8x8 Queens Puzzle #196
Difficulty: easy. 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 14-step reasoning is written out below.
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Step-by-step solution for puzzle #196
What follows is a complete solve of puzzle #196, worked the way a person works it rather than the way a computer does. It runs to 14 deductions — 8 queen placements and 6 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: region confined to one line, region shadow, last square in a region, line confined to one region, last square in a row.
Show the full walkthrough (10 steps) — contains the solution
Step 1. Amber cannot leave row 2 — every one of its open squares (2 open squares) sits there. That row belongs to amber, so every square on it owned by another colour is dead: 10 squares in all.
Step 2. Indigo is down to 4 candidates in rows 1 and 3, columns 3–6, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about indigo itself.
Step 3. Slate cannot leave column 1 — every one of its open squares (3 open squares) sits there. That column belongs to slate, so every square in it owned by another colour is dead: 5 squares in all.
The board after step 3 — 0 of 8 queens placed. Step 4. The khaki region is down to one open square, at row 8, column 2. Every colour holds exactly one queen, so that square is forced. Row 8 and column 2 are now spoken for, along with the squares touching that queen.
Step 5. 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.
Step 6. The amber region is down to one open square, at row 2, column 7. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 2 and column 7, the remaining amber squares, and the ring of neighbours around row 2, column 7.
Step 7. Only row 4, column 6 is still open in mint, and since each colour must take a queen, that settles it. Everything else in row 4, in column 6, in mint and in the ring around that square is now dead.
The board after step 7 — 3 of 8 queens placed. Step 8. Blue is down to 3 candidates in rows 3 and 5, columns 3 and 4, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about blue itself.
Step 9. Row 1 has only indigo squares left (2 open squares). The row needs a queen and only indigo can provide one, which pins that colour to this row and kills its squares elsewhere: 1 square.
Step 10. From here the board cascades. Keep alternating the region sweep and the line sweep and 5 queens fall out in order without any new idea being needed: row 3 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 5; red has one square left, so its queen takes row 6, column 3; slate has one square left, so its queen takes row 5, column 1; pale yellow has one square left, so its queen takes row 7, column 8. 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 8.
The board after step 10 — 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 #196
This is puzzle number 196 in the 8x8 collection, rated easy. The grid holds 64 squares split between eight colored regions, and a finished board carries eight queens — one in every row, one in every column, one in every color, and never two of them touching, diagonals included.
There is exactly one way to finish #196, and it has been verified. More importantly, you can reach it without ever gambling: at every stage some square is provably right or provably wrong. Boards differ only in how deep you must dig before that proof appears, and the geometry of these eight regions is what sets the depth.
How the colors divide this board
From smallest to largest, the regions on puzzle #196 are: amber (2 squares), khaki (2 squares), slate (3 squares), pale yellow (5 squares), indigo (10 squares), mint (10 squares), red (14 squares), blue (18 squares). An even split would hand every color 8 squares, so the amber region is running 6 squares under that average while the blue region is the roomiest area on the grid with 18 squares.
One queen per color, regardless of acreage: that is what turns this uneven split into a solving order. Amber is working with 2 squares while blue has 18 to spare, a gap of 16. Attack the cramped end and the roomy regions tend to resolve themselves.
Shape matters as much as size. The amber region is the most compact color here, filling 100% of the 1×2 box that encloses it, while pale yellow is the most scattered at 56% of its 3×3 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.
Amber covers 2 squares, spanning 1 row and 2 columns (rows 2–2, columns 7–8). It never leaves row 2, so its queen is locked to that row.
Khaki occupies 2 squares within rows 8–8, columns 1–2. It never leaves row 8, so its queen is locked to that row.
Slate: 3 squares across rows 5–7, columns 1–1. It sits wholly inside column 1, so its queen must be in that column.
Pale yellow covers 5 squares, spanning 3 rows and 3 columns (rows 6–8, columns 6–8).
Indigo occupies 10 squares within rows 1–3, columns 3–8.
Mint: 10 squares across rows 3–7, columns 6–8.
Red covers 14 squares, spanning 4 rows and 5 columns (rows 5–8, columns 2–6).
Blue occupies 18 squares within rows 1–5, columns 1–6.
Where to start on this board
The most constrained color is where a solve should begin, and on #196 that is amber with 2 squares. It reaches from row 2 to row 2 and from column 7 to column 8 — 1 row by 2 columns. One queen has to live inside that footprint no matter what else happens, which makes those lines the busiest real estate on the board.
Because amber never leaves row 2, its queen must be in that row — and that instantly settles row 2 for everyone else. Sweep along it and X out every square that is not amber. 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. Khaki 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 #196
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 1 and 4 are the narrowest, touched by only 2 colors. Columns 1, 2, 3, 4 and 5 are the tightest columns, with 3 colors.
Count colors per line and you have a ranking of where to look. The narrowest rows here see only 2 colors, so one of that handful must take the row and the rest are squeezed into the other 7 rows. Row 7 sits at the far end with 4 colors crossing it; it will almost certainly be among the last to settle.
Working through the middle game
The middle of #196 is where careless play costs time. Every queen you place kills a row, a column and the eight surrounding squares; if you do not mark all of that immediately, you will later "discover" a move that was available several turns ago. Mark first, then look.
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.
Resist the plausible-looking queen. On #196 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 #196 is rated easy
Ratings track how generous the opening is. On #196 you get three regions pinned to a single row or column, a smallest color of 2 squares, a tightest row crossed by 2 colors, and a 16-square gap between the largest and smallest regions. Those four numbers largely explain the easy 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.
Stuck on #196 despite the easy rating? The odds strongly favour a bookkeeping error over a hard chain of logic. Re-check each placed queen for its complete set of eliminations, paying particular attention to the four diagonal squares — those are the ones that get overlooked, and one of them is usually sitting on the answer.
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 row 1 on this board.
Use this as a rough check on your progress: the completed board has 4 queens around the border and 4 queens in the middle, and nothing in the corners. Solutions spread out; if yours is bunching up in one region of the grid, retrace a few moves.
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 #196?
Puzzle #196 is rated easy. Its smallest color region holds 2 squares, its tightest row is touched by 2 colors, and three of its regions are confined to a single row or column, which gives you a forced move early.
Does 8x8 puzzle #196 have only one solution?
Yes. Every puzzle in the 8x8 collection, including #196, 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 #196?
Start with the amber region — the most constrained color on this board, with 2 squares spanning rows 2–2 and columns 7–8. Narrowing the smallest region first removes the most squares elsewhere on the grid.