7x7 Queens Puzzle #202
Difficulty: easy. 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 14-step reasoning is written out below.
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Step-by-step solution for puzzle #202
What follows is a complete solve of puzzle #202, worked the way a person works it rather than the way a computer does. It runs to 14 deductions — 7 queen placements and 7 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 columns.
Techniques this board needs: region confined to one line, region shadow, pairing argument on rows, pairing argument on columns, last square in a region.
Show the full walkthrough (10 steps) — contains the solution
Step 1. Indigo cannot leave row 1 — every one of its open squares (2 open squares) sits there. That row belongs to indigo, so every square on it owned by another colour is dead: 7 squares in all.
Step 2. Blue is down to 4 candidates in rows 2–4, columns 4 and 5, and they overlap enough to cover 2 squares elsewhere. Cross those out without deciding anything about blue itself.
Step 3. The mint region has 3 squares left, spread across rows 3 and 4, columns 6 and 7. 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.
The board after step 3 — 0 of 7 queens placed. Step 4. All of the red region's remaining squares (2 open squares) lie in column 1. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 6 squares come off.
Step 5. Amber, blue, and mint are now boxed into rows 2–4 and nothing else. That is 3 colours needing 3 rows, so they fill those rows between them — which locks every remaining colour out and removes 1 square at once.
Step 6. Here is the pairing argument. The indigo and mint regions have no open squares outside columns 6 and 7 — 2 colours confined to 2 columns. Between them they must take one column each, in some order, so every other colour is shut out of all of them: 6 squares come off in one stroke.
Step 7. Only row 7, column 5 is still open in pale yellow, and since each colour must take a queen, that settles it. Everything else in row 7, in column 5, in pale yellow and in the ring around that square is now dead.
The board after step 7 — 1 of 7 queens placed. Step 8. The red region is down to one open square, at row 6, column 1. Every colour holds exactly one queen, so that square is forced. Row 6 and column 1 are now spoken for, along with the squares touching that queen.
Step 9. Blue cannot leave column 4 — 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 10. 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: slate has one square left, so its queen takes row 5, column 3; blue has one square left, so its queen takes row 3, column 4; amber has one square left, so its queen takes row 2, column 2; mint has one square left, so its queen takes row 4, column 7; indigo has one square left, so its queen takes row 1, column 6. 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 1, column 6.
The board after step 10 — 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 #202
Board #202 of the 7x7 bank carries a easy rating. Its 49 squares are shared between seven colored regions, and the solution places seven queens: one per row, one per column, one per region, none of them side by side or corner to corner.
Like every board on this site, #202 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 #202 are: indigo (2 squares), red (2 squares), mint (3 squares), pale yellow (6 squares), blue (7 squares), amber (14 squares), slate (15 squares). An even split would hand every color 7 squares, so the indigo region is running 5 squares under that average while the slate region is the roomiest area on the grid with 15 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 2 places to put its queen; slate has 15. The spread between them on this board is 13 squares, and the wider that spread runs, the more it pays to solve from the small end inward.
Square count is only half the story — how a color is arranged counts too. Indigo is the tidiest shape on #202, packing 100% of its 1×2 bounding box, whereas blue straggles across its 4×4 box at just 44%. Tidy blocks are easy to work around; scattered ones touch more lines and resist resolution.
Region by region
Here is the full footprint of every color on puzzle #202, smallest first. Reading these spans before you place anything is the quickest way to see which parts of the grid are genuinely contested.
Indigo covers 2 squares, spanning 1 row and 2 columns (rows 1–1, columns 6–7). It never leaves row 1, so its queen is locked to that row.
Red occupies 2 squares within rows 6–7, columns 1–1. It sits wholly inside column 1, so its queen must be in that column.
Mint: 3 squares across rows 3–4, columns 6–7.
Pale yellow covers 6 squares, spanning 3 rows and 3 columns (rows 5–7, columns 5–7).
Blue occupies 7 squares within rows 1–4, columns 4–7.
Amber: 14 squares across rows 1–5, columns 1–4.
Slate covers 15 squares, spanning 4 rows and 5 columns (rows 4–7, columns 2–6).
Where to start on this board
Begin where the choices are fewest. On this board that means indigo, which owns just 2 squares inside a 1×2 window running from row 1 to row 1 and column 6 to column 7. 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. Mint and red 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 #202
A quick way to find the next move is to count how many different colors touch each line. On this board, row 2 is the narrowest, touched by only 2 colors. Columns 1, 2 and 3 are the tightest columns, with 2 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 6 rows. Row 4, meeting 4 colors, is the opposite case — the busiest line on #202 and the last one you should expect to crack.
Working through the middle game
Once two or three queens are down, the board changes character. Each queen removes an entire row, an entire column and the ring of up to eight squares around it, so the grid shrinks faster than most people expect. The habit that pays here is marking rather than remembering: after every placement, cross out the full row, the full column and all eight neighbours before hunting for the next move.
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 #202 is rated easy
The rating reflects how much the board concedes up front. Puzzle #202 has two regions confined to a single row or column, its smallest color holds 2 squares, its tightest row meets just 2 colors, and the gap between its largest and smallest regions is 13 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 #202 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.
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 #202 the place to look for one is around row 2.
Here is a shape check that gives nothing away: when #202 is solved, 4 queens sit on the outer edge of the grid and 3 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 7x7 Queens puzzle #202?
Puzzle #202 is rated easy. Its smallest color region holds 2 squares, 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 #202 have only one solution?
Yes. Every puzzle in the 7x7 collection, including #202, 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 #202?
Start with the indigo region — the most constrained color on this board, with 2 squares spanning rows 1–1 and columns 6–7. Narrowing the smallest region first removes the most squares elsewhere on the grid.