11x11 Queens Puzzle #167
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 16-step reasoning is written out below.
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Step-by-step solution for puzzle #167
What follows is a complete solve of puzzle #167, worked the way a person works it rather than the way a computer does. It runs to 16 deductions — 11 queen placements and 5 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, last square in a row.
Show the full walkthrough (11 steps) — contains the solution
Step 1. Only row 11, column 7 is still open in teal, and since each colour must take a queen, that settles it. That clears row 11, column 7, the rest of the teal region and every square adjacent to it — diagonals included.
Step 2. Blue is down to 3 candidates in rows 3 and 4, columns 1 and 2, and they overlap enough to cover 2 squares elsewhere. Cross those out without deciding anything about blue itself.
Step 3. Only row 4, column 3 is still open in mint, and since each colour must take a queen, that settles it. Everything else in row 4, in column 3, in mint and in the ring around that square is now dead.
Step 4. The blue region is down to one open square, at row 3, column 1. Every colour holds exactly one queen, so that square is forced. Row 3 and column 1 are now spoken for, along with the squares touching that queen.
The board after step 4 — 3 of 11 queens placed. Step 5. Amber cannot leave column 11 — 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: 8 squares in all.
Step 6. The sea green region is down to one open square, at row 10, column 10. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 10 and column 10, the remaining sea green squares, and the ring of neighbours around row 10, column 10.
Step 7. Wherever red ends up among its 6 squares, the same squares fall within reach of it — 1 square in total, impossible regardless of how the colour resolves.
The board after step 7 — 4 of 11 queens placed. Step 8. The khaki region is down to one open square, at row 8, column 9. Every colour holds exactly one queen, so that square is forced. Row 8 and column 9 are now spoken for, along with the squares touching that queen.
Step 9. The red region has 2 squares left, spread across rows 6 and 7, columns 6 and 8. 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 10. All of the orange region's remaining squares (2 open squares) lie in row 9. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 2 squares come off.
Step 11. 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: pale yellow has one square left, so its queen takes row 7, column 5; red has one square left, so its queen takes row 6, column 8; row 5 is down to one square, putting a queen on row 5, column 6; orange has one square left, so its queen takes row 9, column 2; indigo has one square left, so its queen takes row 1, column 4; amber has one square left, so its queen takes row 2, 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 2, column 11.
The board after step 11 — 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 #167
11x11 puzzle #167 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.
Puzzle #167 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 #167 are: teal (1 square), mint (2 squares), blue (3 squares), amber (6 squares), sea green (8 squares), red (10 squares), pale yellow (10 squares), khaki (10 squares), indigo (14 squares), orange (23 squares), slate (34 squares). An even split would hand every color 11 squares, so the teal region is running 10 squares under that average while the slate region is the roomiest area on the grid with 34 squares.
That imbalance is the first thing to read, because every region takes exactly one queen regardless of how much space it owns. Teal has only 1 place to put its queen; slate has 34. The spread between them on this board is 33 squares, and the wider that spread runs, the more it pays to solve from the small end inward.
Look at arrangement as well as area. Mint is the densest region on this grid at 100% of a 1×2 frame; pale yellow is the loosest, occupying only 42% of its 4×6 frame. The loose one reaches into more rows and columns, which is exactly why it usually settles last.
Region by region
Here is the full footprint of every color on puzzle #167, smallest first. Reading these spans before you place anything is the quickest way to see which parts of the grid are genuinely contested.
Teal occupies 1 square within rows 11–11, columns 7–7. It never leaves row 11, so its queen is locked to that row.
Mint: 2 squares across rows 4–4, columns 2–3. It never leaves row 4, so its queen is locked to that row.
Blue covers 3 squares, spanning 2 rows and 2 columns (rows 3–4, columns 1–2).
Amber occupies 6 squares within rows 1–4, columns 9–11.
Sea green: 8 squares across rows 10–11, columns 7–11.
Red covers 10 squares, spanning 4 rows and 6 columns (rows 5–8, columns 6–11).
Pale yellow occupies 10 squares within rows 7–10, columns 4–9.
Khaki: 10 squares across rows 6–9, columns 9–11.
Indigo covers 14 squares, spanning 3 rows and 8 columns (rows 1–3, columns 1–8).
Orange occupies 23 squares within rows 5–11, columns 1–6.
Slate: 34 squares across rows 1–7, columns 2–10.
Where to start on this board
The most constrained color is where a solve should begin, and on #167 that is teal with 1 square. It reaches from row 11 to row 11 and from column 7 to column 7 — 1 row 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 teal never leaves row 11, its queen must be in that row — and that instantly settles row 11 for everyone else. Sweep along it and X out every square that is not teal. 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, blue 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 #167
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 1, 2, 5, 9, 10 and 11 are the narrowest, touched by only 3 colors. Column 1 is the tightest column, with 3 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 5 colors — worth revisiting later, not now.
Working through the middle game
The middle of #167 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.
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 #167 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 #167 is rated easy
The rating reflects how much the board concedes up front. Puzzle #167 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 33 squares. Flat, lopsided boards open quickly; even, sprawling ones make you earn the first placement.
Difficulty in Queens is never arithmetic and never luck. Every board has one solution and none require guessing. What varies is the length of the chain you must follow before the next queen becomes certain — one or two steps on an easy board, five or six on a hard one, sometimes with several partial eliminations held in play at once.
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.
One pattern is worth learning at every size, and it is available here. When two regions can only fit inside the same two rows, they must take one row each — which locks every other region out of both. The same argument works for columns, and for any matching count: three regions sharing three rows, four sharing four. Spotting these pairings turns a slow grind into a quick cascade, and on #167 the place to look for one is around row 1.
A non-spoiling distribution check: solved, #167 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 #167?
Puzzle #167 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 #167 have only one solution?
Yes. Every puzzle in the 11x11 collection, including #167, 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 #167?
Start with the teal region — the most constrained color on this board, with 1 square spanning rows 11–11 and columns 7–7. Narrowing the smallest region first removes the most squares elsewhere on the grid.