7x7 Queens Puzzle #93

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 12-step reasoning is written out below.

Previous puzzle · All 7x7 puzzles · Next puzzle

Step-by-step solution for puzzle #93

What follows is a complete solve of puzzle #93, worked the way a person works it rather than the way a computer does. It runs to 12 deductions — 7 queen placements and 5 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, pairing argument on rows, last square in a region, region shadow.

Show the full walkthrough (7 steps) — contains the solution

  1. 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.

  2. Step 2. 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.

  3. Step 3. Amber cannot leave column 2 — 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: 4 squares in all.

  4. Step 4. Here is the pairing argument. The red and pale yellow regions have no open squares outside rows 6 and 7 — 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.

    Puzzle #93 after step 4: 0 of 7 queens placed
    The board after step 4 — 0 of 7 queens placed.

  5. Step 5. Only row 5, column 5 is still open in slate, and since each colour must take a queen, that settles it. That clears row 5, column 5, the rest of the slate region and every square adjacent to it — diagonals included.

  6. Step 6. The mint region has 2 squares left, spread across rows 3 and 4, columns 3 and 6. You do not need to know which of them takes the queen: every one of those options attacks the same 3 squares, so they can be crossed out now.

  7. Step 7. From here the board cascades. Keep alternating the region sweep and the line sweep and 6 queens fall out in order without any new idea being needed: amber has one square left, so its queen takes row 2, column 2; blue has one square left, so its queen takes row 3, column 7; indigo has one square left, so its queen takes row 1, column 6; mint has one square left, so its queen takes row 4, column 3; pale yellow has one square left, so its queen takes row 7, column 4; red has one square left, so its queen takes row 6, 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 6, column 1.

    Puzzle #93 after step 7: 7 of 7 queens placed
    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 #93

Puzzle #93 is one of the easy-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, #93 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 #93 are: indigo (2 squares), red (2 squares), amber (6 squares), slate (6 squares), pale yellow (7 squares), blue (12 squares), mint (14 squares). An even split would hand every color 7 squares, so the indigo region is running 5 squares under that average while the mint region is the roomiest area on the grid with 14 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 2 squares, is under far more pressure than mint with 14. A 12-square gap like this one rewards players who start where the choices are fewest.

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 mint is the most scattered at 47% of its 5×6 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

Below is every color on #93 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: 2 squares across rows 1–1, columns 6–7. It never leaves row 1, so its queen is locked to that row.

Red covers 2 squares, spanning 2 rows and 1 column (rows 6–7, columns 1–1). It sits wholly inside column 1, so its queen must be in that column.

Amber occupies 6 squares within rows 1–3, columns 1–2.

Slate: 6 squares across rows 5–7, columns 5–7.

Pale yellow covers 7 squares, spanning 2 rows and 4 columns (rows 6–7, columns 2–5).

Blue occupies 12 squares within rows 1–5, columns 4–7.

Mint: 14 squares across rows 1–5, columns 1–6.

Where to start on this board

Indigo is the natural opening on #93: it is the smallest region on the grid at 2 squares, boxed into rows 1–1 and columns 6–7. 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.

Work outward to the other flat regions next. Red and pale yellow 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 #93

A quick way to find the next move is to count how many different colors touch each line. On this board, row 4 is the narrowest, touched by only 2 colors. Column 3 is the tightest column, 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 1, meeting 4 colors, is the opposite case — the busiest line on #93 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.

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 #93 is rated easy

What earns a board its rating is the shape of its opening. Here that opening offers two single-line regions, a 2-square smallest color, a tightest row touched by 2 colors, and a region-size spread of 12. 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.

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.

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 #93, start hunting for it near row 4.

Here is a shape check that gives nothing away: when #93 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

  1. The board is an N×N grid divided into N colored regions.
  2. Place exactly one queen (♛) in each row, each column, and each colored region.
  3. No two queens may touch each other — not horizontally, vertically, or diagonally.
  4. 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.
  5. There is always exactly one valid solution. Use logic, never guessing, to find it.

Full rules · Strategy library · Puzzle statistics

Questions about this puzzle

How hard is 7x7 Queens puzzle #93?

Puzzle #93 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 #93 have only one solution?

Yes. Every puzzle in the 7x7 collection, including #93, 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 #93?

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.