7x7 Queens Puzzle #168

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.

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Step-by-step solution for puzzle #168

What follows is a complete solve of puzzle #168, 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 region shadow.

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

Show the full walkthrough (6 steps) — contains the solution

  1. Step 1. Wherever blue ends up among its 5 squares, the same squares fall within reach of it — 1 square in total, impossible regardless of how the colour resolves.

  2. Step 2. All of the red region's remaining squares (2 open squares) lie in row 6. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 9 squares come off.

  3. Step 3. Pale yellow cannot leave row 7 — every one of its open squares (2 open squares) sits there. That row belongs to pale yellow, so every square on it owned by another colour is dead: 3 squares in all.

    Puzzle #168 after step 3: 0 of 7 queens placed
    The board after step 3 — 0 of 7 queens placed.

  4. Step 4. All of the slate region's remaining squares (2 open squares) lie in row 5. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 4 squares come off.

  5. Step 5. Mint cannot leave row 4 — every one of its open squares (4 open squares) sits there. That row belongs to mint, so every square on it owned by another colour is dead: 2 squares in all.

  6. Step 6. 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: blue has one square left, so its queen takes row 3, column 1; 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; red has one square left, so its queen takes row 6, column 5; pale yellow has one square left, so its queen takes row 7, column 7; mint has one square left, so its queen takes row 4, column 6; amber has one square left, so its queen takes row 2, 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 2, column 4.

    Puzzle #168 after step 6: 7 of 7 queens placed
    The board after step 6 — 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 #168

This is puzzle number 168 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.

Like every board on this site, #168 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 #168 are: red (2 squares), blue (5 squares), pale yellow (5 squares), indigo (8 squares), slate (8 squares), mint (9 squares), amber (12 squares). An even split would hand every color 7 squares, so the red region is running 5 squares under that average while the amber region is the roomiest area on the grid with 12 squares.

One queen per color, regardless of acreage: that is what turns this uneven split into a solving order. Red is working with 2 squares while amber has 12 to spare, a gap of 10. Attack the cramped end and the roomy regions tend to resolve themselves.

Shape matters as much as size. The amber region is the most compact color here, filling 100% of the 3×4 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

Here is the full footprint of every color on puzzle #168, smallest first. Reading these spans before you place anything is the quickest way to see which parts of the grid are genuinely contested.

Red: 2 squares across rows 6–6, columns 4–5. It never leaves row 6, so its queen is locked to that row.

Blue covers 5 squares, spanning 3 rows and 3 columns (rows 3–5, columns 1–3).

Pale yellow occupies 5 squares within rows 6–7, columns 4–7.

Indigo: 8 squares across rows 1–3, columns 1–3.

Slate covers 8 squares, spanning 3 rows and 3 columns (rows 5–7, columns 1–3).

Mint occupies 9 squares within rows 4–6, columns 4–7.

Amber: 12 squares across rows 1–3, columns 4–7.

Where to start on this board

Open on the tightest color. Here that is red, confined to 2 squares between rows 6 and 6 and columns 4 and 5. Its queen has nowhere else to go, which means those 1 row and 2 columns carry more constraint than anywhere else on #168.

Because red never leaves row 6, its queen must be in that row — and that instantly settles row 6 for everyone else. Sweep along it and X out every square that is not red. 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 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 #168

A quick way to find the next move is to count how many different colors touch each line. On this board, rows 1, 2, 4 and 7 are the narrowest, touched by only 2 colors. Columns 1, 2, 3, 6 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 6 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

The middle of #168 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 #168 is rated easy

The rating reflects how much the board concedes up front. Puzzle #168 has one region 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 10 squares. Flat, lopsided boards open quickly; even, sprawling ones make you earn the first placement.

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.

If #168 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.

Whatever the grid size, the pairing rule is the technique to internalise. When a pair of regions is boxed into the same pair of rows, they split those rows between them and nobody else may enter — and the same holds for columns, or for any n regions confined to n lines. Look for an instance of it around row 1 on this board.

As a sanity check rather than a spoiler: the finished solution to #168 puts 3 queens on the outer border and 4 queens in the interior, 1 of them in an actual 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

  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 #168?

Puzzle #168 is rated easy. 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 #168 have only one solution?

Yes. Every puzzle in the 7x7 collection, including #168, 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 #168?

Start with the red region — the most constrained color on this board, with 2 squares spanning rows 6–6 and columns 4–5. Narrowing the smallest region first removes the most squares elsewhere on the grid.