7x7 Queens Puzzle #73

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 8-step reasoning is written out below.

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Step-by-step solution for puzzle #73

What follows is a complete solve of puzzle #73, worked the way a person works it rather than the way a computer does. It runs to 8 deductions — 7 queen placements and 1 elimination step 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 region confined to one line.

Techniques this board needs: last square in a region, region confined to one line.

Show the full walkthrough (5 steps) — contains the solution

  1. Step 1. 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.

  2. Step 2. The mint region is down to one open square, at row 4, column 7. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 4 and column 7, the remaining mint squares, and the ring of neighbours around row 4, column 7.

  3. Step 3. Only row 7, column 6 is still open in pale yellow, and since each colour must take a queen, that settles it. Everything else in row 7, in column 6, in pale yellow and in the ring around that square is now dead.

    Puzzle #73 after step 3: 3 of 7 queens placed
    The board after step 3 — 3 of 7 queens placed.

  4. Step 4. All of the indigo region's remaining squares (3 open squares) lie in column 4. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 1 square come off.

  5. Step 5. From here the board cascades. Keep alternating the region sweep and the line sweep and 4 queens fall out in order without any new idea being needed: blue has one square left, so its queen takes row 3, column 3; indigo has one square left, so its queen takes row 1, column 4; amber has one square left, so its queen takes row 2, column 1; red has one square left, so its queen takes row 6, column 2. 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 2.

    Puzzle #73 after step 5: 7 of 7 queens placed
    The board after step 5 — 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 #73

Puzzle #73 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.

There is exactly one way to finish #73, and it has been verified. More importantly, you can reach it without ever gambling: at every stage some square is provably right or provably wrong. Boards differ only in how deep you must dig before that proof appears, and the geometry of these seven regions is what sets the depth.

How the colors divide this board

From smallest to largest, the regions on puzzle #73 are: slate (1 square), mint (3 squares), blue (5 squares), pale yellow (6 squares), amber (7 squares), red (13 squares), indigo (14 squares). An even split would hand every color 7 squares, so the slate region is running 6 squares under that average while the indigo 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 slate, with 1 square, is under far more pressure than indigo with 14. A 13-square gap like this one rewards players who start where the choices are fewest.

Shape matters as much as size. The slate region is the most compact color here, filling 100% of the 1×1 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.

Slate covers 1 square, spanning 1 row and 1 column (rows 5–5, columns 5–5). It never leaves row 5, so its queen is locked to that row.

Mint occupies 3 squares within rows 4–5, columns 6–7.

Blue: 5 squares across rows 2–4, columns 1–3.

Pale yellow covers 6 squares, spanning 3 rows and 3 columns (rows 5–7, columns 5–7).

Amber occupies 7 squares within rows 1–3, columns 1–3.

Red: 13 squares across rows 5–7, columns 1–5.

Indigo covers 14 squares, spanning 4 rows and 4 columns (rows 1–4, columns 4–7).

Where to start on this board

Slate is the natural opening on #73: it is the smallest region on the grid at 1 square, boxed into rows 5–5 and columns 5–5. Since one of those squares must hold a queen, that block of 1 row and 1 column is the most contested part of the board.

Because slate never leaves row 5, its queen must be in that row — and that instantly settles row 5 for everyone else. Sweep along it and X out every square that is not slate. 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 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 #73

A quick way to find the next move is to count how many different colors touch each line. On this board, rows 1, 6 and 7 are the narrowest, touched by only 2 colors. Column 4 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 5, meeting 4 colors, is the opposite case — the busiest line on #73 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 #73 is rated easy

Ratings track how generous the opening is. On #73 you get two regions pinned to a single row or column, a smallest color of 1 square, a tightest row crossed by 2 colors, and a 13-square gap between the largest and smallest regions. Those four numbers largely explain the easy label.

The scale has nothing to do with maths or luck — every puzzle here is solvable by deduction and has exactly one answer. It measures reasoning depth: how many eliminations must stack up before a placement becomes provable. That depth is what separates a easy board from the rest.

Stuck on #73 despite the easy rating? The odds strongly favour a bookkeeping error over a hard chain of logic. Re-check each placed queen for its complete set of eliminations, paying particular attention to the four diagonal squares — those are the ones that get overlooked, and one of them is usually sitting on the answer.

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 #73, start hunting for it near row 1.

Here is a shape check that gives nothing away: when #73 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.

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Questions about this puzzle

How hard is 7x7 Queens puzzle #73?

Puzzle #73 is rated easy. 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 #73 have only one solution?

Yes. Every puzzle in the 7x7 collection, including #73, 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 #73?

Start with the slate region — the most constrained color on this board, with 1 square spanning rows 5–5 and columns 5–5. Narrowing the smallest region first removes the most squares elsewhere on the grid.