8x8 Queens Puzzle #96

About 8x8 Queens puzzle #96

This is puzzle number 96 in the 8x8 collection, rated hard. The grid holds 64 squares split between eight colored regions, and a finished board carries eight 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, #96 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 #96 are: blue (2 squares), khaki (2 squares), pale yellow (3 squares), indigo (4 squares), mint (11 squares), amber (13 squares), red (13 squares), slate (16 squares). An even split would hand every color 8 squares, so the blue region is running 6 squares under that average while the slate region is the roomiest area on the grid with 16 squares.

Every color takes one queen and one only, whatever its size — which is why the 14 square difference between blue and slate 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 1×4 box that encloses it, while red is the most scattered at 52% of its 5×5 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.

Blue: 2 squares across rows 2–3, columns 1–1. It sits wholly inside column 1, so its queen must be in that column.

Khaki covers 2 squares, spanning 1 row and 2 columns (rows 8–8, columns 5–6). It never leaves row 8, so its queen is locked to that row.

Pale yellow occupies 3 squares within rows 7–8, columns 7–8.

Indigo: 4 squares across rows 1–1, columns 5–8. It never leaves row 1, so its queen is locked to that row.

Mint covers 11 squares, spanning 6 rows and 3 columns (rows 2–7, columns 6–8).

Amber occupies 13 squares within rows 1–4, columns 1–6.

Red: 13 squares across rows 4–8, columns 3–7.

Slate covers 16 squares, spanning 6 rows and 4 columns (rows 3–8, columns 1–4).

Where to start on this board

The most constrained color is where a solve should begin, and on #96 that is blue with 2 squares. It reaches from row 2 to row 3 and from column 1 to column 1 — 2 rows by 1 column. One queen has to live inside that footprint no matter what else happens, which makes those lines the busiest real estate on the board.

Because blue stays inside column 1, its queen belongs to that column and no other region may use it. Cross out the rest of column 1 straight away. Any color that was relying on those squares now has a visibly smaller footprint, and that shrinkage is where your second deduction comes from.

Work outward to the other flat regions next. Indigo, khaki 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 #96

A quick way to find the next move is to count how many different colors touch each line. On this board, row 1 is the narrowest, touched by only 2 colors. Column 2 is the tightest column, with 2 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 7 rows. By contrast row 8 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.

The whole middle game reduces to two sweeps. Sweep the eight colors looking for one with a single square left; sweep the eight rows and eight columns looking for the same. Each sweep feeds the next, and switching between them deliberately — rather than drifting — is what separates a fast 8x8 solve from a stalled one.

Resist the plausible-looking queen. On #96 every correct placement has a stated reason behind it, and any move you cannot justify is a guess wearing a disguise. Backing out of a wrong guess on a single-solution board takes far longer than finding the real deduction would have.

Why puzzle #96 is rated hard

Ratings track how generous the opening is. On #96 you get three regions pinned to a single row or column, a smallest color of 2 squares, a tightest row crossed by 2 colors, and a 14-square gap between the largest and smallest regions. Those four numbers largely explain the hard 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 hard board from the rest.

If #96 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.

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 #96 is row 1.

As a sanity check rather than a spoiler: the finished solution to #96 puts 4 queens on the outer border and 4 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.