11x11 Queens Puzzle #224
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 23-step reasoning is written out below.
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Step-by-step solution for puzzle #224
What follows is a complete solve of puzzle #224, worked the way a person works it rather than the way a computer does. It runs to 23 deductions — 11 queen placements and 12 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, region shadow, pairing argument on rows, pairing argument on columns, last square in a row.
Show the full walkthrough (16 steps) — contains the solution
Step 1. Only row 6, column 6 is still open in red, and since each colour must take a queen, that settles it. That clears row 6, column 6, the rest of the red region and every square adjacent to it — diagonals included.
Step 2. All of the indigo region's remaining squares (4 open squares) lie in row 1. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 6 squares come off.
Step 3. The blue region has 4 squares left, spread across rows 2–4, columns 9 and 10. You do not need to know which of them takes the queen: every one of those options attacks the same 2 squares, so they can be crossed out now.
Step 4. Wherever slate ends up among its 4 squares, the same squares fall within reach of it — 2 squares in total, impossible regardless of how the colour resolves.
Step 5. Teal cannot leave row 11 — every one of its open squares (3 open squares) sits there. That row belongs to teal, so every square on it owned by another colour is dead: 8 squares in all.
The board after step 5 — 1 of 11 queens placed. Step 6. The khaki region has 4 squares left, spread across rows 8–10, columns 4 and 5. 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 7. Wherever orange 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 8. Here is the pairing argument. The khaki, orange, and sea green regions have no open squares outside rows 8–10 — 3 colours confined to 3 rows. Between them they must take one row each, in some order, so every other colour is shut out of all of them: 13 squares come off in one stroke.
Step 9. Pale yellow cannot leave row 7 — every one of its open squares (4 open squares) sits there. That row belongs to pale yellow, so every square on it owned by another colour is dead: 4 squares in all.
Step 10. Here is the pairing argument. The blue, slate, and orange regions have no open squares outside columns 9–11 — 3 colours confined to 3 columns. Between them they must take one column each, in some order, so every other colour is shut out of all of them: 5 squares come off in one stroke.
Step 11. Only row 7, column 8 is still open in pale yellow, and since each colour must take a queen, that settles it. Everything else in row 7, in column 8, in pale yellow and in the ring around that square is now dead.
The board after step 11 — 2 of 11 queens placed. Step 12. The teal region is down to one open square, at row 11, column 7. Every colour holds exactly one queen, so that square is forced. Row 11 and column 7 are now spoken for, along with the squares touching that queen.
Step 13. Indigo cannot leave row 1 — every one of its open squares (3 open squares) sits there. That row belongs to indigo, so every square on it owned by another colour is dead: 1 square in all.
Step 14. Mint is down to 3 candidates in rows 3 and 4, columns 4 and 5, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about mint itself.
Step 15. Mint and khaki are now boxed into columns 4 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 5 squares at once.
Step 16. From here the board cascades. Keep alternating the region sweep and the line sweep and 8 queens fall out in order without any new idea being needed: indigo has one square left, so its queen takes row 1, column 3; row 8 is down to one square, putting a queen on row 8, column 5; mint has one square left, so its queen takes row 4, column 4; row 9 is down to one square, putting a queen on row 9, column 11; slate has one square left, so its queen takes row 5, column 10; blue has one square left, so its queen takes row 3, column 9; amber has one square left, so its queen takes row 2, column 1; sea green has one square left, so its queen takes row 10, column 2. 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 10, column 2.
The board after step 16 — 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 #224
This is puzzle number 224 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.
Puzzle #224 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 #224 are: red (1 square), indigo (5 squares), teal (5 squares), blue (6 squares), slate (6 squares), orange (6 squares), khaki (8 squares), sea green (10 squares), pale yellow (23 squares), mint (25 squares), amber (26 squares). An even split would hand every color 11 squares, so the red region is running 10 squares under that average while the amber region is the roomiest area on the grid with 26 squares.
Every color takes one queen and one only, whatever its size — which is why the 25 square difference between red and amber 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.
A region's outline can constrain it more than its size does. Here indigo is the most solid, filling 100% of its 1×5 box, and mint the most diffuse at 51% of its 7×7 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 #224, smallest first. Reading these spans before you place anything is the quickest way to see which parts of the grid are genuinely contested.
Red occupies 1 square within rows 6–6, columns 6–6. It never leaves row 6, so its queen is locked to that row.
Indigo: 5 squares across rows 1–1, columns 3–7. It never leaves row 1, so its queen is locked to that row.
Teal covers 5 squares, spanning 2 rows and 4 columns (rows 10–11, columns 6–9).
Blue occupies 6 squares within rows 1–4, columns 9–10.
Slate: 6 squares across rows 1–5, columns 10–11.
Orange covers 6 squares, spanning 3 rows and 3 columns (rows 9–11, columns 9–11).
Khaki occupies 8 squares within rows 8–11, columns 4–6.
Sea green: 10 squares across rows 8–11, columns 1–4.
Pale yellow covers 23 squares, spanning 6 rows and 6 columns (rows 5–10, columns 6–11).
Mint occupies 25 squares within rows 1–7, columns 3–9.
Amber: 26 squares across rows 1–9, columns 1–5.
Where to start on this board
Open on the tightest color. Here that is red, confined to 1 square between rows 6 and 6 and columns 6 and 6. Its queen has nowhere else to go, which means those 1 row and 1 column carry more constraint than anywhere else on #224.
Because red never leaves row 6, its queen must be in that row — and that instantly settles row 6 for everyone else. Sweep along it and X out every square that is not red. 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 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 #224
A quick way to find the next move is to count how many different colors touch each line. On this board, row 7 is the narrowest, touched by only 3 colors. Columns 1 and 2 are the tightest columns, with 2 colors.
Count colors per line and you have a ranking of where to look. The narrowest rows here see only 3 colors, so one of that handful must take the row and the rest are squeezed into the other 10 rows. Row 10 sits at the far end with 5 colors crossing it; it will almost certainly be among the last to settle.
Working through the middle game
After the first few queens the puzzle becomes bookkeeping. A placed queen wipes its row, its column and every square it touches — as many as eight neighbours — so the space collapses quickly. Record those eliminations on the board instead of carrying them in your head, and the next forced move tends to announce itself.
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 #224 is rated easy
The rating reflects how much the board concedes up front. Puzzle #224 has three 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 25 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.
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 #224 is column 1.
Use this as a rough check on your progress: the completed board has 4 queens around the border and 7 queens in the middle, and nothing in the corners. Solutions spread out; if yours is bunching up in one region of the grid, retrace a few moves.
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 #224?
Puzzle #224 is rated easy. Its smallest color region holds 1 square, its tightest row is touched by 3 colors, and three of its regions are confined to a single row or column, which gives you a forced move early.
Does 11x11 puzzle #224 have only one solution?
Yes. Every puzzle in the 11x11 collection, including #224, 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 #224?
Start with the red region — the most constrained color on this board, with 1 square spanning rows 6–6 and columns 6–6. Narrowing the smallest region first removes the most squares elsewhere on the grid.