7x7 Queens Puzzle #112

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 13-step reasoning is written out below.

Previous puzzle · All 7x7 puzzles · Next puzzle

Step-by-step solution for puzzle #112

What follows is a complete solve of puzzle #112, 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 region shadow.

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

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

  1. Step 1. Indigo cannot leave row 1 — every one of its open squares (3 open squares) sits there. That row belongs to indigo, so every square on it owned by another colour is dead: 5 squares in all.

  2. Step 2. Amber is down to 5 candidates in rows 2–4, columns 5–7, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about amber itself.

  3. Step 3. The mint region has 5 squares left, spread across rows 4–7, columns 2 and 3. You do not need to know which of them takes the queen: every one of those options attacks the same 2 squares, so they can be crossed out now.

  4. Step 4. Wherever red 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.

    Puzzle #112 after step 4: 0 of 7 queens placed
    The board after step 4 — 0 of 7 queens placed.

  5. Step 5. Slate is down to 4 candidates in rows 5–7, columns 6 and 7, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about slate itself.

  6. Step 6. All of the pale yellow region's remaining squares (2 open squares) lie in row 7. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 5 squares come off.

  7. 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 5; slate has one square left, so its queen takes row 5, column 7; 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; blue has one square left, so its queen takes row 3, column 4; indigo has one square left, so its queen takes row 1, column 3; 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.

    Puzzle #112 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 #112

This is puzzle number 112 in the 7x7 collection, rated easy. The grid holds 49 squares split between seven colored regions, and a finished board carries seven queens — one in every row, one in every column, one in every color, and never two of them touching, diagonals included.

As with every puzzle in this collection, #112 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 #112 are: indigo (3 squares), red (3 squares), pale yellow (3 squares), mint (5 squares), slate (5 squares), amber (7 squares), blue (23 squares). An even split would hand every color 7 squares, so the indigo region is running 4 squares under that average while the blue region is the roomiest area on the grid with 23 squares.

Every color takes one queen and one only, whatever its size — which is why the 20 square difference between indigo and blue 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 1×3 box that encloses it, while blue is the most scattered at 55% of its 7×6 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 #112 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 covers 3 squares, spanning 1 row and 3 columns (rows 1–1, columns 3–5). It never leaves row 1, so its queen is locked to that row.

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

Pale yellow: 3 squares across rows 6–7, columns 1–2.

Mint covers 5 squares, spanning 4 rows and 2 columns (rows 4–7, columns 2–3).

Slate occupies 5 squares within rows 5–7, columns 6–7.

Amber: 7 squares across rows 1–4, columns 5–7.

Blue covers 23 squares, spanning 7 rows and 6 columns (rows 1–7, columns 1–6).

Where to start on this board

Open on the tightest color. Here that is indigo, confined to 3 squares between rows 1 and 1 and columns 3 and 5. Its queen has nowhere else to go, which means those 1 row and 3 columns carry more constraint than anywhere else on #112.

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. Pale yellow 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 #112

A quick way to find the next move is to count how many different colors touch each line. On this board, rows 2 and 3 are the narrowest, touched by only 2 colors. Columns 1, 4 and 7 are the tightest columns, with 2 colors.

A line with few colors is a line close to resolving. Where only 2 colors appear, one of them owns the row outright and the others must fit into the remaining 6 rows. Row 7 is the crowded extreme at 5 colors — worth revisiting later, not now.

Working through the middle game

The middle of #112 is where careless play costs time. Every queen you place kills a row, a column and the eight surrounding squares; if you do not mark all of that immediately, you will later "discover" a move that was available several turns ago. Mark first, then look.

With seven queens to seat and seven regions competing over 49 squares, keep two questions in rotation. Does any region now have exactly one open square left? That queen is forced. Does any row or column now have exactly one open square left? That queen is forced too. Alternating between the region view and the row-and-column view is what keeps a solve moving, and it is the clearest difference between players who finish 7x7 boards quickly and players who stall halfway.

Say the reason out loud: "this region has one square left", "this column has one square left". If no such sentence is available, the eliminating is not finished. One more pass of X marks is almost always quicker than committing to a placement you cannot defend.

Why puzzle #112 is rated easy

What earns a board its rating is the shape of its opening. Here that opening offers one single-line region, a 3-square smallest color, a tightest row touched by 2 colors, and a region-size spread of 20. Lopsided grids with flat regions fall quickly; balanced ones like this take more patience.

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 #112 is row 2.

A non-spoiling distribution check: solved, #112 carries 3 queens on the perimeter against 4 queens inside, 1 of them cornered. Because no two queens may touch, real solutions always look fairly evenly spread — a lopsided board in progress is a warning sign.

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 #112?

Puzzle #112 is rated easy. Its smallest color region holds 3 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 #112 have only one solution?

Yes. Every puzzle in the 7x7 collection, including #112, 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 #112?

Start with the indigo region — the most constrained color on this board, with 3 squares spanning rows 1–1 and columns 3–5. Narrowing the smallest region first removes the most squares elsewhere on the grid.