10x10 Queens Puzzle #197
Difficulty: hard. 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 15-step reasoning is written out below.
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Step-by-step solution for puzzle #197
What follows is a complete solve of puzzle #197, worked the way a person works it rather than the way a computer does. It runs to 15 deductions — 10 queen placements and 5 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 confined to one line, region shadow, pairing argument on columns, last square in a row.
Show the full walkthrough (8 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. All of the indigo region's remaining squares (2 open squares) lie in row 1. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 9 squares come off.
Step 3. The red region has 6 squares left, spread across rows 5–7, columns 8–10. 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 (2 open squares) lie in row 8. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 10 squares come off.
The board after step 4 — 1 of 10 queens placed. Step 5. Only row 9, column 10 is still open in orange, and since each colour must take a queen, that settles it. That clears row 9, column 10, the rest of the orange region and every square adjacent to it — diagonals included.
Step 6. The red region has 3 squares left, spread across rows 6 and 7, columns 8 and 9. 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 7. Indigo and khaki are now boxed into columns 2 and 3 and nothing else. That is 2 colours needing 2 columns, so they fill those columns between them — which locks every remaining colour out and removes 8 squares at once.
Step 8. From here the board cascades. Keep alternating the region sweep and the line sweep and 8 queens fall out in order without any new idea being needed: amber has one square left, so its queen takes row 2, column 4; indigo has one square left, so its queen takes row 1, column 2; pale yellow has one square left, so its queen takes row 7, column 5; red has one square left, so its queen takes row 6, column 8; khaki has one square left, so its queen takes row 8, column 3; row 5 is down to one square, putting a queen on row 5, column 6; blue has one square left, so its queen takes row 3, column 7; mint has one square left, so its queen takes row 4, column 9. 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 4, column 9.
The board after step 8 — 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 #197
Puzzle #197 is one of the hard-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, #197 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 #197 are: sea green (1 square), indigo (3 squares), khaki (3 squares), red (6 squares), orange (7 squares), mint (9 squares), amber (12 squares), blue (13 squares), slate (14 squares), pale yellow (32 squares). An even split would hand every color 10 squares, so the sea green region is running 9 squares under that average while the pale yellow region is the roomiest area on the grid with 32 squares.
Every color takes one queen and one only, whatever its size — which is why the 31 square difference between sea green and pale yellow 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 47% 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
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.
Sea green occupies 1 square within rows 10–10, columns 1–1. It never leaves row 10, so its queen is locked to that row.
Indigo: 3 squares across rows 1–1, columns 1–3. It never leaves row 1, so its queen is locked to that row.
Khaki covers 3 squares, spanning 1 row and 3 columns (rows 8–8, columns 1–3). It never leaves row 8, so its queen is locked to that row.
Red occupies 6 squares within rows 5–7, columns 8–10.
Orange: 7 squares across rows 8–10, columns 8–10.
Mint covers 9 squares, spanning 5 rows and 3 columns (rows 2–6, columns 8–10).
Amber occupies 12 squares within rows 1–4, columns 1–5.
Blue: 13 squares across rows 1–4, columns 5–10.
Slate covers 14 squares, spanning 6 rows and 5 columns (rows 3–8, columns 4–8).
Pale yellow occupies 32 squares within rows 4–10, columns 1–9.
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. Indigo and khaki 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 #197
A quick way to find the next move is to count how many different colors touch each line. On this board, row 9 is the narrowest, touched by only 2 colors. Columns 4, 6 and 7 are the tightest columns, with 3 colors.
A line with few colors is a line close to resolving. Where only 2 colors appear, one of them owns the row outright and the others must fit into the remaining 9 rows. Row 4 is the crowded extreme at 5 colors — worth revisiting later, not now.
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 #197 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 #197 is rated hard
Ratings track how generous the opening is. On #197 you get four regions pinned to a single row or column, a smallest color of 1 square, a tightest row crossed by 2 colors, and a 31-square gap between the largest and smallest regions. Those four numbers largely explain the hard label.
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.
If #197 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 #197 is row 9.
A non-spoiling distribution check: solved, #197 carries 3 queens on the perimeter against 7 queens inside, 1 of them cornered. Because no two queens may touch, real solutions always look fairly evenly spread — a lopsided board in progress is a warning sign.
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 #197?
Puzzle #197 is rated hard. Its smallest color region holds 1 square, its tightest row is touched by 2 colors, and four of its regions are confined to a single row or column, which gives you a forced move early.
Does 10x10 puzzle #197 have only one solution?
Yes. Every puzzle in the 10x10 collection, including #197, 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 #197?
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.