11x11 Queens Puzzle #111
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 22-step reasoning is written out below.
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Step-by-step solution for puzzle #111
What follows is a complete solve of puzzle #111, worked the way a person works it rather than the way a computer does. It runs to 22 deductions — 11 queen placements and 11 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 proof by contradiction.
Techniques this board needs: region shadow, region confined to one line, last square in a region, pairing argument on rows, proof by contradiction, pairing argument on columns, last square in a row, last square in a column.
Show the full walkthrough (14 steps) — contains the solution
Step 1. Wherever indigo 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 2. All of the red region's remaining squares (4 open squares) lie in column 11. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 7 squares come off.
Step 3. Only row 1, column 10 is still open in indigo, and since each colour must take a queen, that settles it. Everything else in row 1, in column 10, in indigo and in the ring around that square is now dead.
Step 4. All of the amber region's remaining squares (2 open squares) lie in row 2. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 7 squares come off.
Step 5. Sea green cannot leave column 1 — every one of its open squares (2 open squares) sits there. That column belongs to sea green, so every square in it owned by another colour is dead: 9 squares in all.
The board after step 5 — 1 of 11 queens placed. Step 6. Here is the pairing argument. The sea green and teal regions have no open squares outside rows 10 and 11 — 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: 7 squares come off in one stroke.
Step 7. Wherever orange ends up among its 8 squares, the same squares fall within reach of it — 1 square in total, impossible regardless of how the colour resolves.
Step 8. Here is the pairing argument. The red, pale yellow, khaki, and orange regions have no open squares outside rows 6–9 — 4 colours confined to 4 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 9. Test row 2, column 5 for amber: place a queen there, run the forced consequences through, and the teal region is left with nowhere to put its queen. The assumption breaks, so the square is eliminated.
The board after step 9 — 1 of 11 queens placed. Step 10. The amber region is down to one open square, at row 2, column 7. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 2 and column 7, the remaining amber squares, and the ring of neighbours around row 2, column 7.
Step 11. Blue is down to 7 candidates in rows 3–5, columns 4, 5, 6, 8, and 9, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about blue itself.
Step 12. The pale yellow region has 4 squares left, spread across rows 6–8, columns 8 and 9. 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 13. Slate, pale yellow, khaki, and teal are now boxed into columns 5, 6, 8, and 9 and nothing else. That is 4 colours needing 4 columns, so they fill those columns between them — which locks every remaining colour out and removes 7 squares at once.
Step 14. From here the board cascades. Keep alternating the region sweep and the line sweep and 9 queens fall out in order without any new idea being needed: blue has one square left, so its queen takes row 3, column 4; row 4 is down to one square, putting a queen on row 4, column 2; orange has one square left, so its queen takes row 9, column 3; khaki has one square left, so its queen takes row 8, column 6; column 5 is down to one square, putting a queen on row 11, column 5; sea green has one square left, so its queen takes row 10, column 1; column 9 is down to one square, putting a queen on row 5, column 9; pale yellow has one square left, so its queen takes row 7, column 8; red has one square left, so its queen takes row 6, column 11. 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 6, column 11.
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 #111
11x11 puzzle #111 is rated easy. Eleven colored regions cover its 121 squares, and your job is to seat eleven queens so that every row, column and color contains exactly one — with no queen touching another, including diagonally.
As with every puzzle in this collection, #111 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 #111 are: sea green (2 squares), indigo (4 squares), red (4 squares), pale yellow (8 squares), amber (9 squares), khaki (10 squares), teal (11 squares), slate (14 squares), orange (18 squares), blue (19 squares), mint (22 squares). An even split would hand every color 11 squares, so the sea green region is running 9 squares under that average while the mint region is the roomiest area on the grid with 22 squares.
One queen per color, regardless of acreage: that is what turns this uneven split into a solving order. Sea green is working with 2 squares while mint has 22 to spare, a gap of 20. Attack the cramped end and the roomy regions tend to resolve themselves.
Look at arrangement as well as area. Red is the densest region on this grid at 100% of a 4×1 frame; blue is the loosest, occupying only 39% of its 7×7 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.
Sea green: 2 squares across rows 10–11, columns 1–1. It sits wholly inside column 1, so its queen must be in that column.
Indigo covers 4 squares, spanning 3 rows and 2 columns (rows 1–3, columns 10–11).
Red occupies 4 squares within rows 6–9, columns 11–11. It sits wholly inside column 11, so its queen must be in that column.
Pale yellow: 8 squares across rows 6–9, columns 7–10.
Amber covers 9 squares, spanning 2 rows and 6 columns (rows 1–2, columns 5–10).
Khaki occupies 10 squares within rows 7–10, columns 5–9.
Teal: 11 squares across rows 10–11, columns 5–11.
Slate covers 14 squares, spanning 5 rows and 6 columns (rows 3–7, columns 6–11).
Orange occupies 18 squares within rows 7–11, columns 1–5.
Blue: 19 squares across rows 1–7, columns 3–9.
Mint covers 22 squares, spanning 8 rows and 4 columns (rows 1–8, columns 1–4).
Where to start on this board
The most constrained color is where a solve should begin, and on #111 that is sea green with 2 squares. It reaches from row 10 to row 11 and from column 1 to column 1 — 2 rows by 1 column. One queen has to live inside that footprint no matter what else happens, which makes those lines the busiest real estate on the board.
Because sea green stays inside column 1, its queen belongs to that column and no other region may use it. Cross out the rest of column 1 straight away. Any color that was relying on those squares now has a visibly smaller footprint, and that shrinkage is where your second deduction comes from.
Work outward to the other flat regions next. Amber 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 #111
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 4, 5 and 11 are the narrowest, touched by only 3 colors. Column 2 is the tightest column, with 2 colors.
A line with few colors is a line close to resolving. Where only 3 colors appear, one of them owns the row outright and the others must fit into the remaining 10 rows. Row 7 is the crowded extreme at 7 colors — worth revisiting later, not now.
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.
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.
Resist the plausible-looking queen. On #111 every correct placement has a stated reason behind it, and any move you cannot justify is a guess wearing a disguise. Backing out of a wrong guess on a single-solution board takes far longer than finding the real deduction would have.
Why puzzle #111 is rated easy
Ratings track how generous the opening is. On #111 you get two regions pinned to a single row or column, a smallest color of 2 squares, a tightest row crossed by 3 colors, and a 20-square gap between the largest and smallest regions. Those four numbers largely explain the easy label.
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.
Whatever the grid size, the pairing rule is the technique to internalise. When a pair of regions is boxed into the same pair of rows, they split those rows between them and nobody else may enter — and the same holds for columns, or for any n regions confined to n lines. Look for an instance of it around column 2 on this board.
A non-spoiling distribution check: solved, #111 carries 4 queens on the perimeter against 7 queens inside, with the corners empty. Because no two queens may touch, real solutions always look fairly evenly spread — a lopsided board in progress is a warning sign.
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 #111?
Puzzle #111 is rated easy. Its smallest color region holds 2 squares, 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 #111 have only one solution?
Yes. Every puzzle in the 11x11 collection, including #111, 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 #111?
Start with the sea green region — the most constrained color on this board, with 2 squares spanning rows 10–11 and columns 1–1. Narrowing the smallest region first removes the most squares elsewhere on the grid.