11x11 Queens Puzzle #158
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 #158
What follows is a complete solve of puzzle #158, 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 confined to one line, region shadow, last square in a row.
Show the full walkthrough (13 steps) — contains the solution
Step 1. Only row 10, column 10 is still open in sea green, and since each colour must take a queen, that settles it. That clears row 10, column 10, the rest of the sea green region and every square adjacent to it — diagonals included.
Step 2. The teal region is down to one open square, at row 11, column 8. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 11 and column 8, the remaining teal squares, and the ring of neighbours around row 11, column 8.
Step 3. Only row 9, column 4 is still open in orange, and since each colour must take a queen, that settles it. Everything else in row 9, in column 4, in orange 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 column 11. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 6 squares come off.
The board after step 4 — 3 of 11 queens placed. Step 5. Only row 6, column 9 is still open in red, and since each colour must take a queen, that settles it. That clears row 6, column 9, the rest of the red region and every square adjacent to it — diagonals included.
Step 6. The slate region is down to one open square, at row 5, column 3. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 5 and column 3, the remaining slate squares, and the ring of neighbours around row 5, column 3.
Step 7. Wherever blue ends up among its 5 squares, the same squares fall within reach of it — 1 square in total, impossible regardless of how the colour resolves.
Step 8. Pale yellow is down to 2 candidates in rows 7 and 8, columns 5 and 6, and they overlap enough to cover 2 squares elsewhere. Cross those out without deciding anything about pale yellow itself.
Step 9. Only row 8, column 7 is still open in khaki, and since each colour must take a queen, that settles it. That clears row 8, column 7, the rest of the khaki region and every square adjacent to it — diagonals included.
The board after step 9 — 6 of 11 queens placed. Step 10. The pale yellow region is down to one open square, at row 7, column 5. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 7 and column 5, the remaining pale yellow squares, and the ring of neighbours around row 7, column 5.
Step 11. Blue cannot leave column 2 — every one of its open squares (2 open squares) sits there. That column belongs to blue, so every square in it owned by another colour is dead: 3 squares in all.
Step 12. All of the mint region's remaining squares (2 open squares) lie in column 6. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 2 squares come off.
Step 13. From here the board cascades. Keep alternating the region sweep and the line sweep and 4 queens fall out in order without any new idea being needed: row 3 is down to one square, putting a queen on row 3, column 2; indigo has one square left, so its queen takes row 1, column 1; amber has one square left, so its queen takes row 2, column 11; mint has one square left, so its queen takes row 4, column 6. 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 4, column 6.
The board after step 13 — 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 #158
Board #158 of the 11x11 bank carries a easy rating. Its 121 squares are shared between eleven colored regions, and the solution places eleven queens: one per row, one per column, one per region, none of them side by side or corner to corner.
There is exactly one way to finish #158, 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 #158 are: sea green (1 square), amber (4 squares), slate (4 squares), teal (7 squares), orange (11 squares), indigo (12 squares), pale yellow (12 squares), khaki (12 squares), blue (13 squares), red (16 squares), mint (29 squares). An even split would hand every color 11 squares, so the sea green region is running 10 squares under that average while the mint region is the roomiest area on the grid with 29 squares.
That imbalance is the first thing to read, because every region takes exactly one queen regardless of how much space it owns. Sea green has only 1 place to put its queen; mint has 29. The spread between them on this board is 28 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. Amber is the densest region on this grid at 100% of a 2×2 frame; blue is the loosest, occupying only 41% of its 8×4 frame. The loose one reaches into more rows and columns, which is exactly why it usually settles last.
Region by region
Below is every color on #158 with its exact reach, smallest region first. It is worth a slow read: the spans reveal which rows and columns several regions are fighting over.
Sea green occupies 1 square within rows 10–10, columns 10–10. It never leaves row 10, so its queen is locked to that row.
Amber: 4 squares across rows 1–2, columns 10–11.
Slate covers 4 squares, spanning 3 rows and 2 columns (rows 5–7, columns 3–4).
Teal occupies 7 squares within rows 10–11, columns 8–11.
Orange: 11 squares across rows 9–11, columns 1–5.
Indigo covers 12 squares, spanning 4 rows and 6 columns (rows 1–4, columns 1–6).
Pale yellow occupies 12 squares within rows 7–10, columns 2–6.
Khaki: 12 squares across rows 6–11, columns 6–9.
Blue covers 13 squares, spanning 8 rows and 4 columns (rows 2–9, columns 1–4).
Red occupies 16 squares within rows 3–9, columns 8–11.
Mint: 29 squares across rows 1–7, columns 4–10.
Where to start on this board
Begin where the choices are fewest. On this board that means sea green, which owns just 1 square inside a 1×1 window running from row 10 to row 10 and column 10 to column 10. A queen is guaranteed somewhere in there, so every line that window crosses is under pressure from the very first move.
Because sea green never leaves row 10, its queen must be in that row — and that instantly settles row 10 for everyone else. Sweep along it and X out every square that is not sea green. 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. 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 #158
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 1 and 11 are the narrowest, touched by only 3 colors. Column 7 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 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.
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.
The trap on a board like this is placing a queen that is merely plausible. Every placement should be traceable to an elimination you can point at. If you cannot name the rule that forced it, you are guessing — and on a single-solution grid a guess costs more to unwind than the deduction would have taken to find.
Why puzzle #158 is rated easy
What earns a board its rating is the shape of its opening. Here that opening offers two single-line regions, a 1-square smallest color, a tightest row touched by 3 colors, and a region-size spread of 28. Lopsided grids with flat regions fall quickly; balanced ones like this take more patience.
The scale has nothing to do with maths or luck — every puzzle here is solvable by deduction and has exactly one answer. It measures reasoning depth: how many eliminations must stack up before a placement becomes provable. That depth is what separates a easy board from the rest.
Stuck on #158 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.
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 #158 the place to look for one is around column 7.
A non-spoiling distribution check: solved, #158 carries 3 queens on the perimeter against 8 queens inside, 1 of them cornered. 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 #158?
Puzzle #158 is rated easy. Its smallest color region holds 1 square, 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 #158 have only one solution?
Yes. Every puzzle in the 11x11 collection, including #158, 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 #158?
Start with the sea green region — the most constrained color on this board, with 1 square spanning rows 10–10 and columns 10–10. Narrowing the smallest region first removes the most squares elsewhere on the grid.