11x11 Queens Puzzle #162
Difficulty: hard. 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 17-step reasoning is written out below.
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Step-by-step solution for puzzle #162
What follows is a complete solve of puzzle #162, worked the way a person works it rather than the way a computer does. It runs to 17 deductions — 11 queen placements and 6 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, last square in a region, region shadow, line confined to one region, last square in a row.
Show the full walkthrough (13 steps) — contains the solution
Step 1. Indigo cannot leave row 1 — every one of its open squares (2 open squares) sits there. That row belongs to indigo, so every square on it owned by another colour is dead: 11 squares in all.
Step 2. The amber region is down to one open square, at row 2, column 8. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 2 and column 8, the remaining amber squares, and the ring of neighbours around row 2, column 8.
Step 3. Only row 1, column 10 is still open in indigo, and since each colour must take a queen, that settles it. Everything else in row 1, in column 10, in indigo 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 11. Every colour holds exactly one queen, so that square is forced. Row 3 and column 11 are now spoken for, along with the squares touching that queen.
The board after step 4 — 3 of 11 queens placed. Step 5. Mint cannot leave row 4 — every one of its open squares (2 open squares) sits there. That row belongs to mint, so every square on it owned by another colour is dead: 8 squares in all.
Step 6. The slate region is down to one open square, at row 5, column 1. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 5 and column 1, the remaining slate squares, and the ring of neighbours around row 5, column 1.
Step 7. Only row 11, column 2 is still open in teal, and since each colour must take a queen, that settles it. Everything else in row 11, in column 2, in teal and in the ring around that square is now dead.
Step 8. Red is down to 4 candidates in rows 6 and 7, columns 4–6, and they overlap enough to cover 2 squares elsewhere. Cross those out without deciding anything about red itself.
Step 9. Pale yellow cannot leave column 3 — every one of its open squares (2 open squares) sits there. That column belongs to pale yellow, so every square in it owned by another colour is dead: 4 squares in all.
The board after step 9 — 5 of 11 queens placed. Step 10. The mint region is down to one open square, at row 4, column 4. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 4 and column 4, the remaining mint squares, and the ring of neighbours around row 4, column 4.
Step 11. Row 10 has only sea green squares left (4 open squares). The row needs a queen and only sea green can provide one, which pins that colour to this row and kills its squares elsewhere: 2 squares.
Step 12. Every open square left in row 9 (3 open squares) belongs to the orange region. Since that row must contain a queen, orange is the colour that supplies it — so orange squares anywhere else on the board are out, 2 squares in all.
Step 13. From here the board cascades. Keep alternating the region sweep and the line sweep and 5 queens fall out in order without any new idea being needed: row 8 is down to one square, putting a queen on row 8, column 7; orange has one square left, so its queen takes row 9, column 5; red has one square left, so its queen takes row 6, column 6; pale yellow has one square left, so its queen takes row 7, column 3; sea green has one square left, so its queen takes row 10, column 9. 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 9.
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 #162
Board #162 of the 11x11 bank carries a hard 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.
Like every board on this site, #162 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 #162 are: indigo (2 squares), amber (4 squares), teal (4 squares), slate (9 squares), khaki (9 squares), red (10 squares), blue (11 squares), orange (13 squares), mint (14 squares), pale yellow (14 squares), sea green (31 squares). An even split would hand every color 11 squares, so the indigo region is running 9 squares under that average while the sea green region is the roomiest area on the grid with 31 squares.
That imbalance is the first thing to read, because every region takes exactly one queen regardless of how much space it owns. Indigo has only 2 places to put its queen; sea green has 31. The spread between them on this board is 29 squares, and the wider that spread runs, the more it pays to solve from the small end inward.
Square count is only half the story — how a color is arranged counts too. Indigo is the tidiest shape on #162, packing 100% of its 1×2 bounding box, whereas blue straggles across its 5×5 box at just 44%. Tidy blocks are easy to work around; scattered ones touch more lines and resist resolution.
Region by region
Here is the full footprint of every color on puzzle #162, smallest first. Reading these spans before you place anything is the quickest way to see which parts of the grid are genuinely contested.
Indigo: 2 squares across rows 1–1, columns 9–10. It never leaves row 1, so its queen is locked to that row.
Amber covers 4 squares, spanning 2 rows and 3 columns (rows 1–2, columns 7–9).
Teal occupies 4 squares within rows 9–11, columns 1–2.
Slate: 9 squares across rows 1–5, columns 1–2.
Khaki covers 9 squares, spanning 3 rows and 4 columns (rows 6–8, columns 6–9).
Red occupies 10 squares within rows 4–7, columns 4–7.
Blue: 11 squares across rows 1–5, columns 7–11.
Orange covers 13 squares, spanning 4 rows and 5 columns (rows 8–11, columns 3–7).
Mint occupies 14 squares within rows 1–4, columns 3–6.
Pale yellow: 14 squares across rows 5–10, columns 1–4.
Sea green covers 31 squares, spanning 8 rows and 7 columns (rows 4–11, columns 5–11).
Where to start on this board
Begin where the choices are fewest. On this board that means indigo, which owns just 2 squares inside a 1×2 window running from row 1 to row 1 and column 9 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 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. Amber 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 #162
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 3 and 11 are the narrowest, touched by only 3 colors. Column 11 is the tightest column, with 2 colors.
The fewer colors a line touches, the sooner it surrenders its queen. A row meeting just 3 colors has to be claimed by one of them, which pushes every remaining region into the other 10 rows. Row 5, meeting 5 colors, is the opposite case — the busiest line on #162 and the last one you should expect to crack.
Working through the middle game
Once two or three queens are down, the board changes character. Each queen removes an entire row, an entire column and the ring of up to eight squares around it, so the grid shrinks faster than most people expect. The habit that pays here is marking rather than remembering: after every placement, cross out the full row, the full column and all eight neighbours before hunting for the next move.
Keep alternating between two views of the board. In the region view you ask which of the eleven colors is down to one open square. In the line view you ask the same of each row and column. Both produce forced queens, and each placement refreshes the other view, so cycling between them deliberately is how a 11x11 board unwinds.
Say the reason out loud: "this region has one square left", "this column has one square left". If no such sentence is available, the eliminating is not finished. One more pass of X marks is almost always quicker than committing to a placement you cannot defend.
Why puzzle #162 is rated hard
The rating reflects how much the board concedes up front. Puzzle #162 has one region confined to a single row or column, its smallest color holds 2 squares, its tightest row meets just 3 colors, and the gap between its largest and smallest regions is 29 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 #162 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.
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 #162 the place to look for one is around column 11.
Here is a shape check that gives nothing away: when #162 is solved, 4 queens sit on the outer edge of the grid and 7 sit inside it, and no queen lands in a corner. A work-in-progress board that clusters its queens in one quadrant while leaving others bare is usually carrying a mistake.
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 #162?
Puzzle #162 is rated hard. Its smallest color region holds 2 squares, its tightest row is touched by 3 colors, and one of its regions is confined to a single row or column, which gives you a forced move early.
Does 11x11 puzzle #162 have only one solution?
Yes. Every puzzle in the 11x11 collection, including #162, 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 #162?
Start with the indigo region — the most constrained color on this board, with 2 squares spanning rows 1–1 and columns 9–10. Narrowing the smallest region first removes the most squares elsewhere on the grid.