11x11 Queens Puzzle #116
Difficulty: medium. 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 18-step reasoning is written out below.
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Step-by-step solution for puzzle #116
What follows is a complete solve of puzzle #116, worked the way a person works it rather than the way a computer does. It runs to 18 deductions — 11 queen placements and 7 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.
Show the full walkthrough (13 steps) — contains the solution
Step 1. Only row 1, column 11 is still open in indigo, and since each colour must take a queen, that settles it. That clears row 1, column 11, the rest of the indigo region and every square adjacent to it — diagonals included.
Step 2. Amber is down to 2 candidates in rows 2 and 3, columns 9 and 10, and they overlap enough to cover 3 squares elsewhere. Cross those out without deciding anything about amber itself.
Step 3. Only row 4, column 8 is still open in mint, and since each colour must take a queen, that settles it. Everything else in row 4, in column 8, in mint and in the ring around that square is now dead.
Step 4. The slate region is down to one open square, at row 5, column 10. Every colour holds exactly one queen, so that square is forced. Row 5 and column 10 are now spoken for, along with the squares touching that queen.
The board after step 4 — 3 of 11 queens placed. Step 5. Only row 2, column 9 is still open in amber, and since each colour must take a queen, that settles it. That clears row 2, column 9, the rest of the amber region and every square adjacent to it — diagonals included.
Step 6. All of the blue region's remaining squares (5 open squares) lie in row 3. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 1 square come off.
Step 7. Red cannot leave row 6 — every one of its open squares (2 open squares) sits there. That row belongs to red, so every square on it owned by another colour is dead: 7 squares in all.
Step 8. Pale yellow is down to 2 candidates in rows 7 and 8, columns 2 and 3, and they overlap enough to cover 4 squares elsewhere. Cross those out without deciding anything about pale yellow itself.
Step 9. Only row 6, column 1 is still open in red, and since each colour must take a queen, that settles it. That clears row 6, column 1, the rest of the red region and every square adjacent to it — diagonals included.
The board after step 9 — 5 of 11 queens placed. Step 10. All of the khaki region's remaining squares (3 open squares) lie in column 7. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 3 squares come off.
Step 11. Orange is down to 2 candidates in rows 9 and 10, columns 2 and 3, and they overlap enough to cover 3 squares elsewhere. Cross those out without deciding anything about orange itself.
Step 12. All of the teal region's remaining squares (2 open squares) lie in row 11. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 4 squares come off.
Step 13. From here the board cascades. Keep alternating the region sweep and the line sweep and 6 queens fall out in order without any new idea being needed: orange has one square left, so its queen takes row 9, column 2; pale yellow has one square left, so its queen takes row 7, column 3; khaki has one square left, so its queen takes row 8, column 7; teal has one square left, so its queen takes row 11, column 4; sea green has one square left, so its queen takes row 10, column 6; blue has one square left, so its queen takes row 3, column 5. 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 3, column 5.
The board after step 13 — 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 #116
This is puzzle number 116 in the 11x11 collection, rated medium. The grid holds 121 squares split between eleven colored regions, and a finished board carries eleven queens — one in every row, one in every column, one in every color, and never two of them touching, diagonals included.
Puzzle #116 has been checked to admit exactly one arrangement of queens, and every step toward it is deducible from what is already on the board. There is no point at which you are expected to pick a square and hope. The only thing that differs between boards is how quickly the first certainty surfaces, and that depends entirely on the shapes the colors happen to take here.
How the colors divide this board
From smallest to largest, the regions on puzzle #116 are: indigo (1 square), mint (4 squares), teal (4 squares), red (5 squares), pale yellow (8 squares), orange (8 squares), amber (9 squares), slate (9 squares), khaki (14 squares), blue (27 squares), sea green (32 squares). An even split would hand every color 11 squares, so the indigo region is running 10 squares under that average while the sea green region is the roomiest area on the grid with 32 squares.
Every color takes one queen and one only, whatever its size — which is why the 31 square difference between indigo and sea green 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 1×1 box that encloses it, while pale yellow is the most scattered at 53% of its 5×3 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 medium board.
Indigo occupies 1 square within rows 1–1, columns 11–11. It never leaves row 1, so its queen is locked to that row.
Mint: 4 squares across rows 3–4, columns 8–9.
Teal covers 4 squares, spanning 2 rows and 3 columns (rows 10–11, columns 2–4).
Red occupies 5 squares within rows 3–6, columns 1–2.
Pale yellow: 8 squares across rows 4–8, columns 1–3.
Orange covers 8 squares, spanning 4 rows and 3 columns (rows 8–11, columns 1–3).
Amber occupies 9 squares within rows 1–3, columns 7–11.
Slate: 9 squares across rows 4–7, columns 8–11.
Khaki covers 14 squares, spanning 4 rows and 5 columns (rows 6–9, columns 7–11).
Blue occupies 27 squares within rows 1–5, columns 1–8.
Sea green: 32 squares across rows 5–11, columns 4–11.
Where to start on this board
Open on the tightest color. Here that is indigo, confined to 1 square between rows 1 and 1 and columns 11 and 11. Its queen has nowhere else to go, which means those 1 row and 1 column carry more constraint than anywhere else on #116.
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. Mint 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 #116
A quick way to find the next move is to count how many different colors touch each line. On this board, row 2 is the narrowest, touched by only 2 colors. Columns 5 and 6 are the tightest columns, with 2 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 6 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
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.
With eleven queens to seat and eleven regions competing over 121 squares, keep two questions in rotation. Does any region now have exactly one open square left? That queen is forced. Does any row or column now have exactly one open square left? That queen is forced too. Alternating between the region view and the row-and-column view is what keeps a solve moving, and it is the clearest difference between players who finish 11x11 boards quickly and players who stall halfway.
Say the reason out loud: "this region has one square left", "this column has one square left". If no such sentence is available, the eliminating is not finished. One more pass of X marks is almost always quicker than committing to a placement you cannot defend.
Why puzzle #116 is rated medium
The medium label comes out of four measurable things about #116: two of its regions are locked to one row or column, its smallest color spans 1 square, its least crowded row meets 2 colors, and its largest and smallest regions differ by 31. Boards that score tight on those measures give up their first queen fast.
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.
When a board plays tougher than its label, look for a missed mark before you look for a clever deduction. Walk back over every queen you have placed and confirm the full row, the full column and all eight surrounding squares are crossed out. The diagonal neighbours are the ones players skip, and a single skipped diagonal will hide the next forced move indefinitely.
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 #116 is row 2.
As a sanity check rather than a spoiler: the finished solution to #116 puts 3 queens on the outer border and 8 queens in the interior, 1 of them in an actual 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 #116?
Puzzle #116 is rated medium. Its smallest color region holds 1 square, its tightest row is touched by 2 colors, and two of its regions are confined to a single row or column, which gives you a forced move early.
Does 11x11 puzzle #116 have only one solution?
Yes. Every puzzle in the 11x11 collection, including #116, 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 #116?
Start with the indigo region — the most constrained color on this board, with 1 square spanning rows 1–1 and columns 11–11. Narrowing the smallest region first removes the most squares elsewhere on the grid.