10x10 Queens Puzzle #130
Difficulty: hard. Place 10 queens on this 10x10 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 18-step reasoning is written out below.
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Step-by-step solution for puzzle #130
What follows is a complete solve of puzzle #130, worked the way a person works it rather than the way a computer does. It runs to 18 deductions — 10 queen placements and 8 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 (14 steps) — contains the solution
Step 1. Only row 1, column 9 is still open in indigo, and since each colour must take a queen, that settles it. That clears row 1, column 9, the rest of the indigo region and every square adjacent to it — diagonals included.
Step 2. The sea green region is down to one open square, at row 10, column 1. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 10 and column 1, the remaining sea green squares, and the ring of neighbours around row 10, column 1.
Step 3. The amber region has 5 squares left, spread across rows 2 and 3, columns 3, 5, 6, and 7. 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.
Step 4. All of the khaki 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: 6 squares come off.
Step 5. Blue cannot leave column 3 — 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: 7 squares in all.
The board after step 5 — 2 of 10 queens placed. Step 6. The amber region has 4 squares left, spread across rows 2 and 3, columns 5–7. 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.
Step 7. Wherever slate ends up among its 3 squares, the same squares fall within reach of it — 3 squares in total, impossible regardless of how the colour resolves.
Step 8. The blue region is down to one open square, at row 3, column 3. Every colour holds exactly one queen, so that square is forced. Row 3 and column 3 are now spoken for, along with the squares touching that queen.
Step 9. Only row 4, column 10 is still open in mint, and since each colour must take a queen, that settles it. That clears row 4, column 10, the rest of the mint region and every square adjacent to it — diagonals included.
The board after step 9 — 4 of 10 queens placed. Step 10. The slate region is down to one open square, at row 5, column 4. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 5 and column 4, the remaining slate squares, and the ring of neighbours around row 5, column 4.
Step 11. Red is down to 3 candidates in rows 6 and 7, columns 6 and 7, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about red itself.
Step 12. The pale yellow region has 4 squares left, spread across rows 7 and 8, columns 5–7. 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.
Step 13. Red cannot leave row 6 — every one of its open squares (2 open squares) sits there. That row belongs to red, so every square on it owned by another colour is dead: 2 squares in all.
Step 14. 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: khaki has one square left, so its queen takes row 8, column 2; pale yellow has one square left, so its queen takes row 7, column 5; red has one square left, so its queen takes row 6, column 7; amber has one square left, so its queen takes row 2, column 6; orange has one square left, so its queen takes row 9, column 8. 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 9, column 8.
The board after step 14 — 10 of 10 queens placed.
That completes the board: 10 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 10x10 Queens puzzle #130
Board #130 of the 10x10 bank carries a hard rating. Its 100 squares are shared between ten colored regions, and the solution places ten queens: one per row, one per column, one per region, none of them side by side or corner to corner.
As with every puzzle in this collection, #130 has a single verified solution and needs no guesswork. Each queen follows from something already visible. What the board controls is tempo — how soon the first forced move shows up and how far apart the rest are spaced — and that is a direct consequence of how these colors are cut.
How the colors divide this board
From smallest to largest, the regions on puzzle #130 are: indigo (1 square), sea green (1 square), slate (9 squares), amber (10 squares), mint (10 squares), khaki (11 squares), blue (12 squares), red (14 squares), pale yellow (15 squares), orange (17 squares). An even split would hand every color 10 squares, so the indigo region is running 9 squares under that average while the orange region is the roomiest area on the grid with 17 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 indigo, with 1 square, is under far more pressure than orange with 17. A 16-square gap like this one rewards players who start where the choices are fewest.
Square count is only half the story — how a color is arranged counts too. Indigo is the tidiest shape on #130, packing 100% of its 1×1 bounding box, whereas khaki straggles across its 5×5 box at just 44%. Tidy blocks are easy to work around; scattered ones touch more lines and resist resolution.
Region by region
Each region's exact extent on this grid is listed below, starting with the most constrained. Knowing which lines a color can and cannot reach is most of the work on a hard board.
Indigo covers 1 square, spanning 1 row and 1 column (rows 1–1, columns 9–9). It never leaves row 1, so its queen is locked to that row.
Sea green occupies 1 square within rows 10–10, columns 1–1. It never leaves row 10, so its queen is locked to that row.
Slate: 9 squares across rows 2–6, columns 3–6.
Amber covers 10 squares, spanning 3 rows and 5 columns (rows 1–3, columns 3–7).
Mint occupies 10 squares within rows 1–4, columns 8–10.
Khaki: 11 squares across rows 6–10, columns 1–5.
Blue covers 12 squares, spanning 5 rows and 3 columns (rows 1–5, columns 1–3).
Red occupies 14 squares within rows 3–7, columns 6–10.
Pale yellow: 15 squares across rows 5–9, columns 2–7.
Orange covers 17 squares, spanning 5 rows and 6 columns (rows 6–10, columns 5–10).
Where to start on this board
The most constrained color is where a solve should begin, and on #130 that is indigo with 1 square. It reaches from row 1 to row 1 and from column 9 to column 9 — 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. Sea green 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 #130
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 8, 9 and 10 are the narrowest, touched by only 3 colors. Columns 1, 2, 8 and 10 are the tightest columns, with 3 colors.
A line with few colors is a line close to resolving. Where only 3 colors appear, one of them owns the row outright and the others must fit into the remaining 9 rows. Row 6 is the crowded extreme at 5 colors — worth revisiting later, not now.
Working through the middle game
The middle of #130 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 ten colors looking for one with a single square left; sweep the ten rows and ten columns looking for the same. Each sweep feeds the next, and switching between them deliberately — rather than drifting — is what separates a fast 10x10 solve from a stalled one.
The trap on a board like this is placing a queen that is merely plausible. Every placement should be traceable to an elimination you can point at. If you cannot name the rule that forced it, you are guessing — and on a single-solution grid a guess costs more to unwind than the deduction would have taken to find.
Why puzzle #130 is rated hard
The hard label comes out of four measurable things about #130: four of its regions are locked to one row or column, its smallest color spans 1 square, its least crowded row meets 3 colors, and its largest and smallest regions differ by 16. Boards that score tight on those measures give up their first queen fast.
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.
A board that feels above its rating is nearly always a board with a missing X. Audit every queen on the grid: full row cleared, full column cleared, all eight touching squares cleared. Diagonals are the common omission, and missing one is far more often the cause of a stall than any genuine difficulty in the puzzle.
Techniques that work well at 10x10
At 10x10 a full re-scan after every move starts to get slow, so work locally instead. Once a queen goes down, check only the regions, rows and columns that placement actually touched — that is where new information appeared. Fall back to a complete sweep only when the local pass turns up nothing, and your solve times will drop noticeably.
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 #130, start hunting for it near row 8.
A non-spoiling distribution check: solved, #130 carries 3 queens on the perimeter against 7 queens inside, 1 of them cornered. 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 10x10 Queens puzzle #130?
Puzzle #130 is rated hard. Its smallest color region holds 1 square, its tightest row is touched by 3 colors, and four of its regions are confined to a single row or column, which gives you a forced move early.
Does 10x10 puzzle #130 have only one solution?
Yes. Every puzzle in the 10x10 collection, including #130, has been verified to have exactly one valid arrangement of ten queens, and it can always be reached by logic alone — no guessing or backtracking needed.
Where should I place my first queen on puzzle #130?
Start with the indigo region — the most constrained color on this board, with 1 square spanning rows 1–1 and columns 9–9. Narrowing the smallest region first removes the most squares elsewhere on the grid.