11x11 Queens Puzzle #24
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 18-step reasoning is written out below.
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Step-by-step solution for puzzle #24
What follows is a complete solve of puzzle #24, 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 line confined to one region.
Techniques this board needs: region confined to one line, line confined to one region, last square in a row, last square in a region.
Show the full walkthrough (9 steps) — contains the solution
Step 1. Khaki cannot leave column 1 — every one of its open squares (4 open squares) sits there. That column belongs to khaki, so every square in it owned by another colour is dead: 7 squares in all.
Step 2. All of the red region's remaining squares (3 open squares) lie in column 2. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 9 squares come off.
Step 3. Amber cannot leave column 3 — 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: 10 squares in all.
The board after step 3 — 0 of 11 queens placed. Step 4. All of the orange 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: 8 squares come off.
Step 5. Mint cannot leave column 5 — every one of its open squares (4 open squares) sits there. That column belongs to mint, so every square in it owned by another colour is dead: 6 squares in all.
Step 6. Every open square left in row 1 (6 open squares) belongs to the indigo region. Since that row must contain a queen, indigo is the colour that supplies it — so indigo squares anywhere else on the board are out, 11 squares in all.
The board after step 6 — 0 of 11 queens placed. Step 7. Look along row 2: one square survives, row 2, column 3, which belongs to amber. A row cannot be left empty, so the queen goes there. That clears row 2, column 3, the rest of the amber region and every square adjacent to it — diagonals included.
Step 8. Every open square left in row 3 (2 open squares) belongs to the blue region. Since that row must contain a queen, blue is the colour that supplies it — so blue squares anywhere else on the board are out, 14 squares in all.
Step 9. From here the board cascades. Keep alternating the region sweep and the line sweep and 10 queens fall out in order without any new idea being needed: row 5 is down to one square, putting a queen on row 5, column 11; row 4 is down to one square, putting a queen on row 4, column 5; blue has one square left, so its queen takes row 3, column 9; row 6 is down to one square, putting a queen on row 6, column 2; row 7 is down to one square, putting a queen on row 7, column 8; teal has one square left, so its queen takes row 11, column 10; orange has one square left, so its queen takes row 9, column 4; sea green has one square left, so its queen takes row 10, column 7; indigo has one square left, so its queen takes row 1, column 6; 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 9 — 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 #24
This is puzzle number 24 in the 11x11 collection, rated easy. 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.
Like every board on this site, #24 has been verified to have exactly one valid solution, and that solution is reachable by deduction alone. You never have to guess and then unwind; every queen can be justified by something already visible on the grid. What changes from puzzle to puzzle is where the first certainty appears and how long the chain of reasoning runs before the next one — and that is entirely a product of how these particular colors are shaped.
How the colors divide this board
From smallest to largest, the regions on puzzle #24 are: khaki (4 squares), red (5 squares), teal (7 squares), amber (8 squares), pale yellow (9 squares), sea green (9 squares), orange (11 squares), slate (12 squares), mint (16 squares), blue (17 squares), indigo (23 squares). An even split would hand every color 11 squares, so the khaki region is running 7 squares under that average while the indigo region is the roomiest area on the grid with 23 squares.
One queen per color, regardless of acreage: that is what turns this uneven split into a solving order. Khaki is working with 4 squares while indigo has 23 to spare, a gap of 19. Attack the cramped end and the roomy regions tend to resolve themselves.
A region's outline can constrain it more than its size does. Here khaki is the most solid, filling 100% of its 4×1 box, and pale yellow the most diffuse at 38% of its 4×6 box. Solid blocks give clean eliminations; diffuse ones spread across the board and stay open longer.
Region by region
Here is the full footprint of every color on puzzle #24, smallest first. Reading these spans before you place anything is the quickest way to see which parts of the grid are genuinely contested.
Khaki: 4 squares across rows 8–11, columns 1–1. It sits wholly inside column 1, so its queen must be in that column.
Red covers 5 squares, spanning 3 rows and 2 columns (rows 6–8, columns 1–2).
Teal occupies 7 squares within rows 10–11, columns 8–11.
Amber: 8 squares across rows 1–3, columns 1–3.
Pale yellow covers 9 squares, spanning 4 rows and 6 columns (rows 7–10, columns 5–10).
Sea green occupies 9 squares within rows 9–11, columns 4–9.
Orange: 11 squares across rows 6–11, columns 2–4.
Slate covers 12 squares, spanning 7 rows and 3 columns (rows 4–10, columns 9–11).
Mint occupies 16 squares within rows 3–8, columns 1–5.
Blue: 17 squares across rows 3–7, columns 5–10.
Indigo covers 23 squares, spanning 4 rows and 9 columns (rows 1–4, columns 3–11).
Where to start on this board
Open on the tightest color. Here that is khaki, confined to 4 squares between rows 8 and 11 and columns 1 and 1. Its queen has nowhere else to go, which means those 4 rows and 1 column carry more constraint than anywhere else on #24.
Because khaki 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. Teal is no more than two rows tall, so its queen is 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 #24
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 1 and 2 are the narrowest, touched by only 2 colors. Column 11 is the tightest column, with 3 colors.
A line with few colors is a line close to resolving. Where only 2 colors appear, one of them owns the row outright and the others must fit into the remaining 10 rows. Row 10 is the crowded extreme at 6 colors — worth revisiting later, not now.
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.
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.
Resist the plausible-looking queen. On #24 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 #24 is rated easy
The rating reflects how much the board concedes up front. Puzzle #24 has one region confined to a single row or column, its smallest color holds 4 squares, its tightest row meets just 2 colors, and the gap between its largest and smallest regions is 19 squares. Flat, lopsided boards open quickly; even, sprawling ones make you earn the first placement.
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.
If #24 feels harder than its rating suggests, the usual culprit is incomplete marking rather than a difficult deduction. Check that every queen already on the grid has its full cross of eliminations recorded — including the diagonal neighbours, which are by far the easiest to miss. More stalled solves come from one forgotten diagonal X than from any genuinely deep chain of logic.
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 row 1 on this board.
A non-spoiling distribution check: solved, #24 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 #24?
Puzzle #24 is rated easy. Its smallest color region holds 4 squares, its tightest row is touched by 2 colors, and one of its regions is confined to a single row or column, which gives you a forced move early.
Does 11x11 puzzle #24 have only one solution?
Yes. Every puzzle in the 11x11 collection, including #24, 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 #24?
Start with the khaki region — the most constrained color on this board, with 4 squares spanning rows 8–11 and columns 1–1. Narrowing the smallest region first removes the most squares elsewhere on the grid.