7x7 Queens Puzzle #170

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 9-step reasoning is written out below.

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Step-by-step solution for puzzle #170

What follows is a complete solve of puzzle #170, worked the way a person works it rather than the way a computer does. It runs to 9 deductions — 7 queen placements and 2 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 confined to one line.

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

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

  1. Step 1. Only row 4, column 1 is still open in mint, and since each colour must take a queen, that settles it. That clears row 4, column 1, the rest of the mint region and every square adjacent to it — diagonals included.

  2. Step 2. The red region is down to one open square, at row 6, column 2. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 6 and column 2, the remaining red squares, and the ring of neighbours around row 6, column 2.

  3. Step 3. Only row 2, column 3 is still open in amber, and since each colour must take a queen, that settles it. Everything else in row 2, in column 3, in amber and in the ring around that square is now dead.

    Puzzle #170 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 (2 open squares) lie in row 1. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 1 square come off.

  5. Step 5. Blue cannot leave column 7 — 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: 1 square in all.

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

    Puzzle #170 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 #170

Board #170 of the 7x7 bank carries a hard rating. Its 49 squares are shared between seven colored regions, and the solution places seven queens: one per row, one per column, one per region, none of them side by side or corner to corner.

There is exactly one way to finish #170, 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 #170 are: mint (1 square), pale yellow (3 squares), indigo (4 squares), red (5 squares), amber (7 squares), blue (7 squares), slate (22 squares). An even split would hand every color 7 squares, so the mint region is running 6 squares under that average while the slate region is the roomiest area on the grid with 22 squares.

That imbalance is the first thing to read, because every region takes exactly one queen regardless of how much space it owns. Mint has only 1 place to put its queen; slate has 22. The spread between them on this board is 21 squares, and the wider that spread runs, the more it pays to solve from the small end inward.

Square count is only half the story — how a color is arranged counts too. Indigo is the tidiest shape on #170, packing 100% of its 1×4 bounding box, whereas blue straggles across its 6×2 box at just 58%. Tidy blocks are easy to work around; scattered ones touch more lines and resist resolution.

Region by region

Here is the full footprint of every color on puzzle #170, smallest first. Reading these spans before you place anything is the quickest way to see which parts of the grid are genuinely contested.

Mint occupies 1 square within rows 4–4, columns 1–1. It never leaves row 4, so its queen is locked to that row.

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

Indigo covers 4 squares, spanning 1 row and 4 columns (rows 1–1, columns 3–6). It never leaves row 1, so its queen is locked to that row.

Red occupies 5 squares within rows 5–7, columns 1–2.

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

Blue covers 7 squares, spanning 6 rows and 2 columns (rows 1–6, columns 6–7).

Slate occupies 22 squares within rows 2–7, columns 2–6.

Where to start on this board

Begin where the choices are fewest. On this board that means mint, which owns just 1 square inside a 1×1 window running from row 4 to row 4 and column 1 to column 1. A queen is guaranteed somewhere in there, so every line that window crosses is under pressure from the very first move.

Because mint never leaves row 4, its queen must be in that row — and that instantly settles row 4 for everyone else. Sweep along it and X out every square that is not mint. 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. Indigo 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 #170

A quick way to find the next move is to count how many different colors touch each line. On this board, rows 1, 2, 3, 4, 5 and 7 are the narrowest, touched by only 3 colors. Columns 4, 5 and 7 are the tightest columns, with 2 colors.

Those lines matter because a row touched by few colors gives its queen away sooner. If a row meets only 3 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

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.

Keep alternating between two views of the board. In the region view you ask which of the seven colors is down to one open square. In the line view you ask the same of each row and column. Both produce forced queens, and each placement refreshes the other view, so cycling between them deliberately is how a 7x7 board unwinds.

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 #170 is rated hard

The rating reflects how much the board concedes up front. Puzzle #170 has three regions confined to a single row or column, its smallest color holds 1 square, its tightest row meets just 3 colors, and the gap between its largest and smallest regions is 21 squares. Flat, lopsided boards open quickly; even, sprawling ones make you earn the first placement.

Rating is a measure of chain length, not of chance. With one guaranteed solution and no guessing required, the only thing that changes across the collection is how many eliminations you must link together before a queen is provably forced.

Stuck on #170 despite the hard 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.

One pattern is worth learning at every size, and it is available here. When two regions can only fit inside the same two rows, they must take one row each — which locks every other region out of both. The same argument works for columns, and for any matching count: three regions sharing three rows, four sharing four. Spotting these pairings turns a slow grind into a quick cascade, and on #170 the place to look for one is around column 4.

As a sanity check rather than a spoiler: the finished solution to #170 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

  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 #170?

Puzzle #170 is rated hard. Its smallest color region holds 1 square, its tightest row is touched by 3 colors, and three of its regions are confined to a single row or column, which gives you a forced move early.

Does 7x7 puzzle #170 have only one solution?

Yes. Every puzzle in the 7x7 collection, including #170, 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 #170?

Start with the mint region — the most constrained color on this board, with 1 square spanning rows 4–4 and columns 1–1. Narrowing the smallest region first removes the most squares elsewhere on the grid.