8x8 Queens Puzzle #202
Difficulty: hard. Place 8 queens on this 8x8 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.
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Step-by-step solution for puzzle #202
What follows is a complete solve of puzzle #202, worked the way a person works it rather than the way a computer does. It runs to 17 deductions — 8 queen placements and 9 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: region shadow, line confined to one region, pairing argument on columns, last square in a region, pairing argument on rows, region confined to one line.
Show the full walkthrough (11 steps) — contains the solution
Step 1. Wherever blue ends up among its 5 squares, the same squares fall within reach of it — 1 square in total, impossible regardless of how the colour resolves.
Step 2. Every open square left in column 8 (8 open squares) belongs to the amber region. Since that column must contain a queen, amber is the colour that supplies it — so amber squares anywhere else on the board are out, 4 squares in all.
Step 3. Indigo, blue, slate, and pale yellow are now boxed into columns 1–4 and nothing else. That is 4 colours needing 4 columns, so they fill those columns between them — which locks every remaining colour out and removes 8 squares at once.
Step 4. The mint region is down to one open square, at row 4, column 5. Every colour holds exactly one queen, so that square is forced. Row 4 and column 5 are now spoken for, along with the squares touching that queen.
The board after step 4 — 1 of 8 queens placed. Step 5. Blue is down to 3 candidates in rows 3 and 5, columns 1 and 2, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about blue itself.
Step 6. The red region has 2 squares left, spread across rows 3 and 6, columns 6 and 7. 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 7. Column 4 has only pale yellow squares left (2 open squares). The column needs a queen and only pale yellow can provide one, which pins that colour to this column and kills its squares elsewhere: 3 squares.
The board after step 7 — 1 of 8 queens placed. Step 8. Every open square left in column 3 (3 open squares) belongs to the indigo region. Since that column must contain a queen, indigo is the colour that supplies it — so indigo squares anywhere else on the board are out, 3 squares in all.
Step 9. Pale yellow and khaki are now boxed into rows 7 and 8 and nothing else. That is 2 colours needing 2 rows, so they fill those rows between them — which locks every remaining colour out and removes 5 squares at once.
Step 10. All of the slate region's remaining squares (2 open squares) lie in column 1. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 2 squares come off.
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: blue has one square left, so its queen takes row 3, column 2; indigo has one square left, so its queen takes row 1, column 3; red has one square left, so its queen takes row 6, column 6; slate has one square left, so its queen takes row 5, column 1; amber has one square left, so its queen takes row 2, column 8; khaki has one square left, so its queen takes row 8, column 7; pale yellow has one square left, so its queen takes row 7, 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 7, column 4.
The board after step 11 — 8 of 8 queens placed.
That completes the board: 8 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 8x8 Queens puzzle #202
Board #202 of the 8x8 bank carries a hard rating. Its 64 squares are shared between eight colored regions, and the solution places eight queens: one per row, one per column, one per region, none of them side by side or corner to corner.
As with every puzzle in this collection, #202 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 #202 are: blue (5 squares), pale yellow (5 squares), slate (6 squares), mint (7 squares), khaki (7 squares), indigo (8 squares), amber (12 squares), red (14 squares). An even split would hand every color 8 squares, so the blue region is running 3 squares under that average while the red region is the roomiest area on the grid with 14 squares.
One queen per color, regardless of acreage: that is what turns this uneven split into a solving order. Blue is working with 5 squares while red has 14 to spare, a gap of 9. Attack the cramped end and the roomy regions tend to resolve themselves.
Look at arrangement as well as area. Pale yellow is the densest region on this grid at 83% of a 2×3 frame; red is the loosest, occupying only 50% of its 7×4 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 #202, smallest first. Reading these spans before you place anything is the quickest way to see which parts of the grid are genuinely contested.
Blue covers 5 squares, spanning 3 rows and 3 columns (rows 3–5, columns 1–3).
Pale yellow occupies 5 squares within rows 7–8, columns 2–4.
Slate: 6 squares across rows 4–8, columns 1–2.
Mint covers 7 squares, spanning 3 rows and 4 columns (rows 4–6, columns 2–5).
Khaki occupies 7 squares within rows 5–8, columns 5–7.
Indigo: 8 squares across rows 1–3, columns 1–4.
Amber covers 12 squares, spanning 8 rows and 3 columns (rows 1–8, columns 6–8).
Red occupies 14 squares within rows 1–7, columns 4–7.
Where to start on this board
Blue is the natural opening on #202: it is the smallest region on the grid at 5 squares, boxed into rows 3–5 and columns 1–3. Since one of those squares must hold a queen, that block of 3 rows and 3 columns is the most contested part of the board.
Blue 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 5 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. Pale yellow 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 #202
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 3 colors. Column 8 is the tightest column, with 1 color.
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 7 rows. By contrast row 5 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
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 64 squares of this grid. First: has any of the eight regions been reduced to a single open square? Second: has any row or column? Either answer forces a queen. Players who stall on 8x8 boards almost always run one of those checks and forget the other.
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 #202 is rated hard
The rating reflects how much the board concedes up front. Puzzle #202 has no region confined to a single row or column, its smallest color holds 5 squares, its tightest row meets just 3 colors, and the gap between its largest and smallest regions is 9 squares. Flat, lopsided boards open quickly; even, sprawling ones make you earn the first placement.
Rating is a measure of chain length, not of chance. With one guaranteed solution and no guessing required, the only thing that changes across the collection is how many eliminations you must link together before a queen is provably forced.
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 8x8
At 8x8 the whole grid stays within a single glance, which makes systematic scanning practical. Read the rows in order and count the colors in each — a row touched by two colors is far more constrained than one touched by five, and that is usually where the next forced move hides. The board is small enough that re-scanning from the top after each placement costs almost nothing.
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 8 on this board.
As a sanity check rather than a spoiler: the finished solution to #202 puts 4 queens on the outer border and 4 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 8x8 Queens puzzle #202?
Puzzle #202 is rated hard. Its smallest color region holds 5 squares, its tightest row is touched by 3 colors, and no region is confined to a single row or column, so the opening move takes some hunting.
Does 8x8 puzzle #202 have only one solution?
Yes. Every puzzle in the 8x8 collection, including #202, has been verified to have exactly one valid arrangement of eight queens, and it can always be reached by logic alone — no guessing or backtracking needed.
Where should I place my first queen on puzzle #202?
Start with the blue region — the most constrained color on this board, with 5 squares spanning rows 3–5 and columns 1–3. Narrowing the smallest region first removes the most squares elsewhere on the grid.