11x11 Queens Puzzle #153
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 11-step reasoning is written out below.
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Step-by-step solution for puzzle #153
What follows is a complete solve of puzzle #153, worked the way a person works it rather than the way a computer does. It runs to 11 deductions, every one of them a forced placement. Each step names the rule that forces it, so nothing below is a guess, and the hardest idea required is the last square in a region.
Techniques this board needs: last square in a region.
Show the full walkthrough (11 steps) — contains the solution
Step 1. Only row 1, column 8 is still open in indigo, and since each colour must take a queen, that settles it. That clears row 1, column 8, the rest of the indigo region and every square adjacent to it — diagonals included.
Step 2. The orange region is down to one open square, at row 9, column 3. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 9 and column 3, the remaining orange squares, and the ring of neighbours around row 9, column 3.
Step 3. Only row 10, column 1 is still open in sea green, and since each colour must take a queen, that settles it. Everything else in row 10, in column 1, in sea green and in the ring around that square is now dead.
Step 4. The pale yellow region is down to one open square, at row 7, column 2. Every colour holds exactly one queen, so that square is forced. Row 7 and column 2 are now spoken for, along with the squares touching that queen.
The board after step 4 — 4 of 11 queens placed. Step 5. Only row 11, column 4 is still open in teal, and since each colour must take a queen, that settles it. That clears row 11, column 4, the rest of the teal region and every square adjacent to it — diagonals included.
Step 6. The amber region is down to one open square, at row 2, column 5. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 2 and column 5, the remaining amber squares, and the ring of neighbours around row 2, column 5.
Step 7. Only row 8, column 11 is still open in khaki, and since each colour must take a queen, that settles it. Everything else in row 8, in column 11, in khaki and in the ring around that square is now dead.
The board after step 7 — 7 of 11 queens placed. Step 8. The slate region is down to one open square, at row 5, column 10. Every colour holds exactly one queen, so that square is forced. Row 5 and column 10 are now spoken for, along with the squares touching that queen.
Step 9. Only row 3, column 9 is still open in blue, and since each colour must take a queen, that settles it. That clears row 3, column 9, the rest of the blue region and every square adjacent to it — diagonals included.
Step 10. The red region is down to one open square, at row 6, column 7. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 6 and column 7, the remaining red squares, and the ring of neighbours around row 6, column 7.
Step 11. Only row 4, column 6 is still open in mint, and since each colour must take a queen, that settles it. Everything else in row 4, in column 6, in mint and in the ring around that square is now dead.
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 #153
Puzzle #153 is one of the easy-rated boards in the 11x11 set. Eleven colors divide its 121 squares, and you win by placing eleven queens so that each row, each column and each color holds exactly one, with no two queens adjacent in any direction.
There is exactly one way to finish #153, and it has been verified. More importantly, you can reach it without ever gambling: at every stage some square is provably right or provably wrong. Boards differ only in how deep you must dig before that proof appears, and the geometry of these eleven regions is what sets the depth.
How the colors divide this board
From smallest to largest, the regions on puzzle #153 are: indigo (1 square), orange (1 square), slate (3 squares), sea green (3 squares), blue (10 squares), teal (10 squares), pale yellow (11 squares), amber (14 squares), red (14 squares), khaki (22 squares), mint (32 squares). An even split would hand every color 11 squares, so the indigo region is running 10 squares under that average while the mint region is the roomiest area on the grid with 32 squares.
Every color takes one queen and one only, whatever its size — which is why the 31 square difference between indigo and mint 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.
Shape matters as much as size. The indigo region is the most compact color here, filling 100% of the 1×1 box that encloses it, while mint is the most scattered at 50% of its 8×8 box. Compact regions are easy to eliminate around; straggling ones reach into more rows and columns and tend to stay unresolved until late.
Region by region
Here is the full footprint of every color on puzzle #153, smallest first. Reading these spans before you place anything is the quickest way to see which parts of the grid are genuinely contested.
Indigo: 1 square across rows 1–1, columns 8–8. It never leaves row 1, so its queen is locked to that row.
Orange covers 1 square, spanning 1 row and 1 column (rows 9–9, columns 3–3). It never leaves row 9, so its queen is locked to that row.
Slate occupies 3 squares within rows 5–6, columns 10–11.
Sea green: 3 squares across rows 9–10, columns 1–2.
Blue covers 10 squares, spanning 4 rows and 3 columns (rows 1–4, columns 9–11).
Teal occupies 10 squares within rows 9–11, columns 1–6.
Pale yellow: 11 squares across rows 4–9, columns 1–3.
Amber covers 14 squares, spanning 3 rows and 6 columns (rows 1–3, columns 1–6).
Red occupies 14 squares within rows 5–8, columns 5–10.
Khaki: 22 squares across rows 7–11, columns 5–11.
Mint covers 32 squares, spanning 8 rows and 8 columns (rows 1–8, columns 2–9).
Where to start on this board
Indigo is the natural opening on #153: it is the smallest region on the grid at 1 square, boxed into rows 1–1 and columns 8–8. Since one of those squares must hold a queen, that block of 1 row and 1 column is the most contested part of the board.
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. Orange, slate 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 #153
A quick way to find the next move is to count how many different colors touch each line. On this board, row 11 is the narrowest, touched by only 2 colors. Columns 4, 7 and 11 are the tightest columns, 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 9 is the crowded extreme at 5 colors — worth revisiting later, not now.
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.
The whole middle game reduces to two sweeps. Sweep the eleven colors looking for one with a single square left; sweep the eleven rows and eleven columns looking for the same. Each sweep feeds the next, and switching between them deliberately — rather than drifting — is what separates a fast 11x11 solve from a stalled one.
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 #153 is rated easy
The rating reflects how much the board concedes up front. Puzzle #153 has four regions confined to a single row or column, its smallest color holds 1 square, its tightest row meets just 2 colors, and the gap between its largest and smallest regions is 31 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.
Stuck on #153 despite the easy rating? The odds strongly favour a bookkeeping error over a hard chain of logic. Re-check each placed queen for its complete set of eliminations, paying particular attention to the four diagonal squares — those are the ones that get overlooked, and one of them is usually sitting on the answer.
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 #153 is row 11.
A non-spoiling distribution check: solved, #153 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 #153?
Puzzle #153 is rated easy. Its smallest color region holds 1 square, its tightest row is touched by 2 colors, and four of its regions are confined to a single row or column, which gives you a forced move early.
Does 11x11 puzzle #153 have only one solution?
Yes. Every puzzle in the 11x11 collection, including #153, 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 #153?
Start with the indigo region — the most constrained color on this board, with 1 square spanning rows 1–1 and columns 8–8. Narrowing the smallest region first removes the most squares elsewhere on the grid.