7x7 Queens Puzzle #101
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 17-step reasoning is written out below.
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Step-by-step solution for puzzle #101
What follows is a complete solve of puzzle #101, worked the way a person works it rather than the way a computer does. It runs to 17 deductions — 7 queen placements and 10 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 proof by contradiction.
Techniques this board needs: last square in a region, region shadow, region confined to one line, line confined to one region, proof by contradiction.
Show the full walkthrough (13 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. Amber is down to 5 candidates in rows 2 and 3, columns 3–6, and they overlap enough to cover 2 squares elsewhere. Cross those out without deciding anything about amber itself.
Step 3. Blue cannot leave column 7 — every one of its open squares (2 open squares) sits there. That column belongs to blue, so every square in it owned by another colour is dead: 4 squares in all.
Step 4. All of the indigo region's remaining squares (2 open squares) lie in row 1. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 4 squares come off.
The board after step 4 — 1 of 7 queens placed. Step 5. Amber is down to 4 candidates in rows 2 and 3, columns 3–6, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about amber itself.
Step 6. All of the pale yellow region's remaining squares (2 open squares) lie in row 7. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 5 squares come off.
Step 7. Wherever red ends up among its 5 squares, the same squares fall within reach of it — 1 square in total, impossible regardless of how the colour resolves.
Step 8. Slate is down to 2 candidates in rows 2 and 5, columns 2 and 3, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about slate itself.
Step 9. Row 6 has only red squares left (3 open squares). The row needs a queen and only red can provide one, which pins that colour to this row and kills its squares elsewhere: 2 squares.
The board after step 9 — 1 of 7 queens placed. Step 10. Now a short proof by contradiction. Suppose the indigo queen went to row 1, column 5. Follow the forced moves that would create and the pale yellow region is left with nowhere to put its queen — impossible. So that square is ruled out for good.
Step 11. Only row 1, column 6 is still open in indigo, and since each colour must take a queen, that settles it. Everything else in row 1, in column 6, in indigo and in the ring around that square is now dead.
Step 12. Now a short proof by contradiction. Suppose the amber queen went to row 3, column 5. Follow the forced moves that would create and the pale yellow region is left with nowhere to put its queen — impossible. So that square is ruled out for good.
Step 13. 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: amber has one square left, so its queen takes row 2, column 4; slate has one square left, so its queen takes row 5, column 3; blue has one square left, so its queen takes row 3, column 7; red has one square left, so its queen takes row 6, column 5; pale yellow has one square left, so its queen takes row 7, 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 7, column 2.
The board after step 13 — 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 #101
Puzzle #101 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.
Like every board on this site, #101 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 #101 are: mint (1 square), blue (3 squares), pale yellow (3 squares), indigo (5 squares), amber (6 squares), red (12 squares), slate (19 squares). An even split would hand every color 7 squares, so the mint region is running 6 squares under that average while the slate region is the roomiest area on the grid with 19 squares.
Every color takes one queen and one only, whatever its size — which is why the 18 square difference between mint and slate is worth noting before you touch the grid. The cramped colors resolve first and hand you information; the roomy ones absorb whatever is left over at the end.
Shape matters as much as size. The blue region is the most compact color here, filling 100% of the 3×1 box that encloses it, while amber is the most scattered at 50% of its 3×4 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
Below is every color on #101 with its exact reach, smallest region first. It is worth a slow read: the spans reveal which rows and columns several regions are fighting over.
Mint occupies 1 square within rows 4–4, columns 1–1. It never leaves row 4, so its queen is locked to that row.
Blue: 3 squares across rows 3–5, columns 7–7. It sits wholly inside column 7, so its queen must be in that column.
Pale yellow covers 3 squares, spanning 1 row and 3 columns (rows 7–7, columns 1–3). It never leaves row 7, so its queen is locked to that row.
Indigo occupies 5 squares within rows 1–2, columns 5–7.
Amber: 6 squares across rows 2–4, columns 3–6.
Red covers 12 squares, spanning 3 rows and 6 columns (rows 5–7, columns 2–7).
Slate occupies 19 squares within rows 1–6, columns 1–5.
Where to start on this board
Mint is the natural opening on #101: it is the smallest region on the grid at 1 square, boxed into rows 4–4 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 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. Pale yellow and indigo 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 #101
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 1, 6 and 7 are the narrowest, touched by only 2 colors. Columns 1, 2, 4, 6 and 7 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 6 rows. Row 4 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 #101 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.
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 #101 is rated easy
What earns a board its rating is the shape of its opening. Here that opening offers four single-line regions, a 1-square smallest color, a tightest row touched by 2 colors, and a region-size spread of 18. Lopsided grids with flat regions fall quickly; balanced ones like this take more patience.
Rating is a measure of chain length, not of chance. With one guaranteed solution and no guessing required, the only thing that changes across the collection is how many eliminations you must link together before a queen is provably forced.
If #101 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.
There is one technique that repays study at every grid size. Two regions restricted to the same two rows must occupy one row apiece, which excludes all other regions from those rows entirely; the identical logic applies to columns and to larger matched sets. It converts slow boards into fast ones, and the likeliest place to find it on #101 is row 1.
Use this as a rough check on your progress: the completed board has 4 queens around the border and 3 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 7x7 Queens puzzle #101?
Puzzle #101 is rated easy. Its smallest color region holds 1 square, its tightest row is touched by 2 colors, and four of its regions are confined to a single row or column, which gives you a forced move early.
Does 7x7 puzzle #101 have only one solution?
Yes. Every puzzle in the 7x7 collection, including #101, 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 #101?
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.