 #97
What follows is a complete solve of puzzle #97, 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: last square in a region, region confined to one line, pairing argument on rows, pairing argument on columns, last square in a row, region shadow.
Show the full walkthrough (11 steps) — contains the solution
Step 1. Only row 10, column 7 is still open in sea green, and since each colour must take a queen, that settles it. That clears row 10, column 7, the rest of the sea green region and every square adjacent to it — diagonals included.
Step 2. All of the indigo region's remaining squares (2 open squares) lie in column 9. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 12 squares come off.
Step 3. Amber cannot leave column 11 — every one of its open squares (2 open squares) sits there. That column belongs to amber, so every square in it owned by another colour is dead: 8 squares in all.
Step 4. All of the pale yellow region's remaining squares (2 open squares) lie in column 4. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 12 squares come off.
The board after step 4 — 1 of 11 queens placed. Step 5. Indigo and amber are now boxed into rows 1 and 2 and nothing else. That is 2 colours needing 2 rows, so they fill those rows between them — which locks every remaining colour out and removes 10 squares at once.
Step 6. Here is the pairing argument. The red and teal regions have no open squares outside columns 1 and 2 — 2 colours confined to 2 columns. Between them they must take one column each, in some order, so every other colour is shut out of all of them: 7 squares come off in one stroke.
Step 7. Mint and slate are now boxed into columns 3 and 5 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 4 squares at once.
The board after step 7 — 1 of 11 queens placed. Step 8. 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: 4 squares come off.
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: pale yellow has one square left, so its queen takes row 7, column 4; slate has one square left, so its queen takes row 5, column 3; red has one square left, so its queen takes row 6, column 1; teal has one square left, so its queen takes row 11, column 2; row 9 is down to one square, putting a queen on 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 10. Blue is down to 3 candidates in rows 3 and 4, columns 6 and 8, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about blue itself.
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: mint has one square left, so its queen takes row 4, column 5; blue has one square left, so its queen takes row 3, column 8; indigo has one square left, so its queen takes row 1, column 9; amber has one square left, so its queen takes row 2, column 11; khaki has one square left, so its queen takes row 8, 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 8, column 6.
The board after step 11 — 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 #97
Puzzle #97 is one of the easy-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, #97 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 #97 are: sea green (1 square), indigo (2 squares), pale yellow (2 squares), amber (4 squares), red (6 squares), teal (6 squares), mint (15 squares), slate (16 squares), khaki (20 squares), blue (24 squares), orange (25 squares). An even split would hand every color 11 squares, so the sea green region is running 10 squares under that average while the orange region is the roomiest area on the grid with 25 squares.
Every color takes one queen and one only, whatever its size — which is why the 24 square difference between sea green and orange is worth noting before you touch the grid. The cramped colors resolve first and hand you information; the roomy ones absorb whatever is left over at the end.
Shape matters as much as size. The indigo region is the most compact color here, filling 100% of the 2×1 box that encloses it, while slate is the most scattered at 40% of its 8×5 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
Here is the full footprint of every color on puzzle #97, smallest first. Reading these spans before you place anything is the quickest way to see which parts of the grid are genuinely contested.
Sea green covers 1 square, spanning 1 row and 1 column (rows 10–10, columns 7–7). It never leaves row 10, so its queen is locked to that row.
Indigo occupies 2 squares within rows 1–2, columns 9–9. It sits wholly inside column 9, so its queen must be in that column.
Pale yellow: 2 squares across rows 7–8, columns 4–4. It sits wholly inside column 4, so its queen must be in that column.
Amber covers 4 squares, spanning 2 rows and 2 columns (rows 1–2, columns 10–11).
Red occupies 6 squares within rows 5–8, columns 1–2.
Teal: 6 squares across rows 9–11, columns 1–3.
Mint covers 15 squares, spanning 5 rows and 5 columns (rows 1–5, columns 2–6).
Slate occupies 16 squares within rows 1–8, columns 1–5.
Khaki: 20 squares across rows 7–11, columns 2–8.
Blue covers 24 squares, spanning 7 rows and 6 columns (rows 1–7, columns 6–11).
Orange occupies 25 squares within rows 4–11, columns 8–11.
Where to start on this board
Sea green is the natural opening on #97: it is the smallest region on the grid at 1 square, boxed into rows 10–10 and columns 7–7. Since one of those squares must hold a queen, that block of 1 row and 1 column is the most contested part of the board.
Because sea green never leaves row 10, its queen must be in that row — and that instantly settles row 10 for everyone else. Sweep along it and X out every square that is not sea green. 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. Indigo, amber and pale yellow 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 #97
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 3, 9 and 11 are the narrowest, touched by only 3 colors. Columns 1, 5, 6, 7, 8, 9, 10 and 11 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 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 7 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
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.
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 #97 is rated easy
The rating reflects how much the board concedes up front. Puzzle #97 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 24 squares. Flat, lopsided boards open quickly; even, sprawling ones make you earn the first placement.
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.
There is one technique that repays study at every grid size. Two regions restricted to the same two rows must occupy one row apiece, which excludes all other regions from those rows entirely; the identical logic applies to columns and to larger matched sets. It converts slow boards into fast ones, and the likeliest place to find it on #97 is row 3.
As a sanity check rather than a spoiler: the finished solution to #97 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 #97?
Puzzle #97 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 #97 have only one solution?
Yes. Every puzzle in the 11x11 collection, including #97, 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 #97?
Start with the sea green region — the most constrained color on this board, with 1 square spanning rows 10–10 and columns 7–7. Narrowing the smallest region first removes the most squares elsewhere on the grid.