10x10 Queens Puzzle #201
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 22-step reasoning is written out below.
Previous puzzle · All 10x10 puzzles · Next puzzle
Step-by-step solution for puzzle #201
What follows is a complete solve of puzzle #201, worked the way a person works it rather than the way a computer does. It runs to 22 deductions — 10 queen placements and 12 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 proof by contradiction.
Techniques this board needs: last square in a region, region confined to one line, region shadow, pairing argument on rows, pairing argument on columns, proof by contradiction.
Show the full walkthrough (16 steps) — contains the solution
Step 1. Only row 8, column 8 is still open in khaki, and since each colour must take a queen, that settles it. That clears row 8, column 8, the rest of the khaki region and every square adjacent to it — diagonals included.
Step 2. All of the blue region's remaining squares (2 open squares) lie in row 3. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 11 squares come off.
Step 3. The mint region has 2 squares left, spread across rows 2 and 4, columns 5 and 6. You do not need to know which of them takes the queen: every one of those options attacks the same 4 squares, so they can be crossed out now.
Step 4. Here is the pairing argument. The indigo, amber, and mint regions have no open squares outside rows 1, 2, and 4 — 3 colours confined to 3 rows. Between them they must take one row each, in some order, so every other colour is shut out of all of them: 7 squares come off in one stroke.
Step 5. Only row 5, column 10 is still open in slate, and since each colour must take a queen, that settles it. That clears row 5, column 10, the rest of the slate region and every square adjacent to it — diagonals included.
The board after step 5 — 2 of 10 queens placed. Step 6. All of the sea green region's remaining squares (2 open squares) lie in row 10. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 6 squares come off.
Step 7. Blue and pale yellow are now boxed into columns 1 and 2 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 4 squares at once.
Step 8. All of the amber region's remaining squares (3 open squares) lie in column 3. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 3 squares come off.
Step 9. Test row 1, column 4 for indigo: place a queen there, run the forced consequences through, and row 2 runs out of open squares entirely. The assumption breaks, so the square is eliminated.
Step 10. Now a short proof by contradiction. Suppose the indigo queen went to row 1, column 7. Follow the forced moves that would create and column 4 runs out of open squares entirely — impossible. So that square is ruled out for good.
Step 11. Indigo is down to 4 candidates in rows 1 and 2, columns 4, 5, 7, and 9, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about indigo itself.
The board after step 11 — 2 of 10 queens placed. Step 12. The mint region is down to one open square, at row 4, column 6. Every colour holds exactly one queen, so that square is forced. Row 4 and column 6 are now spoken for, along with the squares touching that queen.
Step 13. Amber cannot leave column 3 — 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: 1 square in all.
Step 14. Red is down to 4 candidates in rows 6, 7, and 9, columns 4, 5, and 7, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about red itself.
Step 15. The orange region has 2 squares left, spread across rows 7 and 9, columns 4 and 5. You do not need to know which of them takes the queen: every one of those options attacks the same 3 squares, so they can be crossed out now.
Step 16. 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: red has one square left, so its queen takes row 6, column 7; sea green has one square left, so its queen takes row 10, column 9; indigo has one square left, so its queen takes row 1, column 5; amber has one square left, so its queen takes row 2, column 3; blue has one square left, so its queen takes row 3, column 1; pale yellow has one square left, so its queen takes row 7, column 2; orange has one square left, so its queen takes row 9, column 4. 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 4.
The board after step 16 — 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 #201
Puzzle #201 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.
As with every puzzle in this collection, #201 has a single verified solution and needs no guesswork. Each queen follows from something already visible. What the board controls is tempo — how soon the first forced move shows up and how far apart the rest are spaced — and that is a direct consequence of how these colors are cut.
How the colors divide this board
From smallest to largest, the regions on puzzle #201 are: khaki (1 square), blue (2 squares), slate (7 squares), mint (8 squares), pale yellow (8 squares), indigo (10 squares), amber (10 squares), sea green (11 squares), orange (18 squares), red (25 squares). An even split would hand every color 10 squares, so the khaki region is running 9 squares under that average while the red region is the roomiest area on the grid with 25 squares.
Every color takes one queen and one only, whatever its size — which is why the 24 square difference between khaki and red 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.
A region's outline can constrain it more than its size does. Here blue is the most solid, filling 100% of its 1×2 box, and red the most diffuse at 45% of its 7×8 box. Solid blocks give clean eliminations; diffuse ones spread across the board and stay open longer.
Region by region
Here is the full footprint of every color on puzzle #201, smallest first. Reading these spans before you place anything is the quickest way to see which parts of the grid are genuinely contested.
Khaki: 1 square across rows 8–8, columns 8–8. It never leaves row 8, so its queen is locked to that row.
Blue covers 2 squares, spanning 1 row and 2 columns (rows 3–3, columns 1–2). It never leaves row 3, so its queen is locked to that row.
Slate occupies 7 squares within rows 1–5, columns 8–10.
Mint: 8 squares across rows 2–4, columns 5–9.
Pale yellow covers 8 squares, spanning 4 rows and 3 columns (rows 5–8, columns 1–3).
Indigo occupies 10 squares within rows 1–3, columns 4–9.
Amber: 10 squares across rows 1–4, columns 1–3.
Sea green covers 11 squares, spanning 4 rows and 4 columns (rows 7–10, columns 7–10).
Orange occupies 18 squares within rows 6–10, columns 1–6.
Red: 25 squares across rows 4–10, columns 3–10.
Where to start on this board
Begin where the choices are fewest. On this board that means khaki, which owns just 1 square inside a 1×1 window running from row 8 to row 8 and column 8 to column 8. A queen is guaranteed somewhere in there, so every line that window crosses is under pressure from the very first move.
Because khaki never leaves row 8, its queen must be in that row — and that instantly settles row 8 for everyone else. Sweep along it and X out every square that is not khaki. 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. Blue 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 #201
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 1, 5, 6, 9 and 10 are the narrowest, touched by only 3 colors. Columns 4 and 10 are the tightest columns, with 3 colors.
Those lines matter because a row touched by few colors gives its queen away sooner. If a row meets only 3 colors, then one of those regions has to own it, and every other region is competing for the remaining 9 rows. By contrast row 8 meets 5 colors — the most crowded line here, and the one least likely to resolve early. Spend your attention accordingly.
Working through the middle game
After the first few queens the puzzle becomes bookkeeping. A placed queen wipes its row, its column and every square it touches — as many as eight neighbours — so the space collapses quickly. Record those eliminations on the board instead of carrying them in your head, and the next forced move tends to announce itself.
The whole middle game reduces to two sweeps. Sweep the ten colors looking for one with a single square left; sweep the ten rows and ten columns looking for the same. Each sweep feeds the next, and switching between them deliberately — rather than drifting — is what separates a fast 10x10 solve from a stalled one.
The trap on a board like this is placing a queen that is merely plausible. Every placement should be traceable to an elimination you can point at. If you cannot name the rule that forced it, you are guessing — and on a single-solution grid a guess costs more to unwind than the deduction would have taken to find.
Why puzzle #201 is rated hard
The rating reflects how much the board concedes up front. Puzzle #201 has three regions confined to a single row or column, its smallest color holds 1 square, its tightest row meets just 3 colors, and the gap between its largest and smallest regions is 24 squares. Flat, lopsided boards open quickly; even, sprawling ones make you earn the first placement.
Nothing about the rating involves computation or chance. Each grid has a single solution reachable by pure logic; the rating simply measures how far ahead you have to reason. Easy boards resolve a queen every step or two, while hard ones can ask you to carry three unfinished lines of thought before any of them pays off.
A board that feels above its rating is nearly always a board with a missing X. Audit every queen on the grid: full row cleared, full column cleared, all eight touching squares cleared. Diagonals are the common omission, and missing one is far more often the cause of a stall than any genuine difficulty in the puzzle.
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 #201 is row 1.
As a sanity check rather than a spoiler: the finished solution to #201 puts 4 queens on the outer border and 6 queens in the interior, with none in a 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.
Full rules · Strategy library · Puzzle statistics
Questions about this puzzle
How hard is 10x10 Queens puzzle #201?
Puzzle #201 is rated hard. 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 #201 have only one solution?
Yes. Every puzzle in the 10x10 collection, including #201, 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 #201?
Start with the khaki region — the most constrained color on this board, with 1 square spanning rows 8–8 and columns 8–8. Narrowing the smallest region first removes the most squares elsewhere on the grid.