10x10 Queens Puzzle #203
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 20-step reasoning is written out below.
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Step-by-step solution for puzzle #203
What follows is a complete solve of puzzle #203, worked the way a person works it rather than the way a computer does. It runs to 20 deductions — 10 queen placements and 10 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: region shadow, proof by contradiction, line confined to one region, last square in a row, region confined to one line, pairing argument on rows, last square in a column, last square in a region.
Show the full walkthrough (14 steps) — contains the solution
Step 1. Wherever pale yellow ends up among its 6 squares, the same squares fall within reach of it — 1 square in total, impossible regardless of how the colour resolves.
Step 2. Now a short proof by contradiction. Suppose the indigo queen went to row 1, column 10. Follow the forced moves that would create and the pale yellow region is left with nowhere to put its queen — impossible. So that square is ruled out for good.
Step 3. Test row 2, column 10 for indigo: place a queen there, run the forced consequences through, and the pale yellow region is left with nowhere to put its queen. The assumption breaks, so the square is eliminated.
Step 4. Every open square left in row 2 (9 open squares) belongs to the amber region. Since that row must contain a queen, amber is the colour that supplies it — so amber squares anywhere else on the board are out, 14 squares in all.
Step 5. Look along row 1: one square survives, row 1, column 9, which belongs to indigo. A row cannot be left empty, so the queen goes there. Everything else in row 1, in column 9, in indigo and in the ring around that square is now dead.
The board after step 5 — 1 of 10 queens placed. Step 6. Row 3 has a single open square left, at column 4 in the blue region. Every row needs a queen, so this one is forced. Row 3 and column 4 are now spoken for, along with the squares touching that queen.
Step 7. Look along row 4: one square survives, row 4, column 1, which belongs to mint. A row cannot be left empty, so the queen goes there. That clears row 4, column 1, the rest of the mint region and every square adjacent to it — diagonals included.
Step 8. All of the slate region's remaining squares (3 open squares) lie in column 10. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 3 squares come off.
Step 9. Pale yellow cannot leave column 8 — every one of its open squares (2 open squares) sits there. That column belongs to pale yellow, so every square in it owned by another colour is dead: 5 squares in all.
The board after step 9 — 3 of 10 queens placed. Step 10. Wherever orange ends up among its 8 squares, the same squares fall within reach of it — 1 square in total, impossible regardless of how the colour resolves.
Step 11. Sea green cannot leave row 10 — every one of its open squares (2 open squares) sits there. That row belongs to sea green, so every square on it owned by another colour is dead: 4 squares in all.
Step 12. Here is the pairing argument. The slate, red, and pale yellow regions have no open squares outside rows 5–7 — 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: 2 squares come off in one stroke.
Step 13. Wherever khaki 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 14. 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 3 is down to one square, putting a queen on row 8, column 3; orange has one square left, so its queen takes row 9, column 5; sea green has one square left, so its queen takes row 10, column 7; red has one square left, so its queen takes row 6, column 6; amber has one square left, so its queen takes row 2, column 2; pale yellow has one square left, so its queen takes row 7, column 8; slate has one square left, so its queen takes row 5, column 10. 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 5, column 10.
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 #203
10x10 puzzle #203 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.
As with every puzzle in this collection, #203 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 #203 are: slate (4 squares), pale yellow (6 squares), blue (8 squares), sea green (8 squares), mint (9 squares), red (9 squares), indigo (11 squares), khaki (11 squares), orange (11 squares), amber (23 squares). An even split would hand every color 10 squares, so the slate region is running 6 squares under that average while the amber region is the roomiest area on the grid with 23 squares.
That imbalance is the first thing to read, because every region takes exactly one queen regardless of how much space it owns. Slate has only 4 places to put its queen; amber has 23. The spread between them on this board is 19 squares, and the wider that spread runs, the more it pays to solve from the small end inward.
Square count is only half the story — how a color is arranged counts too. Sea green is the tidiest shape on #203, packing 80% of its 2×5 bounding box, whereas orange straggles across its 4×6 box at just 46%. Tidy blocks are easy to work around; scattered ones touch more lines and resist resolution.
Region by region
Here is the full footprint of every color on puzzle #203, smallest first. Reading these spans before you place anything is the quickest way to see which parts of the grid are genuinely contested.
Slate occupies 4 squares within rows 5–7, columns 9–10.
Pale yellow: 6 squares across rows 6–9, columns 8–10.
Blue covers 8 squares, spanning 3 rows and 4 columns (rows 3–5, columns 4–7).
Sea green occupies 8 squares within rows 9–10, columns 6–10.
Mint: 9 squares across rows 4–7, columns 1–4.
Red covers 9 squares, spanning 3 rows and 6 columns (rows 5–7, columns 4–9).
Indigo occupies 11 squares within rows 1–4, columns 6–10.
Khaki: 11 squares across rows 7–10, columns 1–4.
Orange covers 11 squares, spanning 4 rows and 6 columns (rows 7–10, columns 3–8).
Amber occupies 23 squares within rows 1–4, columns 1–9.
Where to start on this board
Open on the tightest color. Here that is slate, confined to 4 squares between rows 5 and 7 and columns 9 and 10. Its queen has nowhere else to go, which means those 3 rows and 2 columns carry more constraint than anywhere else on #203.
Slate does not collapse onto a single line, so it will not hand you a queen on move one. What it does give you is a short list of 4 candidates. Take each one in turn, imagine the queen there, cross out its row, its column and the eight squares around it, and ask whether any other region is left with nowhere to go. One or two candidates usually fail that test immediately.
Work outward to the other flat regions next. Sea green 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 #203
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 1 and 2 are the narrowest, touched by only 2 colors. Columns 1 and 2 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 2 colors, then one of those regions has to own it, and every other region is competing for the remaining 9 rows. By contrast row 7 meets 6 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.
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 #203 is rated easy
The rating reflects how much the board concedes up front. Puzzle #203 has no region confined to a single row or column, its smallest color holds 4 squares, its tightest row meets just 2 colors, and the gap between its largest and smallest regions is 19 squares. Flat, lopsided boards open quickly; even, sprawling ones make you earn the first placement.
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.
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.
One pattern is worth learning at every size, and it is available here. When two regions can only fit inside the same two rows, they must take one row each — which locks every other region out of both. The same argument works for columns, and for any matching count: three regions sharing three rows, four sharing four. Spotting these pairings turns a slow grind into a quick cascade, and on #203 the place to look for one is around row 1.
As a sanity check rather than a spoiler: the finished solution to #203 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.
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Questions about this puzzle
How hard is 10x10 Queens puzzle #203?
Puzzle #203 is rated easy. Its smallest color region holds 4 squares, its tightest row is touched by 2 colors, and no region is confined to a single row or column, so the opening move takes some hunting.
Does 10x10 puzzle #203 have only one solution?
Yes. Every puzzle in the 10x10 collection, including #203, 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 #203?
Start with the slate region — the most constrained color on this board, with 4 squares spanning rows 5–7 and columns 9–10. Narrowing the smallest region first removes the most squares elsewhere on the grid.