7x7 Queens Puzzle #145
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 10-step reasoning is written out below.
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Step-by-step solution for puzzle #145
What follows is a complete solve of puzzle #145, worked the way a person works it rather than the way a computer does. It runs to 10 deductions — 7 queen placements and 3 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 shadow, region confined to one line.
Show the full walkthrough (5 steps) — contains the solution
Step 1. Only row 3, column 1 is still open in blue, and since each colour must take a queen, that settles it. That clears row 3, column 1, the rest of the blue region and every square adjacent to it — diagonals included.
Step 2. Mint is down to 4 candidates in rows 2 and 4, columns 3–5, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about mint itself.
Step 3. Pale yellow cannot leave row 7 — every one of its open squares (3 open squares) sits there. That row belongs to pale yellow, so every square on it owned by another colour is dead: 4 squares in all.
The board after step 3 — 1 of 7 queens placed. Step 4. All of the red region's remaining squares (2 open squares) lie in row 6. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 5 squares come off.
Step 5. 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: slate has one square left, so its queen takes row 5, column 3; indigo has one square left, so its queen takes row 1, column 2; pale yellow has one square left, so its queen takes row 7, column 4; mint has one square left, so its queen takes row 4, column 5; red has one square left, so its queen takes row 6, column 6; amber has one square left, so its queen takes row 2, 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 2, 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 #145
Puzzle #145 is one of the easy-rated boards in the 7x7 set. Seven colors divide its 49 squares, and you win by placing seven queens so that each row, each column and each color holds exactly one, with no two queens adjacent in any direction.
There is exactly one way to finish #145, 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 #145 are: blue (1 square), red (5 squares), pale yellow (5 squares), slate (6 squares), mint (7 squares), amber (12 squares), indigo (13 squares). An even split would hand every color 7 squares, so the blue region is running 6 squares under that average while the indigo region is the roomiest area on the grid with 13 squares.
Why does the split matter? Because a region's square count has no bearing on how many queens it gets — the answer is always one. So blue, with 1 square, is under far more pressure than indigo with 13. A 12-square gap like this one rewards players who start where the choices are fewest.
Shape matters as much as size. The blue region is the most compact color here, filling 100% of the 1×1 box that encloses it, while amber is the most scattered at 50% of its 6×4 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 #145, 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 1 square, spanning 1 row and 1 column (rows 3–3, columns 1–1). It never leaves row 3, so its queen is locked to that row.
Red occupies 5 squares within rows 6–7, columns 5–7.
Pale yellow: 5 squares across rows 6–7, columns 1–4.
Slate covers 6 squares, spanning 2 rows and 4 columns (rows 5–6, columns 3–6).
Mint occupies 7 squares within rows 2–4, columns 3–6.
Amber: 12 squares across rows 1–6, columns 4–7.
Indigo covers 13 squares, spanning 6 rows and 3 columns (rows 1–6, columns 1–3).
Where to start on this board
Blue is the natural opening on #145: it is the smallest region on the grid at 1 square, boxed into rows 3–3 and columns 1–1. Since one of those squares must hold a queen, that block of 1 row and 1 column is the most contested part of the board.
Because blue never leaves row 3, its queen must be in that row — and that instantly settles row 3 for everyone else. Sweep along it and X out every square that is not blue. 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. Slate, pale yellow 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 #145
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 1 and 7 are the narrowest, touched by only 2 colors. Columns 2 and 7 are the tightest columns, 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 6 meets 5 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.
The whole middle game reduces to two sweeps. Sweep the seven colors looking for one with a single square left; sweep the seven rows and seven columns looking for the same. Each sweep feeds the next, and switching between them deliberately — rather than drifting — is what separates a fast 7x7 solve from a stalled one.
A placement without a reason is a guess. Because this board has exactly one solution, a guess that happens to be wrong will not announce itself for several moves — and unwinding it is slower than simply finishing the eliminations first.
Why puzzle #145 is rated easy
The rating reflects how much the board concedes up front. Puzzle #145 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 12 squares. Flat, lopsided boards open quickly; even, sprawling ones make you earn the first placement.
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.
Stuck on #145 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 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.
Learn the pairing argument and you will use it on every board, this one included. If two colors can only sit inside the same two rows, between them they consume both rows and every other color is shut out. It generalises to any matching count — three colors across three rows, four across four. On #145, start hunting for it near row 1.
As a sanity check rather than a spoiler: the finished solution to #145 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 #145?
Puzzle #145 is rated easy. 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 7x7 puzzle #145 have only one solution?
Yes. Every puzzle in the 7x7 collection, including #145, 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 #145?
Start with the blue region — the most constrained color on this board, with 1 square spanning rows 3–3 and columns 1–1. Narrowing the smallest region first removes the most squares elsewhere on the grid.