10x10 Queens Puzzle #288
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 #288
What follows is a complete solve of puzzle #288, 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 line confined to one region.
Techniques this board needs: last square in a region, region shadow, region confined to one line, line confined to one region, last square in a column.
Show the full walkthrough (14 steps) — contains the solution
Step 1. Only row 2, column 3 is still open in amber, and since each colour must take a queen, that settles it. That clears row 2, column 3, the rest of the amber region and every square adjacent to it — diagonals included.
Step 2. The indigo region is down to one open square, at row 1, column 7. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 1 and column 7, the remaining indigo squares, and the ring of neighbours around row 1, column 7.
Step 3. The khaki region has 4 squares left, spread across rows 8–10, columns 9 and 10. You do not need to know which of them takes the queen: every one of those options attacks the same 2 squares, so they can be crossed out now.
Step 4. The sea green region is down to one open square, at row 10, column 9. Every colour holds exactly one queen, so that square is forced. Row 10 and column 9 are now spoken for, along with the squares touching that queen.
Step 5. Only row 8, column 10 is still open in khaki, and since each colour must take a queen, that settles it. That clears row 8, column 10, the rest of the khaki region and every square adjacent to it — diagonals included.
The board after step 5 — 4 of 10 queens placed. Step 6. All of the mint region's remaining squares (4 open squares) lie in column 8. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 1 square come off.
Step 7. Wherever pale yellow ends up among its 3 squares, the same squares fall within reach of it — 1 square in total, impossible regardless of how the colour resolves.
Step 8. 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: 2 squares come off.
Step 9. Only row 7, column 4 is still open in pale yellow, and since each colour must take a queen, that settles it. That clears row 7, column 4, the rest of the pale yellow region and every square adjacent to it — diagonals included.
The board after step 9 — 5 of 10 queens placed. Step 10. Wherever slate ends up among its 3 squares, the same squares fall within reach of it — 1 square in total, impossible regardless of how the colour resolves.
Step 11. Red is down to 5 candidates in rows 4–6, columns 1 and 2, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about red itself.
Step 12. The slate region has 2 squares left, spread across rows 5 and 6, columns 5 and 6. 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 13. Column 2 has only red squares left (2 open squares). The column needs a queen and only red can provide one, which pins that colour to this column and kills its squares elsewhere: 3 squares.
Step 14. 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 1 is down to one square, putting a queen on row 3, column 1; red has one square left, so its queen takes row 6, column 2; slate has one square left, so its queen takes row 5, column 5; mint has one square left, so its queen takes row 4, column 8; orange has one square left, so its queen takes row 9, 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 9, column 6.
The board after step 14 — 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 #288
This is puzzle number 288 in the 10x10 collection, rated easy. The grid holds 100 squares split between ten colored regions, and a finished board carries ten queens — one in every row, one in every column, one in every color, and never two of them touching, diagonals included.
Puzzle #288 has been checked to admit exactly one arrangement of queens, and every step toward it is deducible from what is already on the board. There is no point at which you are expected to pick a square and hope. The only thing that differs between boards is how quickly the first certainty surfaces, and that depends entirely on the shapes the colors happen to take here.
How the colors divide this board
From smallest to largest, the regions on puzzle #288 are: amber (1 square), sea green (2 squares), khaki (4 squares), indigo (5 squares), red (7 squares), pale yellow (10 squares), slate (12 squares), blue (19 squares), mint (19 squares), orange (21 squares). An even split would hand every color 10 squares, so the amber region is running 9 squares under that average while the orange region is the roomiest area on the grid with 21 squares.
One queen per color, regardless of acreage: that is what turns this uneven split into a solving order. Amber is working with 1 square while orange has 21 to spare, a gap of 20. Attack the cramped end and the roomy regions tend to resolve themselves.
Look at arrangement as well as area. Amber is the densest region on this grid at 100% of a 1×1 frame; pale yellow is the loosest, occupying only 50% of its 5×4 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 #288, smallest first. Reading these spans before you place anything is the quickest way to see which parts of the grid are genuinely contested.
Amber: 1 square across rows 2–2, columns 3–3. It never leaves row 2, so its queen is locked to that row.
Sea green covers 2 squares, spanning 2 rows and 1 column (rows 9–10, columns 9–9). It sits wholly inside column 9, so its queen must be in that column.
Khaki occupies 4 squares within rows 8–10, columns 9–10.
Indigo: 5 squares across rows 1–2, columns 5–8.
Red covers 7 squares, spanning 4 rows and 2 columns (rows 4–7, columns 1–2).
Pale yellow occupies 10 squares within rows 6–10, columns 1–4.
Slate: 12 squares across rows 4–7, columns 2–7.
Blue covers 19 squares, spanning 5 rows and 6 columns (rows 1–5, columns 1–6).
Mint occupies 19 squares within rows 1–6, columns 7–10.
Orange: 21 squares across rows 7–10, columns 3–10.
Where to start on this board
Amber is the natural opening on #288: it is the smallest region on the grid at 1 square, boxed into rows 2–2 and columns 3–3. Since one of those squares must hold a queen, that block of 1 row and 1 column is the most contested part of the board.
Because amber never leaves row 2, its queen must be in that row — and that instantly settles row 2 for everyone else. Sweep along it and X out every square that is not amber. 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 #288
A quick way to find the next move is to count how many different colors touch each line. On this board, row 3 is the narrowest, touched by only 2 colors. Columns 1, 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 10, meeting 4 colors, is the opposite case — the busiest line on #288 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.
Resist the plausible-looking queen. On #288 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 #288 is rated easy
The rating reflects how much the board concedes up front. Puzzle #288 has three 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 20 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.
When a board plays tougher than its label, look for a missed mark before you look for a clever deduction. Walk back over every queen you have placed and confirm the full row, the full column and all eight surrounding squares are crossed out. The diagonal neighbours are the ones players skip, and a single skipped diagonal will hide the next forced move indefinitely.
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.
Whatever the grid size, the pairing rule is the technique to internalise. When a pair of regions is boxed into the same pair of rows, they split those rows between them and nobody else may enter — and the same holds for columns, or for any n regions confined to n lines. Look for an instance of it around row 3 on this board.
Here is a shape check that gives nothing away: when #288 is solved, 4 queens sit on the outer edge of the grid and 6 sit inside it, and no queen lands 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.
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Questions about this puzzle
How hard is 10x10 Queens puzzle #288?
Puzzle #288 is rated easy. Its smallest color region holds 1 square, its tightest row is touched by 2 colors, and three of its regions are confined to a single row or column, which gives you a forced move early.
Does 10x10 puzzle #288 have only one solution?
Yes. Every puzzle in the 10x10 collection, including #288, 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 #288?
Start with the amber region — the most constrained color on this board, with 1 square spanning rows 2–2 and columns 3–3. Narrowing the smallest region first removes the most squares elsewhere on the grid.