10x10 Queens Puzzle #133

About 10x10 Queens puzzle #133

Puzzle #133 is one of the medium-rated boards in the 10x10 set. Ten colors divide its 100 squares, and you win by placing ten queens so that each row, each column and each color holds exactly one, with no two queens adjacent in any direction.

Like every board on this site, #133 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 #133 are: orange (1 square), sea green (2 squares), indigo (3 squares), mint (5 squares), blue (10 squares), red (12 squares), pale yellow (14 squares), slate (17 squares), amber (18 squares), khaki (18 squares). An even split would hand every color 10 squares, so the orange region is running 9 squares under that average while the khaki region is the roomiest area on the grid with 18 squares.

Every color takes one queen and one only, whatever its size — which is why the 17 square difference between orange and khaki 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 slate is the most scattered at 57% of its 6×5 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

Here is the full footprint of every color on puzzle #133, smallest first. Reading these spans before you place anything is the quickest way to see which parts of the grid are genuinely contested.

Orange covers 1 square, spanning 1 row and 1 column (rows 9–9, columns 4–4). It never leaves row 9, so its queen is locked to that row.

Sea green occupies 2 squares within rows 9–10, columns 1–1. It sits wholly inside column 1, so its queen must be in that column.

Indigo: 3 squares across rows 1–1, columns 8–10. It never leaves row 1, so its queen is locked to that row.

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

Blue occupies 10 squares within rows 2–7, columns 9–10.

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

Pale yellow covers 14 squares, spanning 4 rows and 5 columns (rows 7–10, columns 6–10).

Slate occupies 17 squares within rows 2–7, columns 5–9.

Amber: 18 squares across rows 1–4, columns 2–7.

Khaki covers 18 squares, spanning 5 rows and 6 columns (rows 6–10, columns 1–6).

Where to start on this board

Begin where the choices are fewest. On this board that means orange, which owns just 1 square inside a 1×1 window running from row 9 to row 9 and column 4 to column 4. A queen is guaranteed somewhere in there, so every line that window crosses is under pressure from the very first move.

Because orange never leaves row 9, its queen must be in that row — and that instantly settles row 9 for everyone else. Sweep along it and X out every square that is not orange. 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 sea green 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 #133

A quick way to find the next move is to count how many different colors touch each line. On this board, row 8 is the narrowest, touched by only 2 colors. Columns 1, 2, 3, 7, 8 and 10 are the tightest columns, with 3 colors.

The fewer colors a line touches, the sooner it surrenders its queen. A row meeting just 2 colors has to be claimed by one of them, which pushes every remaining region into the other 9 rows. Row 7, meeting 5 colors, is the opposite case — the busiest line on #133 and the last one you should expect to crack.

Working through the middle game

After the first few queens the puzzle becomes bookkeeping. A placed queen wipes its row, its column and every square it touches — as many as eight neighbours — so the space collapses quickly. Record those eliminations on the board instead of carrying them in your head, and the next forced move tends to announce itself.

Two checks, run alternately, will carry you through the 100 squares of this grid. First: has any of the ten regions been reduced to a single open square? Second: has any row or column? Either answer forces a queen. Players who stall on 10x10 boards almost always run one of those checks and forget the other.

Resist the plausible-looking queen. On #133 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 #133 is rated medium

The rating reflects how much the board concedes up front. Puzzle #133 has four regions confined to a single row or column, its smallest color holds 1 square, its tightest row meets just 2 colors, and the gap between its largest and smallest regions is 17 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 medium board from the rest.

If #133 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 10x10

At 10x10 a full re-scan after every move starts to get slow, so work locally instead. Once a queen goes down, check only the regions, rows and columns that placement actually touched — that is where new information appeared. Fall back to a complete sweep only when the local pass turns up nothing, and your solve times will drop noticeably.

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 #133 is row 8.

Here is a shape check that gives nothing away: when #133 is solved, 3 queens sit on the outer edge of the grid and 7 sit inside it, with 1 queen in a corner. A work-in-progress board that clusters its queens in one quadrant while leaving others bare is usually carrying a mistake.