10x10 Queens Puzzle #147
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 17-step reasoning is written out below.
Previous puzzle · All 10x10 puzzles · Next puzzle
Step-by-step solution for puzzle #147
What follows is a complete solve of puzzle #147, worked the way a person works it rather than the way a computer does. It runs to 17 deductions — 10 queen placements and 7 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 (11 steps) — contains the solution
Step 1. Only row 5, column 2 is still open in slate, and since each colour must take a queen, that settles it. That clears row 5, column 2, the rest of the slate region and every square adjacent to it — diagonals included.
Step 2. The pale yellow region is down to one open square, at row 7, column 10. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 7 and column 10, the remaining pale yellow squares, and the ring of neighbours around row 7, column 10.
Step 3. Only row 6, column 8 is still open in red, and since each colour must take a queen, that settles it. Everything else in row 6, in column 8, in red and in the ring around that square is now dead.
Step 4. Wherever indigo 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 — 3 of 10 queens placed. Step 5. Amber cannot leave column 9 — every one of its open squares (2 open squares) sits there. That column belongs to amber, so every square in it owned by another colour is dead: 4 squares in all.
Step 6. All of the orange region's remaining squares (2 open squares) lie in column 7. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 7 squares come off.
Step 7. Wherever sea green ends up among its 4 squares, the same squares fall within reach of it — 1 square in total, impossible regardless of how the colour resolves.
The board after step 7 — 3 of 10 queens placed. Step 8. Every open square left in row 4 (3 open squares) belongs to the mint region. Since that row must contain a queen, mint is the colour that supplies it — so mint squares anywhere else on the board are out, 3 squares in all.
Step 9. Mint cannot leave row 4 — every one of its open squares (3 open squares) sits there. That row belongs to mint, so every square on it owned by another colour is dead: 1 square in all.
Step 10. Every open square left in row 3 (3 open squares) belongs to the blue region. Since that row must contain a queen, blue is the colour that supplies it — so blue squares anywhere else on the board are out, 5 squares in all.
Step 11. From here the board cascades. Keep alternating the region sweep and the line sweep and 7 queens fall out in order without any new idea being needed: column 6 is down to one square, putting a queen on row 4, column 6; column 5 is down to one square, putting a queen on row 10, column 5; orange has one square left, so its queen takes row 9, column 7; column 4 is down to one square, putting a queen on row 3, column 4; indigo has one square left, so its queen takes row 1, column 1; amber has one square left, so its queen takes row 2, 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 #147
10x10 puzzle #147 is rated easy. Ten colored regions cover its 100 squares, and your job is to seat ten queens so that every row, column and color contains exactly one — with no queen touching another, including diagonally.
Like every board on this site, #147 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 #147 are: slate (1 square), pale yellow (1 square), indigo (4 squares), sea green (4 squares), red (6 squares), amber (8 squares), orange (10 squares), khaki (16 squares), blue (18 squares), mint (32 squares). An even split would hand every color 10 squares, so the slate region is running 9 squares under that average while the mint region is the roomiest area on the grid with 32 squares.
One queen per color, regardless of acreage: that is what turns this uneven split into a solving order. Slate is working with 1 square while mint has 32 to spare, a gap of 31. Attack the cramped end and the roomy regions tend to resolve themselves.
Look at arrangement as well as area. Slate is the densest region on this grid at 100% of a 1×1 frame; red is the loosest, occupying only 50% of its 4×3 frame. The loose one reaches into more rows and columns, which is exactly why it usually settles last.
Region by region
Each region's exact extent on this grid is listed below, starting with the most constrained. Knowing which lines a color can and cannot reach is most of the work on a easy board.
Slate: 1 square across rows 5–5, columns 2–2. It never leaves row 5, so its queen is locked to that row.
Pale yellow covers 1 square, spanning 1 row and 1 column (rows 7–7, columns 10–10). It never leaves row 7, so its queen is locked to that row.
Indigo occupies 4 squares within rows 1–2, columns 1–3.
Sea green: 4 squares across rows 8–10, columns 4–5.
Red covers 6 squares, spanning 4 rows and 3 columns (rows 5–8, columns 8–10).
Amber occupies 8 squares within rows 1–4, columns 8–10.
Orange: 10 squares across rows 8–10, columns 7–10.
Khaki covers 16 squares, spanning 6 rows and 4 columns (rows 5–10, columns 1–4).
Blue occupies 18 squares within rows 1–4, columns 1–7.
Mint: 32 squares across rows 3–10, columns 3–9.
Where to start on this board
Open on the tightest color. Here that is slate, confined to 1 square between rows 5 and 5 and columns 2 and 2. Its queen has nowhere else to go, which means those 1 row and 1 column carry more constraint than anywhere else on #147.
Because slate never leaves row 5, its queen must be in that row — and that instantly settles row 5 for everyone else. Sweep along it and X out every square that is not slate. 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. Pale yellow and indigo 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 #147
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 1, 2, 3, 4 and 6 are the narrowest, touched by only 3 colors. Column 6 is the tightest column, 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 #147 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.
Keep alternating between two views of the board. In the region view you ask which of the ten colors is down to one open square. In the line view you ask the same of each row and column. Both produce forced queens, and each placement refreshes the other view, so cycling between them deliberately is how a 10x10 board unwinds.
Say the reason out loud: "this region has one square left", "this column has one square left". If no such sentence is available, the eliminating is not finished. One more pass of X marks is almost always quicker than committing to a placement you cannot defend.
Why puzzle #147 is rated easy
The easy label comes out of four measurable things about #147: four of its regions are locked to one row or column, its smallest color spans 1 square, its least crowded row meets 3 colors, and its largest and smallest regions differ by 31. Boards that score tight on those measures give up their first queen fast.
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 #147 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.
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 column 6 on this board.
Here is a shape check that gives nothing away: when #147 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 #147?
Puzzle #147 is rated easy. Its smallest color region holds 1 square, its tightest row is touched by 3 colors, and four of its regions are confined to a single row or column, which gives you a forced move early.
Does 10x10 puzzle #147 have only one solution?
Yes. Every puzzle in the 10x10 collection, including #147, 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 #147?
Start with the slate region — the most constrained color on this board, with 1 square spanning rows 5–5 and columns 2–2. Narrowing the smallest region first removes the most squares elsewhere on the grid.