10x10 Queens Puzzle #266
Difficulty: easy. Place 10 queens on this 10x10 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 18-step reasoning is written out below.
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Step-by-step solution for puzzle #266
What follows is a complete solve of puzzle #266, worked the way a person works it rather than the way a computer does. It runs to 18 deductions — 10 queen placements and 8 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 pairing argument on rows.
Techniques this board needs: region confined to one line, region shadow, last square in a region, pairing argument on rows, line confined to one region, last square in a column.
Show the full walkthrough (11 steps) — contains the solution
Step 1. Indigo cannot leave row 1 — every one of its open squares (2 open squares) sits there. That row belongs to indigo, so every square on it owned by another colour is dead: 10 squares in all.
Step 2. Orange is down to 5 candidates in rows 8–10, columns 8–10, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about orange itself.
Step 3. Only row 10, column 10 is still open in sea green, and since each colour must take a queen, that settles it. Everything else in row 10, in column 10, in sea green and in the ring around that square is now dead.
Step 4. Wherever orange ends up among its 2 squares, the same squares fall within reach of it — 3 squares in total, impossible regardless of how the colour resolves.
The board after step 4 — 1 of 10 queens placed. Step 5. Khaki and orange are now boxed into rows 8 and 9 and nothing else. That is 2 colours needing 2 rows, so they fill those rows between them — which locks every remaining colour out and removes 6 squares at once.
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 2; indigo has one square left, so its queen takes row 1, column 1; red has one square left, so its queen takes row 6, column 4; slate has one square left, so its queen takes row 5, column 6. 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 5, column 6.
Step 7. Wherever blue ends up among its 2 squares, the same squares fall within reach of it — 3 squares in total, impossible regardless of how the colour resolves.
The board after step 7 — 5 of 10 queens placed. Step 8. Amber cannot leave row 2 — every one of its open squares (2 open squares) sits there. That row belongs to amber, so every square on it owned by another colour is dead: 3 squares in all.
Step 9. Every open square left in column 3 (2 open squares) belongs to the mint region. Since that column must contain a queen, mint is the colour that supplies it — so mint squares anywhere else on the board are out, 1 square in all.
Step 10. Column 5 has only khaki squares left (2 open squares). The column needs a queen and only khaki can provide one, which pins that colour to this column and kills its squares elsewhere: 1 square.
Step 11. From here the board cascades. Keep alternating the region sweep and the line sweep and 5 queens fall out in order without any new idea being needed: column 7 is down to one square, putting a queen on row 3, column 7; amber has one square left, so its queen takes row 2, column 9; mint has one square left, so its queen takes row 4, column 3; orange has one square left, so its queen takes row 9, column 8; khaki has one square left, so its queen takes row 8, column 5. 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 8, column 5.
The board after step 11 — 10 of 10 queens placed.
That completes the board: 10 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 10x10 Queens puzzle #266
Board #266 of the 10x10 bank carries a easy rating. Its 100 squares are shared between ten colored regions, and the solution places ten 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, #266 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 #266 are: indigo (2 squares), sea green (2 squares), orange (5 squares), slate (9 squares), red (9 squares), pale yellow (10 squares), amber (13 squares), blue (14 squares), khaki (14 squares), mint (22 squares). An even split would hand every color 10 squares, so the indigo region is running 8 squares under that average while the mint region is the roomiest area on the grid with 22 squares.
Why does the split matter? Because a region's square count has no bearing on how many queens it gets — the answer is always one. So indigo, with 2 squares, is under far more pressure than mint with 22. A 20-square gap like this one rewards players who start where the choices are fewest.
Look at arrangement as well as area. Indigo is the densest region on this grid at 100% of a 1×2 frame; orange is the loosest, occupying only 56% of its 3×3 frame. The loose one reaches into more rows and columns, which is exactly why it usually settles last.
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.
Indigo occupies 2 squares within rows 1–1, columns 1–2. It never leaves row 1, so its queen is locked to that row.
Sea green: 2 squares across rows 9–10, columns 10–10. It sits wholly inside column 10, so its queen must be in that column.
Orange covers 5 squares, spanning 3 rows and 3 columns (rows 8–10, columns 8–10).
Slate occupies 9 squares within rows 5–7, columns 3–7.
Red: 9 squares across rows 5–7, columns 1–5.
Pale yellow covers 10 squares, spanning 4 rows and 3 columns (rows 7–10, columns 1–3).
Amber occupies 13 squares within rows 1–4, columns 6–10.
Blue: 14 squares across rows 3–7, columns 6–10.
Khaki covers 14 squares, spanning 3 rows and 5 columns (rows 8–10, columns 4–8).
Mint occupies 22 squares within rows 1–5, columns 1–7.
Where to start on this board
The most constrained color is where a solve should begin, and on #266 that is indigo with 2 squares. It reaches from row 1 to row 1 and from column 1 to column 2 — 1 row by 2 columns. 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 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.
Work outward to the other flat regions next. Sea green 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 #266
A quick way to find the next move is to count how many different colors touch each line. On this board, row 2 is the narrowest, touched by only 2 colors. Column 9 is the tightest column, 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 9 rows. By contrast row 10 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
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.
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 #266 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 #266 is rated easy
Ratings track how generous the opening is. On #266 you get two regions pinned to a single row or column, a smallest color of 2 squares, a tightest row crossed by 2 colors, and a 20-square gap between the largest and smallest regions. Those four numbers largely explain the easy 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 easy board from the rest.
If #266 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.
Learn the pairing argument and you will use it on every board, this one included. If two colors can only sit inside the same two rows, between them they consume both rows and every other color is shut out. It generalises to any matching count — three colors across three rows, four across four. On #266, start hunting for it near row 2.
As a sanity check rather than a spoiler: the finished solution to #266 puts 2 queens on the outer border and 8 queens in the interior, 2 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
- The board is an N×N grid divided into N colored regions.
- Place exactly one queen (♛) in each row, each column, and each colored region.
- No two queens may touch each other — not horizontally, vertically, or diagonally.
- 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.
- 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 10x10 Queens puzzle #266?
Puzzle #266 is rated easy. Its smallest color region holds 2 squares, its tightest row is touched by 2 colors, and two of its regions are confined to a single row or column, which gives you a forced move early.
Does 10x10 puzzle #266 have only one solution?
Yes. Every puzzle in the 10x10 collection, including #266, has been verified to have exactly one valid arrangement of ten queens, and it can always be reached by logic alone — no guessing or backtracking needed.
Where should I place my first queen on puzzle #266?
Start with the indigo region — the most constrained color on this board, with 2 squares spanning rows 1–1 and columns 1–2. Narrowing the smallest region first removes the most squares elsewhere on the grid.