11x11 Queens Puzzle #133
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 25-step reasoning is written out below.
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Step-by-step solution for puzzle #133
What follows is a complete solve of puzzle #133, worked the way a person works it rather than the way a computer does. It runs to 25 deductions — 11 queen placements and 14 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 proof by contradiction.
Techniques this board needs: last square in a region, region confined to one line, region shadow, pairing argument on columns, line confined to one region, proof by contradiction, last square in a row, pairing argument on rows.
Show the full walkthrough (21 steps) — contains the solution
Step 1. Only row 4, column 7 is still open in mint, and since each colour must take a queen, that settles it. That clears row 4, column 7, the rest of the mint region and every square adjacent to it — diagonals included.
Step 2. 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: 10 squares come off.
Step 3. The red region has 3 squares left, spread across rows 5 and 6, columns 9 and 10. You do not need to know which of them takes the queen: every one of those options attacks the same 1 square, so they can be crossed out now.
Step 4. Wherever teal ends up among its 4 squares, the same squares fall within reach of it — 1 square in total, impossible regardless of how the colour resolves.
Step 5. Pale yellow and teal are now boxed into columns 1 and 2 and nothing else. That is 2 colours needing 2 columns, so they fill those columns between them — which locks every remaining colour out and removes 7 squares at once.
The board after step 5 — 1 of 11 queens placed. 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. Only row 6, column 9 is still open in red, and since each colour must take a queen, that settles it. Everything else in row 6, in column 9, in red and in the ring around that square is now dead.
Step 8. Blue is down to 3 candidates in rows 2, 3, and 7, columns 4 and 5, and they overlap enough to cover 4 squares elsewhere. Cross those out without deciding anything about blue itself.
Step 9. The pale yellow region has 4 squares left, spread across rows 7–9, columns 1 and 2. You do not need to know which of them takes the queen: every one of those options attacks the same 1 square, so they can be crossed out now.
Step 10. Wherever sea green 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.
Step 11. Row 1 has only indigo squares left (5 open squares). The row needs a queen and only indigo can provide one, which pins that colour to this row and kills its squares elsewhere: 2 squares.
The board after step 11 — 3 of 11 queens placed. Step 12. Now a short proof by contradiction. Suppose the indigo queen went to row 1, column 4. Follow the forced moves that would create and row 3 runs out of open squares entirely — impossible. So that square is ruled out for good.
Step 13. Test row 1, column 6 for indigo: place a queen there, run the forced consequences through, and the sea green region is left with nowhere to put its queen. The assumption breaks, so the square is eliminated.
Step 14. Now a short proof by contradiction. Suppose the indigo queen went to row 1, column 10. Follow the forced moves that would create and row 2 runs out of open squares entirely — impossible. So that square is ruled out for good.
Step 15. Test row 3, column 11 for amber: place a queen there, run the forced consequences through, and the orange region is left with nowhere to put its queen. The assumption breaks, so the square is eliminated.
Step 16. The amber region is down to one open square, at row 2, column 11. Every colour holds exactly one queen, so that square is forced. Row 2 and column 11 are now spoken for, along with the squares touching that queen.
The board after step 16 — 4 of 11 queens placed. Step 17. Look along row 3: one square survives, row 3, column 4, which belongs to blue. A row cannot be left empty, so the queen goes there. Everything else in row 3, in column 4, in blue and in the ring around that square is now dead.
Step 18. Here is the pairing argument. The sea green and teal regions have no open squares outside rows 10 and 11 — 2 colours confined to 2 rows. Between them they must take one row each, in some order, so every other colour is shut out of all of them: 4 squares come off in one stroke.
Step 19. Only row 8, column 10 is still open in khaki, and since each colour must take a queen, that settles it. Everything else in row 8, in column 10, in khaki and in the ring around that square is now dead.
Step 20. Pale yellow is down to 2 candidates in rows 7 and 9, columns 1 and 2, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about pale yellow itself.
Step 21. 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 10 is down to one square, putting a queen on row 10, column 6; orange has one square left, so its queen takes row 9, column 8; indigo has one square left, so its queen takes row 1, column 5; pale yellow has one square left, so its queen takes row 7, column 1; teal has one square left, so its queen takes row 11, column 2. 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 11, column 2.
The board after step 21 — 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 #133
Puzzle #133 is one of the hard-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.
As with every puzzle in this collection, #133 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 #133 are: mint (1 square), amber (2 squares), teal (4 squares), slate (8 squares), pale yellow (9 squares), khaki (11 squares), red (13 squares), blue (14 squares), sea green (16 squares), orange (21 squares), indigo (22 squares). An even split would hand every color 11 squares, so the mint region is running 10 squares under that average while the indigo region is the roomiest area on the grid with 22 squares.
Every color takes one queen and one only, whatever its size — which is why the 21 square difference between mint and indigo 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 amber region is the most compact color here, filling 100% of the 2×1 box that encloses it, while sea green is the most scattered at 44% of its 6×6 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 #133, smallest first. Reading these spans before you place anything is the quickest way to see which parts of the grid are genuinely contested.
Mint covers 1 square, spanning 1 row and 1 column (rows 4–4, columns 7–7). It never leaves row 4, so its queen is locked to that row.
Amber occupies 2 squares within rows 2–3, columns 11–11. It sits wholly inside column 11, so its queen must be in that column.
Teal: 4 squares across rows 9–11, columns 1–2.
Slate covers 8 squares, spanning 5 rows and 3 columns (rows 1–5, columns 1–3).
Pale yellow occupies 9 squares within rows 5–10, columns 1–2.
Khaki: 11 squares across rows 6–11, columns 8–11.
Red covers 13 squares, spanning 6 rows and 4 columns (rows 2–7, columns 8–11).
Blue occupies 14 squares within rows 2–7, columns 3–7.
Sea green: 16 squares across rows 6–11, columns 2–7.
Orange covers 21 squares, spanning 5 rows and 6 columns (rows 6–10, columns 5–10).
Indigo occupies 22 squares within rows 1–3, columns 2–11.
Where to start on this board
Mint is the natural opening on #133: it is the smallest region on the grid at 1 square, boxed into rows 4–4 and columns 7–7. 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 mint never leaves row 4, its queen must be in that row — and that instantly settles row 4 for everyone else. Sweep along it and X out every square that is not mint. 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 #133
A quick way to find the next move is to count how many different colors touch each line. On this board, row 1 is the narrowest, touched by only 2 colors. Columns 1 and 4 are the tightest columns, with 3 colors.
The fewer colors a line touches, the sooner it surrenders its queen. A row meeting just 2 colors has to be claimed by one of them, which pushes every remaining region into the other 10 rows. Row 7, meeting 6 colors, is the opposite case — the busiest line on #133 and the last one you should expect to crack.
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 #133 is rated hard
The rating reflects how much the board concedes up front. Puzzle #133 has three 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 21 squares. Flat, lopsided boards open quickly; even, sprawling ones make you earn the first placement.
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 hard 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.
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 #133 is row 1.
Here is a shape check that gives nothing away: when #133 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 #133?
Puzzle #133 is rated hard. Its smallest color region holds 1 square, its tightest row is touched by 2 colors, and three of its regions are confined to a single row or column, which gives you a forced move early.
Does 11x11 puzzle #133 have only one solution?
Yes. Every puzzle in the 11x11 collection, including #133, 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 #133?
Start with the mint region — the most constrained color on this board, with 1 square spanning rows 4–4 and columns 7–7. Narrowing the smallest region first removes the most squares elsewhere on the grid.