11x11 Queens Puzzle #114
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 #114
What follows is a complete solve of puzzle #114, 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 pairing argument on rows.
Techniques this board needs: last square in a region, region shadow, pairing argument on rows, line confined to one region, last square in a column, region confined to one line.
Show the full walkthrough (14 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. The teal region is down to one open square, at row 11, column 1. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 11 and column 1, the remaining teal squares, and the ring of neighbours around row 11, column 1.
Step 3. Only row 10, column 7 is still open in sea green, and since each colour must take a queen, that settles it. Everything else in row 10, in column 7, in sea green and in the ring around that square is now dead.
Step 4. Wherever amber ends up among its 4 squares, the same squares fall within reach of it — 1 square in total, impossible regardless of how the colour resolves.
Step 5. Blue 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 blue itself.
The board after step 5 — 3 of 11 queens placed. Step 6. The orange region has 2 squares left, spread across rows 8 and 9, columns 5 and 6. You do not need to know which of them takes the queen: every one of those options attacks the same 3 squares, so they can be crossed out now.
Step 7. Amber and blue are now boxed into rows 2 and 3 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 6 squares at once.
Step 8. Mint is down to 3 candidates in rows 4 and 5, columns 2 and 3, and they overlap enough to cover 2 squares elsewhere. Cross those out without deciding anything about mint itself.
Step 9. Column 4 has only pale yellow squares left (4 open squares). The column needs a queen and only pale yellow can provide one, which pins that colour to this column and kills its squares elsewhere: 12 squares.
The board after step 9 — 3 of 11 queens placed. Step 10. 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: column 2 is down to one square, putting a queen on row 4, column 2; column 3 is down to one square, putting a queen on row 2, column 3; blue has one square left, so its queen takes row 3, column 10; column 5 is down to one square, putting a queen on row 9, column 5; column 6 is down to one square, putting a queen on row 5, 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 5, column 6.
Step 11. Red cannot leave column 9 — every one of its open squares (2 open squares) sits there. That column belongs to red, so every square in it owned by another colour is dead: 2 squares in all.
Step 12. The khaki region is down to one open square, at row 8, column 8. Every colour holds exactly one queen, so that square is forced. Row 8 and column 8 are now spoken for, along with the squares touching that queen.
Step 13. Only row 6, column 9 is still open in red, and since each colour must take a queen, that settles it. That clears row 6, column 9, the rest of the red region and every square adjacent to it — diagonals included.
Step 14. The pale yellow region is down to one open square, at row 7, column 4. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 7 and column 4, the remaining pale yellow squares, and the ring of neighbours around row 7, column 4.
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 #114
Board #114 of the 11x11 bank carries a medium 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, #114 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 #114 are: indigo (1 square), teal (1 square), sea green (3 squares), amber (8 squares), blue (12 squares), slate (13 squares), mint (14 squares), red (14 squares), khaki (15 squares), orange (18 squares), pale yellow (22 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 22 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 22. A 21-square gap like this one rewards players who start where the choices are fewest.
A region's outline can constrain it more than its size does. Here indigo is the most solid, filling 100% of its 1×1 box, and slate the most diffuse at 43% of its 6×5 box. Solid blocks give clean eliminations; diffuse ones spread across the board and stay open longer.
Region by region
Below is every color on #114 with its exact reach, smallest region first. It is worth a slow read: the spans reveal which rows and columns several regions are fighting over.
Indigo: 1 square across rows 1–1, columns 11–11. It never leaves row 1, so its queen is locked to that row.
Teal covers 1 square, spanning 1 row and 1 column (rows 11–11, columns 1–1). It never leaves row 11, so its queen is locked to that row.
Sea green occupies 3 squares within rows 10–11, columns 6–7.
Amber: 8 squares across rows 1–3, columns 3–6.
Blue covers 12 squares, spanning 4 rows and 5 columns (rows 1–4, columns 7–11).
Slate occupies 13 squares within rows 2–7, columns 5–9.
Mint: 14 squares across rows 1–5, columns 1–4.
Red covers 14 squares, spanning 5 rows and 4 columns (rows 4–8, columns 8–11).
Khaki occupies 15 squares within rows 7–11, columns 8–11.
Orange: 18 squares across rows 7–11, columns 1–7.
Pale yellow covers 22 squares, spanning 6 rows and 6 columns (rows 4–9, columns 1–6).
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 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 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 sea green 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 #114
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 6, 9 and 10 are the narrowest, touched by only 3 colors. Columns 2 and 10 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 5 colors — the most crowded line here, and the one least likely to resolve early. Spend your attention accordingly.
Working through the middle game
The middle of #114 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.
Two checks, run alternately, will carry you through the 121 squares of this grid. First: has any of the eleven regions been reduced to a single open square? Second: has any row or column? Either answer forces a queen. Players who stall on 11x11 boards almost always run one of those checks and forget the other.
A placement without a reason is a guess. Because this board has exactly one solution, a guess that happens to be wrong will not announce itself for several moves — and unwinding it is slower than simply finishing the eliminations first.
Why puzzle #114 is rated medium
What earns a board its rating is the shape of its opening. Here that opening offers four single-line regions, a 1-square smallest color, a tightest row touched by 3 colors, and a region-size spread of 21. Lopsided grids with flat regions fall quickly; balanced ones like this take more patience.
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.
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 #114, start hunting for it near row 6.
As a sanity check rather than a spoiler: the finished solution to #114 puts 2 queens on the outer border and 9 queens in the interior, 2 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 #114?
Puzzle #114 is rated medium. 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 #114 have only one solution?
Yes. Every puzzle in the 11x11 collection, including #114, 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 #114?
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.