7x7 Queens Puzzle #143
Difficulty: easy. 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 9-step reasoning is written out below.
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Step-by-step solution for puzzle #143
What follows is a complete solve of puzzle #143, worked the way a person works it rather than the way a computer does. It runs to 9 deductions — 7 queen placements and 2 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 region shadow.
Techniques this board needs: last square in a region, region confined to one line, region shadow.
Show the full walkthrough (5 steps) — contains the solution
Step 1. Only row 1, column 3 is still open in indigo, and since each colour must take a queen, that settles it. That clears row 1, column 3, the rest of the indigo region and every square adjacent to it — diagonals included.
Step 2. The amber region is down to one open square, at row 2, column 1. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 2 and column 1, the remaining amber squares, and the ring of neighbours around row 2, column 1.
Step 3. Slate cannot leave column 2 — 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: 1 square in all.
The board after step 3 — 2 of 7 queens placed. Step 4. Wherever red ends up among its 3 squares, the same squares fall within reach of it — 2 squares in total, impossible regardless of how the colour resolves.
Step 5. 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: 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 4; mint has one square left, so its queen takes row 4, column 5; slate has one square left, so its queen takes row 5, column 2; blue has one square left, so its queen takes row 3, column 7. 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 3, column 7.
The board after step 5 — 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 #143
7x7 puzzle #143 is rated easy. 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.
Like every board on this site, #143 has been verified to have exactly one valid solution, and that solution is reachable by deduction alone. You never have to guess and then unwind; every queen can be justified by something already visible on the grid. What changes from puzzle to puzzle is where the first certainty appears and how long the chain of reasoning runs before the next one — and that is entirely a product of how these particular colors are shaped.
How the colors divide this board
From smallest to largest, the regions on puzzle #143 are: indigo (1 square), pale yellow (2 squares), amber (3 squares), red (4 squares), slate (9 squares), blue (15 squares), mint (15 squares). An even split would hand every color 7 squares, so the indigo region is running 6 squares under that average while the mint 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. Indigo is working with 1 square while mint has 15 to spare, a gap of 14. Attack the cramped end and the roomy regions tend to resolve themselves.
Look at arrangement as well as area. Indigo is the densest region on this grid at 100% of a 1×1 frame; mint is the loosest, occupying only 36% of its 6×7 frame. The loose one reaches into more rows and columns, which is exactly why it usually settles last.
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.
Indigo occupies 1 square within rows 1–1, columns 3–3. It never leaves row 1, so its queen is locked to that row.
Pale yellow: 2 squares across rows 7–7, columns 5–6. It never leaves row 7, so its queen is locked to that row.
Amber covers 3 squares, spanning 2 rows and 2 columns (rows 1–2, columns 1–2).
Red occupies 4 squares within rows 6–7, columns 3–5.
Slate: 9 squares across rows 4–7, columns 1–3.
Blue covers 15 squares, spanning 5 rows and 4 columns (rows 1–5, columns 4–7).
Mint occupies 15 squares within rows 2–7, columns 1–7.
Where to start on this board
The most constrained color is where a solve should begin, and on #143 that is indigo with 1 square. It reaches from row 1 to row 1 and from column 3 to column 3 — 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 indigo never leaves row 1, its queen must be in that row — and that instantly settles row 1 for everyone else. Sweep along it and X out every square that is not indigo. 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. Pale yellow, amber and red are no more than two rows tall, so their queens are 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 #143
A quick way to find the next move is to count how many different colors touch each line. On this board, row 3 is the narrowest, touched by only 2 colors. Column 7 is the tightest column, with 2 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 6 rows. By contrast row 7 meets 4 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.
With seven queens to seat and seven regions competing over 49 squares, keep two questions in rotation. Does any region now have exactly one open square left? That queen is forced. Does any row or column now have exactly one open square left? That queen is forced too. Alternating between the region view and the row-and-column view is what keeps a solve moving, and it is the clearest difference between players who finish 7x7 boards quickly and players who stall halfway.
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 #143 is rated easy
Ratings track how generous the opening is. On #143 you get three regions pinned to a single row or column, a smallest color of 1 square, a tightest row crossed by 2 colors, and a 14-square gap between the largest and smallest regions. Those four numbers largely explain the easy label.
Nothing about the rating involves computation or chance. Each grid has a single solution reachable by pure logic; the rating simply measures how far ahead you have to reason. Easy boards resolve a queen every step or two, while hard ones can ask you to carry three unfinished lines of thought before any of them pays off.
If #143 feels harder than its rating suggests, the usual culprit is incomplete marking rather than a difficult deduction. Check that every queen already on the grid has its full cross of eliminations recorded — including the diagonal neighbours, which are by far the easiest to miss. More stalled solves come from one forgotten diagonal X than from any genuinely deep chain of logic.
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.
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 3 on this board.
As a sanity check rather than a spoiler: the finished solution to #143 puts 4 queens on the outer border and 3 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 7x7 Queens puzzle #143?
Puzzle #143 is rated easy. Its smallest color region holds 1 square, 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 7x7 puzzle #143 have only one solution?
Yes. Every puzzle in the 7x7 collection, including #143, 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 #143?
Start with the indigo region — the most constrained color on this board, with 1 square spanning rows 1–1 and columns 3–3. Narrowing the smallest region first removes the most squares elsewhere on the grid.