8x8 Queens Puzzle #170

About 8x8 Queens puzzle #170

Board #170 of the 8x8 bank carries a medium rating. Its 64 squares are shared between eight colored regions, and the solution places eight queens: one per row, one per column, one per region, none of them side by side or corner to corner.

Like every board on this site, #170 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 #170 are: indigo (2 squares), slate (5 squares), khaki (5 squares), amber (6 squares), mint (8 squares), red (9 squares), pale yellow (9 squares), blue (20 squares). An even split would hand every color 8 squares, so the indigo region is running 6 squares under that average while the blue region is the roomiest area on the grid with 20 squares.

That imbalance is the first thing to read, because every region takes exactly one queen regardless of how much space it owns. Indigo has only 2 places to put its queen; blue has 20. The spread between them on this board is 18 squares, and the wider that spread runs, the more it pays to solve from the small end inward.

Look at arrangement as well as area. Indigo is the densest region on this grid at 100% of a 1×2 frame; amber is the loosest, occupying only 50% of its 3×4 frame. The loose one reaches into more rows and columns, which is exactly why it usually settles last.

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.

Indigo occupies 2 squares within rows 1–1, columns 5–6. It never leaves row 1, so its queen is locked to that row.

Slate: 5 squares across rows 4–7, columns 1–2.

Khaki covers 5 squares, spanning 3 rows and 3 columns (rows 6–8, columns 1–3).

Amber occupies 6 squares within rows 1–3, columns 1–4.

Mint: 8 squares across rows 2–5, columns 2–4.

Red covers 9 squares, spanning 3 rows and 4 columns (rows 6–8, columns 5–8).

Pale yellow occupies 9 squares within rows 5–8, columns 3–5.

Blue: 20 squares across rows 1–6, columns 4–8.

Where to start on this board

Indigo is the natural opening on #170: it is the smallest region on the grid at 2 squares, boxed into rows 1–1 and columns 5–6. 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.

No region here is pinned to a shallow band of rows, so turn the same idea sideways: indigo and slate span only two columns. Two narrow regions sharing the same two columns take one column each and lock everyone else out of both, which is usually enough to crack a board that offers no free opening.

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 and 8 are the narrowest, touched by only 3 colors. Columns 7 and 8 are the tightest columns, with 2 colors.

Count colors per line and you have a ranking of where to look. The narrowest rows here see only 3 colors, so one of that handful must take the row and the rest are squeezed into the other 7 rows. Row 6 sits at the far end with 5 colors crossing it; it will almost certainly be among the last to settle.

Working through the middle game

Past the opening, treat this as an elimination exercise rather than a placement exercise. Each queen takes out a row, a column and its eight neighbours, and the value of a move is measured by how much it removes. Cross everything out as you go and let the board do the remembering.

Keep alternating between two views of the board. In the region view you ask which of the eight 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 8x8 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 medium

The rating reflects how much the board concedes up front. Puzzle #170 has one region confined to a single row or column, its smallest color holds 2 squares, its tightest row meets just 3 colors, and the gap between its largest and smallest regions is 18 squares. Flat, lopsided boards open quickly; even, sprawling ones make you earn the first placement.

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.

If #170 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 8x8

At 8x8 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 7.

Use this as a rough check on your progress: the completed board has 4 queens around the border and 4 queens in the middle, and nothing in the corners. Solutions spread out; if yours is bunching up in one region of the grid, retrace a few moves.