7x7 Queens Puzzle #63
Difficulty: hard. Place 7 queens on this 7x7 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.
Previous puzzle · All 7x7 puzzles · Next puzzle
Step-by-step solution for puzzle #63
What follows is a complete solve of puzzle #63, worked the way a person works it rather than the way a computer does. It runs to 14 deductions — 7 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 rows.
Techniques this board needs: region shadow, pairing argument on rows, region confined to one line, last square in a region, last square in a row.
Show the full walkthrough (9 steps) — contains the solution
Step 1. Wherever amber 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 2. Mint is down to 4 candidates in rows 2–4, columns 1 and 2, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about mint itself.
Step 3. The slate region has 6 squares left, spread across rows 4–6, columns 3–5. 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 — 0 of 7 queens placed. Step 4. Here is the pairing argument. The indigo and amber regions have no open squares outside rows 1 and 2 — 2 colours confined to 2 rows. Between them they must take one row each, in some order, so every other colour is shut out of all of them: 5 squares come off in one stroke.
Step 5. Blue cannot leave row 3 — every one of its open squares (3 open squares) sits there. That row belongs to blue, so every square on it owned by another colour is dead: 3 squares in all.
Step 6. The mint region is down to one open square, at row 4, column 2. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 4 and column 2, the remaining mint squares, and the ring of neighbours around row 4, column 2.
The board after step 6 — 1 of 7 queens placed. Step 7. Wherever slate ends up among its 4 squares, the same squares fall within reach of it — 1 square in total, impossible regardless of how the colour resolves.
Step 8. All of the red 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 9. From here the board cascades. Keep alternating the region sweep and the line sweep and 6 queens fall out in order without any new idea being needed: row 2 is down to one square, putting a queen on row 2, column 7; blue has one square left, so its queen takes row 3, column 4; indigo has one square left, so its queen takes row 1, column 3; slate has one square left, so its queen takes row 5, column 5; pale yellow has one square left, so its queen takes row 7, column 6; red has one square left, so its queen takes row 6, column 1. 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 1.
The board after step 9 — 7 of 7 queens placed.
That completes the board: 7 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 7x7 Queens puzzle #63
7x7 puzzle #63 is rated hard. Seven colored regions cover its 49 squares, and your job is to seat seven queens so that every row, column and color contains exactly one — with no queen touching another, including diagonally.
There is exactly one way to finish #63, 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 seven regions is what sets the depth.
How the colors divide this board
From smallest to largest, the regions on puzzle #63 are: amber (3 squares), mint (4 squares), indigo (5 squares), slate (6 squares), red (8 squares), blue (9 squares), pale yellow (14 squares). An even split would hand every color 7 squares, so the amber region is running 4 squares under that average while the pale yellow region is the roomiest area on the grid with 14 squares.
That imbalance is the first thing to read, because every region takes exactly one queen regardless of how much space it owns. Amber has only 3 places to put its queen; pale yellow has 14. The spread between them on this board is 11 squares, and the wider that spread runs, the more it pays to solve from the small end inward.
Look at arrangement as well as area. Amber is the densest region on this grid at 75% of a 2×2 frame; pale yellow is the loosest, occupying only 56% of its 5×5 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 #63, smallest first. Reading these spans before you place anything is the quickest way to see which parts of the grid are genuinely contested.
Amber: 3 squares across rows 1–2, columns 6–7.
Mint covers 4 squares, spanning 3 rows and 2 columns (rows 2–4, columns 1–2).
Indigo occupies 5 squares within rows 1–2, columns 1–4.
Slate: 6 squares across rows 4–6, columns 3–5.
Red covers 8 squares, spanning 4 rows and 3 columns (rows 4–7, columns 1–3).
Blue occupies 9 squares within rows 1–3, columns 3–7.
Pale yellow: 14 squares across rows 3–7, columns 3–7.
Where to start on this board
The most constrained color is where a solve should begin, and on #63 that is amber with 3 squares. It reaches from row 1 to row 2 and from column 6 to column 7 — 2 rows 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.
Amber spans 2 rows, so it stays open for now — but it is still the shortest list on the board at 3 squares. Work through those squares first and mark the ones that would leave another region homeless. That pruning is what makes the rest of the grid legible.
Work outward to the other flat regions next. Indigo 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 #63
A quick way to find the next move is to count how many different colors touch each line. On this board, row 7 is the narrowest, touched by only 2 colors. Columns 1, 2, 5, 6 and 7 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 6 rows. Row 4 is the crowded extreme at 4 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 49 squares of this grid. First: has any of the seven regions been reduced to a single open square? Second: has any row or column? Either answer forces a queen. Players who stall on 7x7 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 #63 is rated hard
The rating reflects how much the board concedes up front. Puzzle #63 has no region confined to a single row or column, its smallest color holds 3 squares, its tightest row meets just 2 colors, and the gap between its largest and smallest regions is 11 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.
Stuck on #63 despite the hard 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 7x7
At 7x7 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.
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 #63 the place to look for one is around row 7.
A non-spoiling distribution check: solved, #63 carries 4 queens on the perimeter against 3 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.
Full rules · Strategy library · Puzzle statistics
Questions about this puzzle
How hard is 7x7 Queens puzzle #63?
Puzzle #63 is rated hard. Its smallest color region holds 3 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 7x7 puzzle #63 have only one solution?
Yes. Every puzzle in the 7x7 collection, including #63, has been verified to have exactly one valid arrangement of seven queens, and it can always be reached by logic alone — no guessing or backtracking needed.
Where should I place my first queen on puzzle #63?
Start with the amber region — the most constrained color on this board, with 3 squares spanning rows 1–2 and columns 6–7. Narrowing the smallest region first removes the most squares elsewhere on the grid.