7x7 Queens Puzzle #191
Difficulty: hard. Place 7 queens on this 7x7 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 #191
What follows is a complete solve of puzzle #191, worked the way a person works it rather than the way a computer does. It runs to 20 deductions — 7 queen placements and 13 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 shadow, line confined to one region, pairing argument on columns, proof by contradiction, region confined to one line.
Show the full walkthrough (16 steps) — contains the solution
Step 1. Only row 6, column 7 is still open in red, and since each colour must take a queen, that settles it. That clears row 6, column 7, the rest of the red region and every square adjacent to it — diagonals included.
Step 2. Indigo is down to 4 candidates in rows 1 and 2, columns 2–4, and they overlap enough to cover 2 squares elsewhere. Cross those out without deciding anything about indigo itself.
Step 3. The blue region has 5 squares left, spread across rows 2–4, columns 4–6. 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 slate 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. Blue is down to 4 candidates in rows 2 and 3, columns 4–6, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about blue itself.
The board after step 5 — 1 of 7 queens placed. Step 6. The mint region has 5 squares left, spread across rows 2–4, columns 1–3. 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 7. Row 7 has only pale yellow squares left (5 open squares). The row needs a queen and only pale yellow can provide one, which pins that colour to this row and kills its squares elsewhere: 2 squares.
Step 8. Every open square left in row 5 (2 open squares) belongs to the slate region. Since that row must contain a queen, slate is the colour that supplies it — so slate squares anywhere else on the board are out, 1 square in all.
Step 9. Amber, blue, and slate are now boxed into columns 4–6 and nothing else. That is 3 colours needing 3 columns, so they fill those columns between them — which locks every remaining colour out and removes 3 squares at once.
Step 10. Now a short proof by contradiction. Suppose the indigo queen went to row 1, column 2. Follow the forced moves that would create and the mint region is left with nowhere to put its queen — impossible. So that square is ruled out for good.
Step 11. Indigo is down to 2 candidates in rows 1 and 2, columns 2 and 3, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about indigo itself.
The board after step 11 — 1 of 7 queens placed. Step 12. All of the blue region's remaining squares (3 open squares) lie in row 3. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 2 squares come off.
Step 13. Test row 2, column 2 for indigo: place a queen there, run the forced consequences through, and column 4 runs out of open squares entirely. The assumption breaks, so the square is eliminated.
Step 14. The indigo region is down to one open square, at row 1, column 3. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 1 and column 3, the remaining indigo squares, and the ring of neighbours around row 1, column 3.
Step 15. Amber cannot leave column 6 — every one of its open squares (2 open squares) sits there. That column belongs to amber, so every square in it owned by another colour is dead: 2 squares in all.
Step 16. 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: blue has one square left, so its queen takes row 3, column 4; slate has one square left, so its queen takes row 5, column 5; amber has one square left, so its queen takes row 2, column 6; mint has one square left, so its queen takes row 4, column 2; pale yellow has one square left, so its queen takes row 7, 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 7, column 1.
The board after step 16 — 7 of 7 queens placed.
That completes the board: 7 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 7x7 Queens puzzle #191
7x7 puzzle #191 is rated hard. Seven colored regions cover its 49 squares, and your job is to seat seven queens so that every row, column and color contains exactly one — with no queen touching another, including diagonally.
Like every board on this site, #191 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 #191 are: red (1 square), indigo (4 squares), blue (6 squares), mint (7 squares), amber (9 squares), slate (9 squares), pale yellow (13 squares). An even split would hand every color 7 squares, so the red region is running 6 squares under that average while the pale yellow region is the roomiest area on the grid with 13 squares.
One queen per color, regardless of acreage: that is what turns this uneven split into a solving order. Red is working with 1 square while pale yellow has 13 to spare, a gap of 12. Attack the cramped end and the roomy regions tend to resolve themselves.
A region's outline can constrain it more than its size does. Here red is the most solid, filling 100% of its 1×1 box, and blue the most diffuse at 50% of its 3×4 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 #191, smallest first. Reading these spans before you place anything is the quickest way to see which parts of the grid are genuinely contested.
Red occupies 1 square within rows 6–6, columns 7–7. It never leaves row 6, so its queen is locked to that row.
Indigo: 4 squares across rows 1–2, columns 2–4.
Blue covers 6 squares, spanning 3 rows and 4 columns (rows 2–4, columns 3–6).
Mint occupies 7 squares within rows 1–4, columns 1–3.
Amber: 9 squares across rows 1–4, columns 5–7.
Slate covers 9 squares, spanning 4 rows and 4 columns (rows 4–7, columns 4–7).
Pale yellow occupies 13 squares within rows 4–7, columns 1–5.
Where to start on this board
The most constrained color is where a solve should begin, and on #191 that is red with 1 square. It reaches from row 6 to row 6 and from column 7 to column 7 — 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 red never leaves row 6, its queen must be in that row — and that instantly settles row 6 for everyone else. Sweep along it and X out every square that is not red. 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. Indigo 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 #191
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 5 and 7 are the narrowest, touched by only 2 colors. Column 1 is the tightest column, with 2 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 6 rows. Row 4 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
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.
Keep alternating between two views of the board. In the region view you ask which of the seven 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 7x7 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 #191 is rated hard
The rating reflects how much the board concedes up front. Puzzle #191 has two 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 12 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 #191 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 7x7
At 7x7 the whole grid stays within a single glance, which makes systematic scanning practical. Read the rows in order and count the colors in each — a row touched by two colors is far more constrained than one touched by five, and that is usually where the next forced move hides. The board is small enough that re-scanning from the top after each placement costs almost nothing.
Whatever the grid size, the pairing rule is the technique to internalise. When a pair of regions is boxed into the same pair of rows, they split those rows between them and nobody else may enter — and the same holds for columns, or for any n regions confined to n lines. Look for an instance of it around row 5 on this board.
Use this as a rough check on your progress: the completed board has 3 queens around the border and 4 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 7x7 Queens puzzle #191?
Puzzle #191 is rated hard. Its smallest color region holds 1 square, its tightest row is touched by 2 colors, and two of its regions are confined to a single row or column, which gives you a forced move early.
Does 7x7 puzzle #191 have only one solution?
Yes. Every puzzle in the 7x7 collection, including #191, has been verified to have exactly one valid arrangement of seven queens, and it can always be reached by logic alone — no guessing or backtracking needed.
Where should I place my first queen on puzzle #191?
Start with the red region — the most constrained color on this board, with 1 square spanning rows 6–6 and columns 7–7. Narrowing the smallest region first removes the most squares elsewhere on the grid.