10x10 Queens Puzzle #101
Difficulty: medium. 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 15-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 15 deductions — 10 queen placements and 5 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 (12 steps) — contains the solution
Step 1. Only row 9, column 1 is still open in orange, and since each colour must take a queen, that settles it. That clears row 9, column 1, the rest of the orange region and every square adjacent to it — diagonals included.
Step 2. 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.
Step 3. Only row 10, column 6 is still open in sea green, and since each colour must take a queen, that settles it. Everything else in row 10, in column 6, in sea green and in the ring around that square is now dead.
Step 4. All of the indigo region's remaining squares (3 open squares) lie in column 10. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 5 squares come off.
The board after step 4 — 3 of 10 queens placed. Step 5. Amber is down to 5 candidates in rows 1 and 2, columns 5, 7, 8, and 9, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about amber itself.
Step 6. The blue region is down to one open square, at row 3, column 9. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 3 and column 9, the remaining blue squares, and the ring of neighbours around row 3, column 9.
Step 7. Only row 1, column 10 is still open in indigo, and since each colour must take a queen, that settles it. Everything else in row 1, in column 10, in indigo and in the ring around that square is now dead.
Step 8. All of the amber region's remaining squares (2 open squares) lie in row 2. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 2 squares come off.
The board after step 8 — 5 of 10 queens placed. Step 9. Slate cannot leave column 5 — every one of its open squares (4 open squares) sits there. That column belongs to slate, so every square in it owned by another colour is dead: 1 square in all.
Step 10. The amber region is down to one open square, at row 2, column 7. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 2 and column 7, the remaining amber squares, and the ring of neighbours around row 2, column 7.
Step 11. Red is down to 5 candidates in rows 5–8, columns 3 and 4, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about red itself.
Step 12. From here the board cascades. Keep alternating the region sweep and the line sweep and 4 queens fall out in order without any new idea being needed: khaki has one square left, so its queen takes row 8, column 4; red has one square left, so its queen takes row 6, 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 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 7, column 8.
The board after step 12 — 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 #101
Puzzle #101 is one of the medium-rated boards in the 10x10 set. Ten colors divide its 100 squares, and you win by placing ten 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: orange (1 square), sea green (2 squares), indigo (3 squares), mint (4 squares), blue (6 squares), amber (7 squares), khaki (9 squares), slate (12 squares), pale yellow (25 squares), red (31 squares). An even split would hand every color 10 squares, so the orange region is running 9 squares under that average while the red region is the roomiest area on the grid with 31 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 orange, with 1 square, is under far more pressure than red with 31. A 30-square gap like this one rewards players who start where the choices are fewest.
Shape matters as much as size. The indigo region is the most compact color here, filling 100% of the 3×1 box that encloses it, while khaki is the most scattered at 45% of its 4×5 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 #101, smallest first. Reading these spans before you place anything is the quickest way to see which parts of the grid are genuinely contested.
Orange occupies 1 square within rows 9–9, columns 1–1. It never leaves row 9, so its queen is locked to that row.
Sea green: 2 squares across rows 9–10, columns 6–6. It sits wholly inside column 6, so its queen must be in that column.
Indigo covers 3 squares, spanning 3 rows and 1 column (rows 1–3, columns 10–10). It sits wholly inside column 10, so its queen must be in that column.
Mint occupies 4 squares within rows 3–5, columns 1–2.
Blue: 6 squares across rows 2–5, columns 8–10.
Amber covers 7 squares, spanning 2 rows and 5 columns (rows 1–2, columns 5–9).
Khaki occupies 9 squares within rows 7–10, columns 1–5.
Slate: 12 squares across rows 3–8, columns 5–8.
Pale yellow covers 25 squares, spanning 6 rows and 5 columns (rows 5–10, columns 6–10).
Red occupies 31 squares within rows 1–9, columns 1–6.
Where to start on this board
Begin where the choices are fewest. On this board that means orange, which owns just 1 square inside a 1×1 window running from row 9 to row 9 and column 1 to column 1. A queen is guaranteed somewhere in there, so every line that window crosses is under pressure from the very first move.
Because orange never leaves row 9, its queen must be in that row — and that instantly settles row 9 for everyone else. Sweep along it and X out every square that is not orange. 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. Amber and sea green 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 10 are the narrowest, touched by only 3 colors. Columns 3 and 4 are the tightest columns, with 2 colors.
Count colors per line and you have a ranking of where to look. The narrowest rows here see only 3 colors, so one of that handful must take the row and the rest are squeezed into the other 9 rows. Row 9 sits at the far end with 5 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.
Two checks, run alternately, will carry you through the 100 squares of this grid. First: has any of the ten regions been reduced to a single open square? Second: has any row or column? Either answer forces a queen. Players who stall on 10x10 boards almost always run one of those checks and forget the other.
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 medium
The rating reflects how much the board concedes up front. Puzzle #101 has four regions confined to a single row or column, its smallest color holds 1 square, its tightest row meets just 3 colors, and the gap between its largest and smallest regions is 30 squares. Flat, lopsided boards open quickly; even, sprawling ones make you earn the first placement.
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 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 #101, start hunting for it near column 3.
Use this as a rough check on your progress: the completed board has 3 queens around the border and 7 queens in the middle, including 1 in a corner. 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 10x10 Queens puzzle #101?
Puzzle #101 is rated medium. 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 #101 have only one solution?
Yes. Every puzzle in the 10x10 collection, including #101, 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 #101?
Start with the orange region — the most constrained color on this board, with 1 square spanning rows 9–9 and columns 1–1. Narrowing the smallest region first removes the most squares elsewhere on the grid.