7x7 Queens Puzzle #281
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 13-step reasoning is written out below.
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Step-by-step solution for puzzle #281
What follows is a complete solve of puzzle #281, worked the way a person works it rather than the way a computer does. It runs to 13 deductions — 7 queen placements and 6 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: region confined to one line, region shadow, pairing argument on rows, last square in a region.
Show the full walkthrough (7 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. Amber is down to 3 candidates in rows 2 and 3, columns 6 and 7, and they overlap enough to cover 2 squares elsewhere. Cross those out without deciding anything about amber itself.
Step 3. Blue cannot leave column 1 — 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: 5 squares in all.
Step 4. Here is the pairing argument. The amber and blue regions have no open squares outside rows 2 and 3 — 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: 5 squares come off in one stroke.
The board after step 4 — 0 of 7 queens placed. Step 5. Mint cannot leave row 4 — every one of its open squares (2 open squares) sits there. That row belongs to mint, so every square on it owned by another colour is dead: 6 squares in all.
Step 6. All of the amber region's remaining squares (2 open squares) lie in column 7. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 3 squares come off.
Step 7. 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: red has one square left, so its queen takes row 6, column 6; mint has one square left, so its queen takes row 4, column 5; slate has one square left, so its queen takes row 5, column 3; indigo has one square left, so its queen takes row 1, column 2; blue has one square left, so its queen takes row 3, column 1; amber has one square left, so its queen takes row 2, column 7; pale yellow has one square left, so its queen takes row 7, column 4. 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 4.
The board after step 7 — 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 #281
Puzzle #281 is one of the hard-rated boards in the 7x7 set. Seven colors divide its 49 squares, and you win by placing seven 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, #281 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 #281 are: indigo (2 squares), blue (5 squares), red (5 squares), amber (6 squares), mint (9 squares), slate (9 squares), pale yellow (13 squares). An even split would hand every color 7 squares, so the indigo region is running 5 squares under that average while the pale yellow region is the roomiest area on the grid with 13 squares.
Every color takes one queen and one only, whatever its size — which is why the 11 square difference between indigo and pale yellow 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 indigo region is the most compact color here, filling 100% of the 1×2 box that encloses it, while blue is the most scattered at 56% of its 3×3 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
The complete breakdown of each region on this board follows, ordered from tightest to roomiest. Skimming the spans first tells you where the board is crowded and where it has slack.
Indigo occupies 2 squares within rows 1–1, columns 2–3. It never leaves row 1, so its queen is locked to that row.
Blue: 5 squares across rows 1–3, columns 1–3.
Red covers 5 squares, spanning 3 rows and 2 columns (rows 5–7, columns 6–7).
Amber occupies 6 squares within rows 1–3, columns 5–7.
Mint: 9 squares across rows 1–4, columns 4–7.
Slate covers 9 squares, spanning 3 rows and 4 columns (rows 3–5, columns 1–4).
Pale yellow occupies 13 squares within rows 5–7, columns 1–6.
Where to start on this board
Indigo is the natural opening on #281: it is the smallest region on the grid at 2 squares, boxed into rows 1–1 and columns 2–3. Since one of those squares must hold a queen, that block of 1 row and 2 columns 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.
No region here is pinned to a shallow band of rows, so turn the same idea sideways: indigo and red span only two columns. Two narrow regions sharing the same two columns take one column each and lock everyone else out of both, which is usually enough to crack a board that offers no free opening.
The tightest lines on puzzle #281
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 4, 6 and 7 are the narrowest, touched by only 2 colors. Columns 1, 4, 5 and 7 are the tightest columns, with 3 colors.
Those lines matter because a row touched by few colors gives its queen away sooner. If a row meets only 2 colors, then one of those regions has to own it, and every other region is competing for the remaining 6 rows. By contrast row 3 meets 4 colors — the most crowded line here, and the one least likely to resolve early. Spend your attention accordingly.
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 seven colors looking for one with a single square left; sweep the seven rows and seven columns looking for the same. Each sweep feeds the next, and switching between them deliberately — rather than drifting — is what separates a fast 7x7 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 #281 is rated hard
Ratings track how generous the opening is. On #281 you get one region pinned to a single row or column, a smallest color of 2 squares, a tightest row crossed by 2 colors, and a 11-square gap between the largest and smallest regions. Those four numbers largely explain the hard label.
Difficulty in Queens is never arithmetic and never luck. Every board has one solution and none require guessing. What varies is the length of the chain you must follow before the next queen becomes certain — one or two steps on an easy board, five or six on a hard one, sometimes with several partial eliminations held in play at once.
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 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.
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 #281 is row 4.
As a sanity check rather than a spoiler: the finished solution to #281 puts 4 queens on the outer border and 3 queens in the interior, with none in a 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 7x7 Queens puzzle #281?
Puzzle #281 is rated hard. Its smallest color region holds 2 squares, its tightest row is touched by 2 colors, and one of its regions is confined to a single row or column, which gives you a forced move early.
Does 7x7 puzzle #281 have only one solution?
Yes. Every puzzle in the 7x7 collection, including #281, 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 #281?
Start with the indigo region — the most constrained color on this board, with 2 squares spanning rows 1–1 and columns 2–3. Narrowing the smallest region first removes the most squares elsewhere on the grid.