10x10 Queens Puzzle #210
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 19-step reasoning is written out below.
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Step-by-step solution for puzzle #210
What follows is a complete solve of puzzle #210, worked the way a person works it rather than the way a computer does. It runs to 19 deductions — 10 queen placements and 9 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 line confined to one region.
Techniques this board needs: last square in a region, region confined to one line, region shadow, line confined to one region, last square in a row, last square in a column.
Show the full walkthrough (14 steps) — contains the solution
Step 1. Only row 8, column 4 is still open in khaki, and since each colour must take a queen, that settles it. That clears row 8, column 4, the rest of the khaki region and every square adjacent to it — diagonals included.
Step 2. 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: 9 squares come off.
Step 3. Only row 2, column 10 is still open in amber, and since each colour must take a queen, that settles it. Everything else in row 2, in column 10, in amber and in the ring around that square is now dead.
Step 4. The indigo region is down to one open square, at row 1, column 8. Every colour holds exactly one queen, so that square is forced. Row 1 and column 8 are now spoken for, along with the squares touching that queen.
Step 5. Blue is down to 6 candidates in rows 3–5, columns 5–7, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about blue itself.
The board after step 5 — 3 of 10 queens placed. Step 6. All of the slate region's remaining squares (2 open squares) lie in column 9. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 4 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. The pale yellow region is down to one open square, at row 7, column 7. Every colour holds exactly one queen, so that square is forced. Row 7 and column 7 are now spoken for, along with the squares touching that queen.
Step 9. The red region has 2 squares left, spread across rows 5 and 6, columns 5 and 6. You do not need to know which of them takes the queen: every one of those options attacks the same 2 squares, so they can be crossed out now.
The board after step 9 — 4 of 10 queens placed. Step 10. All of the blue region's remaining squares (2 open squares) lie in row 3. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 3 squares come off.
Step 11. Mint is down to 7 candidates in rows 4–6, columns 1–3, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about mint itself.
Step 12. The orange region has 2 squares left, spread across rows 6 and 9, columns 1 and 2. You do not need to know which of them takes the queen: every one of those options attacks the same 4 squares, so they can be crossed out now.
Step 13. Row 10 has only sea green squares left (4 open squares). The row needs a queen and only sea green can provide one, which pins that colour to this row and kills its squares elsewhere: 1 square.
Step 14. 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: row 9 is down to one square, putting a queen on row 9, column 1; column 2 is down to one square, putting a queen on row 4, column 2; slate has one square left, so its queen takes row 5, column 9; red has one square left, so its queen takes row 6, column 5; blue has one square left, so its queen takes row 3, column 6; sea green has one square left, so its queen takes row 10, column 3. 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 10, column 3.
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 #210
Board #210 of the 10x10 bank carries a medium 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.
Like every board on this site, #210 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 #210 are: khaki (1 square), indigo (2 squares), amber (4 squares), orange (9 squares), mint (10 squares), red (10 squares), slate (13 squares), sea green (14 squares), pale yellow (15 squares), blue (22 squares). An even split would hand every color 10 squares, so the khaki region is running 9 squares under that average while the blue region is the roomiest area on the grid with 22 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 khaki, with 1 square, is under far more pressure than blue with 22. A 21-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 1×2 box that encloses it, while pale yellow is the most scattered at 50% of its 5×6 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
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 medium board.
Khaki: 1 square across rows 8–8, columns 4–4. It never leaves row 8, so its queen is locked to that row.
Indigo covers 2 squares, spanning 1 row and 2 columns (rows 1–1, columns 8–9). It never leaves row 1, so its queen is locked to that row.
Amber occupies 4 squares within rows 1–2, columns 8–10.
Orange: 9 squares across rows 5–9, columns 1–3.
Mint covers 10 squares, spanning 4 rows and 3 columns (rows 3–6, columns 1–3).
Red occupies 10 squares within rows 4–7, columns 4–7.
Slate: 13 squares across rows 3–7, columns 8–10.
Sea green covers 14 squares, spanning 2 rows and 8 columns (rows 9–10, columns 1–8).
Pale yellow occupies 15 squares within rows 6–10, columns 5–10.
Blue: 22 squares across rows 1–5, columns 1–7.
Where to start on this board
The most constrained color is where a solve should begin, and on #210 that is khaki with 1 square. It reaches from row 8 to row 8 and from column 4 to column 4 — 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 khaki never leaves row 8, its queen must be in that row — and that instantly settles row 8 for everyone else. Sweep along it and X out every square that is not khaki. 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. Indigo, 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 #210
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 2 and 10 are the narrowest, touched by only 2 colors. Column 10 is the tightest column, with 3 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 9 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
The middle of #210 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.
Keep alternating between two views of the board. In the region view you ask which of the ten colors is down to one open square. In the line view you ask the same of each row and column. Both produce forced queens, and each placement refreshes the other view, so cycling between them deliberately is how a 10x10 board unwinds.
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 #210 is rated medium
The medium label comes out of four measurable things about #210: three of its regions are locked to one row or column, its smallest color spans 1 square, its least crowded row meets 2 colors, and its largest and smallest regions differ by 21. Boards that score tight on those measures give up their first queen fast.
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 #210 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 #210, start hunting for it near row 2.
As a sanity check rather than a spoiler: the finished solution to #210 puts 4 queens on the outer border and 6 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 10x10 Queens puzzle #210?
Puzzle #210 is rated medium. 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 10x10 puzzle #210 have only one solution?
Yes. Every puzzle in the 10x10 collection, including #210, 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 #210?
Start with the khaki region — the most constrained color on this board, with 1 square spanning rows 8–8 and columns 4–4. Narrowing the smallest region first removes the most squares elsewhere on the grid.