10x10 Queens Puzzle #253
Difficulty: medium. 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 19-step reasoning is written out below.
Previous puzzle · All 10x10 puzzles · Next puzzle
Step-by-step solution for puzzle #253
What follows is a complete solve of puzzle #253, worked the way a person works it rather than the way a computer does. It runs to 19 deductions — 10 queen placements and 9 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 columns.
Techniques this board needs: last square in a region, region shadow, region confined to one line, pairing argument on rows, pairing argument on columns.
Show the full walkthrough (11 steps) — contains the solution
Step 1. Only row 10, column 1 is still open in sea green, and since each colour must take a queen, that settles it. That clears row 10, column 1, the rest of the sea green region and every square adjacent to it — diagonals included.
Step 2. Amber is down to 3 candidates in rows 1 and 2, columns 9 and 10, and they overlap enough to cover 2 squares elsewhere. Cross those out without deciding anything about amber itself.
Step 3. The slate region has 5 squares left, spread across rows 5–7, columns 2–4. You do not need to know which of them takes the queen: every one of those options attacks the same 1 square, so they can be crossed out now.
Step 4. All of the khaki region's remaining squares (3 open squares) lie in row 8. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 8 squares come off.
The board after step 4 — 1 of 10 queens placed. Step 5. Slate is down to 4 candidates in rows 5 and 6, columns 2–4, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about slate itself.
Step 6. All of the orange region's remaining squares (2 open squares) lie in row 9. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 6 squares come off.
Step 7. Khaki cannot leave row 8 — every one of its open squares (2 open squares) sits there. That row belongs to khaki, so every square on it owned by another colour is dead: 1 square in all.
The board after step 7 — 1 of 10 queens placed. Step 8. Here is the pairing argument. The indigo and amber regions have no open squares outside rows 1 and 2 — 2 colours confined to 2 rows. Between them they must take one row each, in some order, so every other colour is shut out of all of them: 9 squares come off in one stroke.
Step 9. The mint region has 3 squares left, spread across rows 3 and 4, columns 2 and 3. You do not need to know which of them takes the queen: every one of those options attacks the same 1 square, so they can be crossed out now.
Step 10. Here is the pairing argument. The mint and khaki regions have no open squares outside columns 2 and 3 — 2 colours confined to 2 columns. Between them they must take one column each, in some order, so every other colour is shut out of all of them: 3 squares come off in one stroke.
Step 11. From here the board cascades. Keep alternating the region sweep and the line sweep and 9 queens fall out in order without any new idea being needed: slate has one square left, so its queen takes row 5, column 4; orange has one square left, so its queen takes row 9, column 5; pale yellow has one square left, so its queen takes row 7, column 6; blue has one square left, so its queen takes row 3, column 7; indigo has one square left, so its queen takes row 1, column 8; amber has one square left, so its queen takes row 2, column 10; mint has one square left, so its queen takes row 4, column 2; red has one square left, so its queen takes row 6, column 9; khaki has one square left, so its queen takes row 8, column 3. 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 3.
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 #253
Puzzle #253 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, #253 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 #253 are: sea green (1 square), amber (3 squares), khaki (3 squares), slate (5 squares), indigo (6 squares), orange (9 squares), pale yellow (11 squares), blue (16 squares), mint (20 squares), red (26 squares). An even split would hand every color 10 squares, so the sea green region is running 9 squares under that average while the red region is the roomiest area on the grid with 26 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 sea green, with 1 square, is under far more pressure than red with 26. A 25-square gap like this one rewards players who start where the choices are fewest.
Shape matters as much as size. The khaki region is the most compact color here, filling 100% of the 1×3 box that encloses it, while pale yellow is the most scattered at 55% of its 5×4 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
Below is every color on #253 with its exact reach, smallest region first. It is worth a slow read: the spans reveal which rows and columns several regions are fighting over.
Sea green covers 1 square, spanning 1 row and 1 column (rows 10–10, columns 1–1). It never leaves row 10, so its queen is locked to that row.
Amber occupies 3 squares within rows 1–2, columns 9–10.
Khaki: 3 squares across rows 8–8, columns 2–4. It never leaves row 8, so its queen is locked to that row.
Slate covers 5 squares, spanning 3 rows and 3 columns (rows 5–7, columns 2–4).
Indigo occupies 6 squares within rows 1–2, columns 5–9.
Orange: 9 squares across rows 8–10, columns 2–5.
Pale yellow covers 11 squares, spanning 5 rows and 4 columns (rows 6–10, columns 4–7).
Blue occupies 16 squares within rows 2–6, columns 3–7.
Mint: 20 squares across rows 1–9, columns 1–4.
Red covers 26 squares, spanning 8 rows and 4 columns (rows 3–10, columns 7–10).
Where to start on this board
Begin where the choices are fewest. On this board that means sea green, which owns just 1 square inside a 1×1 window running from row 10 to row 10 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 sea green never leaves row 10, its queen must be in that row — and that instantly settles row 10 for everyone else. Sweep along it and X out every square that is not sea green. 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. Khaki, indigo and amber 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 #253
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 1, 3 and 4 are the narrowest, touched by only 3 colors. Columns 1, 8 and 10 are the tightest columns, with 2 colors.
The fewer colors a line touches, the sooner it surrenders its queen. A row meeting just 3 colors has to be claimed by one of them, which pushes every remaining region into the other 9 rows. Row 8, meeting 5 colors, is the opposite case — the busiest line on #253 and the last one you should expect to crack.
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.
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.
A placement without a reason is a guess. Because this board has exactly one solution, a guess that happens to be wrong will not announce itself for several moves — and unwinding it is slower than simply finishing the eliminations first.
Why puzzle #253 is rated medium
What earns a board its rating is the shape of its opening. Here that opening offers three single-line regions, a 1-square smallest color, a tightest row touched by 3 colors, and a region-size spread of 25. Lopsided grids with flat regions fall quickly; balanced ones like this take more patience.
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 #253 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 #253, start hunting for it near column 1.
Here is a shape check that gives nothing away: when #253 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.
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.
Full rules · Strategy library · Puzzle statistics
Questions about this puzzle
How hard is 10x10 Queens puzzle #253?
Puzzle #253 is rated medium. 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 10x10 puzzle #253 have only one solution?
Yes. Every puzzle in the 10x10 collection, including #253, 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 #253?
Start with the sea green region — the most constrained color on this board, with 1 square spanning rows 10–10 and columns 1–1. Narrowing the smallest region first removes the most squares elsewhere on the grid.