11x11 Queens Puzzle #147
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 20-step reasoning is written out below.
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Step-by-step solution for puzzle #147
What follows is a complete solve of puzzle #147, worked the way a person works it rather than the way a computer does. It runs to 20 deductions — 11 queen placements and 9 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 pairing argument on rows.
Techniques this board needs: last square in a region, region shadow, line confined to one region, pairing argument on rows, region confined to one line.
Show the full walkthrough (14 steps) — contains the solution
Step 1. Only row 1, column 1 is still open in indigo, and since each colour must take a queen, that settles it. That clears row 1, column 1, the rest of the indigo region and every square adjacent to it — diagonals included.
Step 2. The amber region is down to one open square, at row 2, column 5. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 2 and column 5, the remaining amber squares, and the ring of neighbours around row 2, column 5.
Step 3. Only row 11, column 3 is still open in teal, and since each colour must take a queen, that settles it. Everything else in row 11, in column 3, in teal and in the ring around that square is now dead.
Step 4. Wherever blue 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.
Step 5. Slate is down to 4 candidates in rows 3–5, columns 9–11, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about slate itself.
The board after step 5 — 3 of 11 queens placed. Step 6. The red region has 4 squares left, spread across rows 4–6, columns 7 and 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 7. Wherever pale yellow ends up among its 8 squares, the same squares fall within reach of it — 1 square in total, impossible regardless of how the colour resolves.
Step 8. Every open square left in row 10 (6 open squares) belongs to the sea green region. Since that row must contain a queen, sea green is the colour that supplies it — so sea green squares anywhere else on the board are out, 12 squares in all.
Step 9. Row 9 has only orange squares left (2 open squares). The row needs a queen and only orange can provide one, which pins that colour to this row and kills its squares elsewhere: 3 squares.
The board after step 9 — 3 of 11 queens placed. Step 10. Here is the pairing argument. The blue, mint, and slate regions have no open squares outside rows 3–5 — 3 colours confined to 3 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 11. Only row 6, column 8 is still open in red, and since each colour must take a queen, that settles it. Everything else in row 6, in column 8, in red and in the ring around that square is now dead.
Step 12. The slate region has 3 squares left, spread across rows 3–5, columns 10 and 11. 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 13. Blue cannot leave column 9 — 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: 2 squares in all.
Step 14. From here the board cascades. Keep alternating the region sweep and the line sweep and 7 queens fall out in order without any new idea being needed: pale yellow has one square left, so its queen takes row 7, column 11; slate has one square left, so its queen takes row 5, column 10; blue has one square left, so its queen takes row 3, column 9; khaki has one square left, so its queen takes row 8, column 2; orange has one square left, so its queen takes row 9, column 4; mint has one square left, so its queen takes row 4, column 6; sea green has one square left, so its queen takes row 10, 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 10, column 7.
The board after step 14 — 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 #147
11x11 puzzle #147 is rated hard. Eleven colored regions cover its 121 squares, and your job is to seat eleven queens so that every row, column and color contains exactly one — with no queen touching another, including diagonally.
Like every board on this site, #147 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 #147 are: indigo (1 square), teal (1 square), amber (3 squares), red (4 squares), slate (6 squares), pale yellow (10 squares), khaki (13 squares), blue (14 squares), orange (20 squares), sea green (24 squares), mint (25 squares). An even split would hand every color 11 squares, so the indigo region is running 10 squares under that average while the mint region is the roomiest area on the grid with 25 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; mint has 25. The spread between them on this board is 24 squares, and the wider that spread runs, the more it pays to solve from the small end inward.
A region's outline can constrain it more than its size does. Here indigo is the most solid, filling 100% of its 1×1 box, and pale yellow the most diffuse at 50% of its 4×5 box. Solid blocks give clean eliminations; diffuse ones spread across the board and stay open longer.
Region by region
Here is the full footprint of every color on puzzle #147, smallest first. Reading these spans before you place anything is the quickest way to see which parts of the grid are genuinely contested.
Indigo: 1 square across rows 1–1, columns 1–1. It never leaves row 1, so its queen is locked to that row.
Teal covers 1 square, spanning 1 row and 1 column (rows 11–11, columns 3–3). It never leaves row 11, so its queen is locked to that row.
Amber occupies 3 squares within rows 1–2, columns 4–5.
Red: 4 squares across rows 4–6, columns 7–8.
Slate covers 6 squares, spanning 4 rows and 3 columns (rows 2–5, columns 9–11).
Pale yellow occupies 10 squares within rows 5–8, columns 7–11.
Khaki: 13 squares across rows 5–9, columns 1–4.
Blue covers 14 squares, spanning 4 rows and 6 columns (rows 1–4, columns 6–11).
Orange occupies 20 squares within rows 6–11, columns 1–6.
Sea green: 24 squares across rows 7–11, columns 6–11.
Mint covers 25 squares, spanning 5 rows and 8 columns (rows 1–5, columns 1–8).
Where to start on this board
The most constrained color is where a solve should begin, and on #147 that is indigo with 1 square. It reaches from row 1 to row 1 and from column 1 to column 1 — 1 row by 1 column. One queen has to live inside that footprint no matter what else happens, which makes those lines the busiest real estate on 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 amber 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 #147
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 2 colors. Columns 2 and 5 are the tightest columns, with 3 colors.
Count colors per line and you have a ranking of where to look. The narrowest rows here see only 2 colors, so one of that handful must take the row and the rest are squeezed into the other 10 rows. Row 5 sits at the far end with 5 colors crossing it; it will almost certainly be among the last to settle.
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.
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.
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 #147 is rated hard
The rating reflects how much the board concedes up front. Puzzle #147 has four 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 24 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 #147 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 #147 the place to look for one is around row 10.
Use this as a rough check on your progress: the completed board has 3 queens around the border and 8 queens in the middle, including 1 in a corner. Solutions spread out; if yours is bunching up in one region of the grid, retrace a few moves.
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 #147?
Puzzle #147 is rated hard. Its smallest color region holds 1 square, its tightest row is touched by 2 colors, and four of its regions are confined to a single row or column, which gives you a forced move early.
Does 11x11 puzzle #147 have only one solution?
Yes. Every puzzle in the 11x11 collection, including #147, 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 #147?
Start with the indigo region — the most constrained color on this board, with 1 square spanning rows 1–1 and columns 1–1. Narrowing the smallest region first removes the most squares elsewhere on the grid.