8x8 Queens Puzzle #116
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 15-step reasoning is written out below.
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Step-by-step solution for puzzle #116
What follows is a complete solve of puzzle #116, worked the way a person works it rather than the way a computer does. It runs to 15 deductions — 8 queen placements and 7 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 shadow, region confined to one line, pairing argument on columns, last square in a row.
Show the full walkthrough (9 steps) — contains the solution
Step 1. Only row 4, column 1 is still open in mint, and since each colour must take a queen, that settles it. That clears row 4, column 1, the rest of the mint region and every square adjacent to it — diagonals included.
Step 2. Blue is down to 3 candidates in rows 2, 3, and 5, columns 5 and 7, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about blue itself.
Step 3. The slate region has 7 squares left, spread across rows 2, 3, 5, 6, and 7, columns 6–8. 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.
The board after step 3 — 1 of 8 queens placed. Step 4. All of the red region's remaining squares (2 open squares) lie in column 2. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 3 squares come off.
Step 5. Khaki cannot leave row 8 — every one of its open squares (2 open squares) sits there. That row belongs to khaki, so every square on it owned by another colour is dead: 6 squares in all.
Step 6. Here is the pairing argument. The amber and khaki regions have no open squares outside columns 3 and 4 — 2 colours confined to 2 columns. Between them they must take one column each, in some order, so every other colour is shut out of all of them: 4 squares come off in one stroke.
The board after step 6 — 1 of 8 queens placed. Step 7. Wherever pale yellow ends up among its 4 squares, the same squares fall within reach of it — 2 squares in total, impossible regardless of how the colour resolves.
Step 8. All of the blue region's remaining squares (2 open squares) lie in column 7. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 7 squares come off.
Step 9. 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: row 7 is down to one square, putting a queen on row 7, column 5; 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 8; indigo has one square left, so its queen takes row 1, column 6; blue has one square left, so its queen takes row 3, column 7; amber has one square left, so its queen takes row 2, column 4; red has one square left, so its queen takes row 6, column 2. 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 6, column 2.
The board after step 9 — 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 #116
This is puzzle number 116 in the 8x8 collection, rated hard. 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.
Puzzle #116 has been checked to admit exactly one arrangement of queens, and every step toward it is deducible from what is already on the board. There is no point at which you are expected to pick a square and hope. The only thing that differs between boards is how quickly the first certainty surfaces, and that depends entirely on the shapes the colors happen to take here.
How the colors divide this board
From smallest to largest, the regions on puzzle #116 are: mint (1 square), khaki (5 squares), indigo (8 squares), amber (8 squares), blue (8 squares), slate (9 squares), red (10 squares), pale yellow (15 squares). An even split would hand every color 8 squares, so the mint region is running 7 squares under that average while the pale yellow region is the roomiest area on the grid with 15 squares.
One queen per color, regardless of acreage: that is what turns this uneven split into a solving order. Mint is working with 1 square while pale yellow has 15 to spare, a gap of 14. Attack the cramped end and the roomy regions tend to resolve themselves.
Shape matters as much as size. The mint region is the most compact color here, filling 100% of the 1×1 box that encloses it, while blue is the most scattered at 40% of its 4×5 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
Here is the full footprint of every color on puzzle #116, smallest first. Reading these spans before you place anything is the quickest way to see which parts of the grid are genuinely contested.
Mint occupies 1 square within rows 4–4, columns 1–1. It never leaves row 4, so its queen is locked to that row.
Khaki: 5 squares across rows 7–8, columns 1–4.
Indigo covers 8 squares, spanning 3 rows and 4 columns (rows 1–3, columns 5–8).
Amber occupies 8 squares within rows 1–3, columns 1–4.
Blue: 8 squares across rows 2–5, columns 3–7.
Slate covers 9 squares, spanning 6 rows and 3 columns (rows 2–7, columns 6–8).
Red occupies 10 squares within rows 2–7, columns 1–2.
Pale yellow: 15 squares across rows 5–8, columns 3–8.
Where to start on this board
The most constrained color is where a solve should begin, and on #116 that is mint with 1 square. It reaches from row 4 to row 4 and from column 1 to column 1 — 1 row by 1 column. 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 mint never leaves row 4, its queen must be in that row — and that instantly settles row 4 for everyone else. Sweep along it and X out every square that is not mint. 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 #116
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 1 and 8 are the narrowest, touched by only 2 colors. Columns 2, 5 and 8 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 7 rows. Row 3 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 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 #116 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 #116 is rated hard
The rating reflects how much the board concedes up front. Puzzle #116 has two regions confined to a single row or column, its smallest color holds 1 square, its tightest row meets just 2 colors, and the gap between its largest and smallest regions is 14 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 hard board from the rest.
When a board plays tougher than its label, look for a missed mark before you look for a clever deduction. Walk back over every queen you have placed and confirm the full row, the full column and all eight surrounding squares are crossed out. The diagonal neighbours are the ones players skip, and a single skipped diagonal will hide the next forced move indefinitely.
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.
A non-spoiling distribution check: solved, #116 carries 4 queens on the perimeter against 4 queens inside, with the corners empty. 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 8x8 Queens puzzle #116?
Puzzle #116 is rated hard. Its smallest color region holds 1 square, its tightest row is touched by 2 colors, and two of its regions are confined to a single row or column, which gives you a forced move early.
Does 8x8 puzzle #116 have only one solution?
Yes. Every puzzle in the 8x8 collection, including #116, 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 #116?
Start with the mint region — the most constrained color on this board, with 1 square spanning rows 4–4 and columns 1–1. Narrowing the smallest region first removes the most squares elsewhere on the grid.