11x11 Queens Puzzle #142
Difficulty: medium. 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 #142
What follows is a complete solve of puzzle #142, 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: last square in a region, region shadow, region confined to one line, line confined to one region, last square in a column.
Show the full walkthrough (13 steps) — contains the solution
Step 1. Only row 1, column 11 is still open in indigo, and since each colour must take a queen, that settles it. That clears row 1, column 11, the rest of the indigo region and every square adjacent to it — diagonals included.
Step 2. The teal region is down to one open square, at row 11, column 2. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 11 and column 2, the remaining teal squares, and the ring of neighbours around row 11, column 2.
Step 3. The amber region has 4 squares left, spread across rows 2 and 3, columns 6–8. 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 4. The blue region is down to one open square, at row 3, column 9. Every colour holds exactly one queen, so that square is forced. Row 3 and column 9 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 row 2 — every one of its open squares (2 open squares) sits there. That row belongs to amber, so every square on it owned by another colour is dead: 4 squares in all.
Step 6. All of the red region's remaining squares (2 open squares) lie in row 6. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 10 squares come off.
Step 7. Khaki cannot leave column 1 — every one of its open squares (2 open squares) sits there. That column belongs to khaki, so every square in it owned by another colour is dead: 3 squares in all.
Step 8. Every open square left in column 10 (5 open squares) belongs to the orange region. Since that column must contain a queen, orange is the colour that supplies it — so orange squares anywhere else on the board are out, 4 squares in all.
Step 9. 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: column 8 is down to one square, putting a queen on row 7, column 8; red has one square left, so its queen takes row 6, column 6; amber has one square left, so its queen takes row 2, column 7; mint has one square left, so its queen takes row 4, column 5; khaki has one square left, so its queen takes row 8, column 1. 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 8, column 1.
The board after step 9 — 8 of 11 queens placed. Step 10. Slate is down to 2 candidates in rows 5 and 9, columns 3 and 4, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about slate itself.
Step 11. Only row 10, column 4 is still open in sea green, and since each colour must take a queen, that settles it. Everything else in row 10, in column 4, in sea green and in the ring around that square is now dead.
Step 12. 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. Row 5 and column 3 are now spoken for, along with the squares touching that queen.
Step 13. Only row 9, column 10 is still open in orange, and since each colour must take a queen, that settles it. That clears row 9, column 10, the rest of the orange region and every square adjacent to it — diagonals included.
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 #142
Board #142 of the 11x11 bank carries a medium 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.
As with every puzzle in this collection, #142 has a single verified solution and needs no guesswork. Each queen follows from something already visible. What the board controls is tempo — how soon the first forced move shows up and how far apart the rest are spaced — and that is a direct consequence of how these colors are cut.
How the colors divide this board
From smallest to largest, the regions on puzzle #142 are: indigo (1 square), teal (1 square), red (2 squares), khaki (3 squares), blue (7 squares), amber (9 squares), pale yellow (9 squares), mint (13 squares), sea green (19 squares), slate (28 squares), orange (29 squares). An even split would hand every color 11 squares, so the indigo region is running 10 squares under that average while the orange 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. Indigo has only 1 place to put its queen; orange 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. Indigo is the densest region on this grid at 100% of a 1×1 frame; pale yellow is the loosest, occupying only 50% of its 6×3 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 #142 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.
Indigo covers 1 square, spanning 1 row and 1 column (rows 1–1, columns 11–11). It never leaves row 1, so its queen is locked to that row.
Teal occupies 1 square within rows 11–11, columns 2–2. It never leaves row 11, so its queen is locked to that row.
Red: 2 squares across rows 6–6, columns 6–7. It never leaves row 6, so its queen is locked to that row.
Khaki covers 3 squares, spanning 2 rows and 2 columns (rows 7–8, columns 1–2).
Blue occupies 7 squares within rows 1–3, columns 9–11.
Amber: 9 squares across rows 1–3, columns 4–8.
Pale yellow covers 9 squares, spanning 6 rows and 3 columns (rows 6–11, columns 6–8).
Mint occupies 13 squares within rows 3–7, columns 5–9.
Sea green: 19 squares across rows 8–11, columns 1–6.
Slate covers 28 squares, spanning 9 rows and 5 columns (rows 1–9, columns 1–5).
Orange occupies 29 squares within rows 3–11, columns 8–11.
Where to start on this board
Begin where the choices are fewest. On this board that means indigo, which owns just 1 square inside a 1×1 window running from row 1 to row 1 and column 11 to column 11. 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. Red, teal and khaki 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 #142
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 2, 4, 5 and 10 are the narrowest, touched by only 3 colors. Columns 3 and 10 are the tightest columns, 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 8 is the crowded extreme at 5 colors — worth revisiting later, not now.
Working through the middle game
The middle of #142 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.
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 #142 is rated medium
What earns a board its rating is the shape of its opening. Here that opening offers five 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 medium board from the rest.
A board that feels above its rating is nearly always a board with a missing X. Audit every queen on the grid: full row cleared, full column cleared, all eight touching squares cleared. Diagonals are the common omission, and missing one is far more often the cause of a stall than any genuine difficulty in the puzzle.
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 #142 the place to look for one is around column 3.
A non-spoiling distribution check: solved, #142 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 #142?
Puzzle #142 is rated medium. Its smallest color region holds 1 square, its tightest row is touched by 3 colors, and five of its regions are confined to a single row or column, which gives you a forced move early.
Does 11x11 puzzle #142 have only one solution?
Yes. Every puzzle in the 11x11 collection, including #142, 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 #142?
Start with the indigo region — the most constrained color on this board, with 1 square spanning rows 1–1 and columns 11–11. Narrowing the smallest region first removes the most squares elsewhere on the grid.