11x11 Queens Puzzle #101
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 14-step reasoning is written out below.
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Step-by-step solution for puzzle #101
What follows is a complete solve of puzzle #101, worked the way a person works it rather than the way a computer does. It runs to 14 deductions — 11 queen placements and 3 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 shadow, region confined to one line, last square in a column.
Show the full walkthrough (7 steps) — contains the solution
Step 1. Only row 1, column 10 is still open in indigo, and since each colour must take a queen, that settles it. That clears row 1, column 10, the rest of the indigo region and every square adjacent to it — diagonals included.
Step 2. The mint region is down to one open square, at row 4, column 11. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 4 and column 11, the remaining mint squares, and the ring of neighbours around row 4, column 11.
Step 3. Only row 11, column 1 is still open in teal, and since each colour must take a queen, that settles it. Everything else in row 11, in column 1, in teal and in the ring around that square is now dead.
Step 4. Wherever amber ends up among its 3 squares, the same squares fall within reach of it — 2 squares in total, impossible regardless of how the colour resolves.
The board after step 4 — 3 of 11 queens placed. Step 5. Slate cannot leave column 2 — every one of its open squares (2 open squares) sits there. That column belongs to slate, so every square in it owned by another colour is dead: 5 squares in all.
Step 6. All of the amber region's remaining squares (2 open squares) lie in column 3. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 6 squares come off.
Step 7. From here the board cascades. Keep alternating the region sweep and the line sweep and 8 queens fall out in order without any new idea being needed: sea green has one square left, so its queen takes row 10, column 4; pale yellow has one square left, so its queen takes row 7, column 5; slate has one square left, so its queen takes row 5, column 2; blue has one square left, so its queen takes row 3, column 9; amber has one square left, so its queen takes row 2, column 3; column 6 is down to one square, putting a queen on row 9, column 6; khaki has one square left, so its queen takes row 8, column 8; red has one square left, so its queen takes row 6, column 7. 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 6, column 7.
The board after step 7 — 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 #101
Puzzle #101 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.
There is exactly one way to finish #101, 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 #101 are: indigo (1 square), teal (1 square), mint (3 squares), pale yellow (5 squares), amber (7 squares), orange (10 squares), slate (13 squares), sea green (17 squares), blue (18 squares), red (21 squares), khaki (25 squares). An even split would hand every color 11 squares, so the indigo region is running 10 squares under that average while the khaki region is the roomiest area on the grid with 25 squares.
Why does the split matter? Because a region's square count has no bearing on how many queens it gets — the answer is always one. So indigo, with 1 square, is under far more pressure than khaki with 25. A 24-square gap like this one rewards players who start where the choices are fewest.
Square count is only half the story — how a color is arranged counts too. Indigo is the tidiest shape on #101, packing 100% of its 1×1 bounding box, whereas blue straggles across its 5×8 box at just 45%. Tidy blocks are easy to work around; scattered ones touch more lines and resist resolution.
Region by region
Below is every color on #101 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 occupies 1 square within rows 1–1, columns 10–10. It never leaves row 1, so its queen is locked to that row.
Teal: 1 square across rows 11–11, columns 1–1. It never leaves row 11, so its queen is locked to that row.
Mint covers 3 squares, spanning 2 rows and 2 columns (rows 4–5, columns 10–11).
Pale yellow occupies 5 squares within rows 6–9, columns 4–5.
Amber: 7 squares across rows 1–4, columns 2–4.
Orange covers 10 squares, spanning 5 rows and 3 columns (rows 7–11, columns 5–7).
Slate occupies 13 squares within rows 1–8, columns 1–2.
Sea green: 17 squares across rows 5–11, columns 1–5.
Blue covers 18 squares, spanning 5 rows and 8 columns (rows 1–5, columns 4–11).
Red occupies 21 squares within rows 2–7, columns 4–9.
Khaki: 25 squares across rows 5–11, columns 7–11.
Where to start on this board
Indigo is the natural opening on #101: it is the smallest region on the grid at 1 square, boxed into rows 1–1 and columns 10–10. 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. Teal and mint 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 #101
A quick way to find the next move is to count how many different colors touch each line. On this board, row 10 is the narrowest, touched by only 3 colors. Column 3 is the tightest column, with 2 colors.
Those lines matter because a row touched by few colors gives its queen away sooner. If a row meets only 3 colors, then one of those regions has to own it, and every other region is competing for the remaining 10 rows. By contrast row 7 meets 6 colors — the most crowded line here, and the one least likely to resolve early. Spend your attention accordingly.
Working through the middle game
The middle of #101 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.
Two checks, run alternately, will carry you through the 121 squares of this grid. First: has any of the eleven regions been reduced to a single open square? Second: has any row or column? Either answer forces a queen. Players who stall on 11x11 boards almost always run one of those checks and forget the other.
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 #101 is rated hard
What earns a board its rating is the shape of its opening. Here that opening offers four single-line regions, a 1-square smallest color, a tightest row touched by 3 colors, and a region-size spread of 24. Lopsided grids with flat regions fall quickly; balanced ones like this take more patience.
Nothing about the rating involves computation or chance. Each grid has a single solution reachable by pure logic; the rating simply measures how far ahead you have to reason. Easy boards resolve a queen every step or two, while hard ones can ask you to carry three unfinished lines of thought before any of them pays off.
Stuck on #101 despite the hard 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.
Learn the pairing argument and you will use it on every board, this one included. If two colors can only sit inside the same two rows, between them they consume both rows and every other color is shut out. It generalises to any matching count — three colors across three rows, four across four. On #101, start hunting for it near column 3.
As a sanity check rather than a spoiler: the finished solution to #101 puts 3 queens on the outer border and 8 queens in the interior, 1 of them in an actual corner. If your part-finished grid has queens bunched into one area while whole stretches sit empty, something probably went wrong a few moves back.
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 #101?
Puzzle #101 is rated hard. Its smallest color region holds 1 square, its tightest row is touched by 3 colors, and four of its regions are confined to a single row or column, which gives you a forced move early.
Does 11x11 puzzle #101 have only one solution?
Yes. Every puzzle in the 11x11 collection, including #101, 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 #101?
Start with the indigo region — the most constrained color on this board, with 1 square spanning rows 1–1 and columns 10–10. Narrowing the smallest region first removes the most squares elsewhere on the grid.