10x10 Queens Puzzle #195
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 18-step reasoning is written out below.
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Step-by-step solution for puzzle #195
What follows is a complete solve of puzzle #195, 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 pairing argument on columns.
Techniques this board needs: last square in a region, region confined to one line, region shadow, pairing argument on rows, pairing argument on columns, last square in a row.
Show the full walkthrough (14 steps) — contains the solution
Step 1. Only row 6, column 2 is still open in red, and since each colour must take a queen, that settles it. That clears row 6, column 2, the rest of the red 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. The khaki region has 3 squares left, spread across rows 8 and 9, columns 9 and 10. 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.
Step 4. The sea green region is down to one open square, at row 10, column 9. Every colour holds exactly one queen, so that square is forced. Row 10 and column 9 are now spoken for, along with the squares touching that queen.
Step 5. Only row 8, column 10 is still open in khaki, and since each colour must take a queen, that settles it. That clears row 8, column 10, the rest of the khaki region and every square adjacent to it — diagonals included.
The board after step 5 — 3 of 10 queens placed. Step 6. The pale yellow region has 2 squares left, spread across rows 7 and 9, columns 1 and 4. 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. Pale yellow and orange are now boxed into rows 7 and 9 and nothing else. That is 2 colours needing 2 rows, so they fill those rows between them — which locks every remaining colour out and removes 3 squares at once.
Step 8. The mint region is down to one open square, at row 4, column 8. Every colour holds exactly one queen, so that square is forced. Row 4 and column 8 are now spoken for, along with the squares touching that queen.
Step 9. The amber region has 4 squares left, spread across rows 2 and 3, columns 4–6. 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.
The board after step 9 — 4 of 10 queens placed. Step 10. Wherever slate ends up among its 2 squares, the same squares fall within reach of it — 2 squares in total, impossible regardless of how the colour resolves.
Step 11. Amber is down to 2 candidates in rows 2 and 3, columns 4 and 5, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about amber itself.
Step 12. The indigo region is down to one open square, at row 1, column 3. Every colour holds exactly one queen, so that square is forced. Row 1 and column 3 are now spoken for, along with the squares touching that queen.
Step 13. Amber, blue, and pale yellow are now boxed into columns 1, 4, and 5 and nothing else. That is 3 colours needing 3 columns, so they fill those columns between them — which locks every remaining colour out and removes 2 squares at once.
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: row 7 is down to one square, putting a queen on row 7, column 4; amber has one square left, so its queen takes row 2, column 5; blue has one square left, so its queen takes row 3, column 1; slate has one square left, so its queen takes row 5, column 6; orange has one square left, so its queen takes row 9, 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 9, column 7.
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 #195
10x10 puzzle #195 is rated medium. Ten colored regions cover its 100 squares, and your job is to seat ten queens so that every row, column and color contains exactly one — with no queen touching another, including diagonally.
Like every board on this site, #195 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 #195 are: red (1 square), sea green (2 squares), khaki (3 squares), indigo (5 squares), slate (11 squares), pale yellow (12 squares), blue (14 squares), amber (16 squares), mint (17 squares), orange (19 squares). An even split would hand every color 10 squares, so the red region is running 9 squares under that average while the orange region is the roomiest area on the grid with 19 squares.
One queen per color, regardless of acreage: that is what turns this uneven split into a solving order. Red is working with 1 square while orange has 19 to spare, a gap of 18. Attack the cramped end and the roomy regions tend to resolve themselves.
Square count is only half the story — how a color is arranged counts too. Red is the tidiest shape on #195, packing 100% of its 1×1 bounding box, whereas blue straggles across its 7×5 box at just 40%. 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 medium board.
Red: 1 square across rows 6–6, columns 2–2. It never leaves row 6, so its queen is locked to that row.
Sea green covers 2 squares, spanning 1 row and 2 columns (rows 10–10, columns 9–10). It never leaves row 10, so its queen is locked to that row.
Khaki occupies 3 squares within rows 8–9, columns 9–10.
Indigo: 5 squares across rows 1–3, columns 2–4.
Slate covers 11 squares, spanning 4 rows and 5 columns (rows 2–5, columns 5–9).
Pale yellow occupies 12 squares within rows 6–10, columns 1–5.
Blue: 14 squares across rows 1–7, columns 1–5.
Amber covers 16 squares, spanning 4 rows and 8 columns (rows 1–4, columns 3–10).
Mint occupies 17 squares within rows 3–8, columns 6–10.
Orange: 19 squares across rows 7–10, columns 2–8.
Where to start on this board
Open on the tightest color. Here that is red, confined to 1 square between rows 6 and 6 and columns 2 and 2. Its queen has nowhere else to go, which means those 1 row and 1 column carry more constraint than anywhere else on #195.
Because red never leaves row 6, its queen must be in that row — and that instantly settles row 6 for everyone else. Sweep along it and X out every square that is not red. 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 and khaki 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 #195
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 1, 5, 9 and 10 are the narrowest, touched by only 3 colors. Column 1 is the tightest column, with 2 colors.
Those lines matter because a row touched by few colors gives its queen away sooner. If a row meets only 3 colors, then one of those regions has to own it, and every other region is competing for the remaining 9 rows. By contrast row 3 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.
With ten queens to seat and ten regions competing over 100 squares, keep two questions in rotation. Does any region now have exactly one open square left? That queen is forced. Does any row or column now have exactly one open square left? That queen is forced too. Alternating between the region view and the row-and-column view is what keeps a solve moving, and it is the clearest difference between players who finish 10x10 boards quickly and players who stall halfway.
Resist the plausible-looking queen. On #195 every correct placement has a stated reason behind it, and any move you cannot justify is a guess wearing a disguise. Backing out of a wrong guess on a single-solution board takes far longer than finding the real deduction would have.
Why puzzle #195 is rated medium
The medium label comes out of four measurable things about #195: three 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 18. Boards that score tight on those measures give up their first queen fast.
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.
If #195 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.
Whatever the grid size, the pairing rule is the technique to internalise. When a pair of regions is boxed into the same pair of rows, they split those rows between them and nobody else may enter — and the same holds for columns, or for any n regions confined to n lines. Look for an instance of it around column 1 on this board.
As a sanity check rather than a spoiler: the finished solution to #195 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 #195?
Puzzle #195 is rated medium. Its smallest color region holds 1 square, its tightest row is touched by 3 colors, and three of its regions are confined to a single row or column, which gives you a forced move early.
Does 10x10 puzzle #195 have only one solution?
Yes. Every puzzle in the 10x10 collection, including #195, 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 #195?
Start with the red region — the most constrained color on this board, with 1 square spanning rows 6–6 and columns 2–2. Narrowing the smallest region first removes the most squares elsewhere on the grid.