10x10 Queens Puzzle #236
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 16-step reasoning is written out below.
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Step-by-step solution for puzzle #236
What follows is a complete solve of puzzle #236, worked the way a person works it rather than the way a computer does. It runs to 16 deductions — 10 queen placements and 6 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: region confined to one line, last square in a region, region shadow.
Show the full walkthrough (12 steps) — contains the solution
Step 1. Indigo cannot leave row 1 — every one of its open squares (2 open squares) sits there. That row belongs to indigo, so every square on it owned by another colour is dead: 10 squares in all.
Step 2. The blue region is down to one open square, at row 3, column 10. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 3 and column 10, the remaining blue squares, and the ring of neighbours around row 3, column 10.
Step 3. Only row 1, column 9 is still open in indigo, and since each colour must take a queen, that settles it. Everything else in row 1, in column 9, in indigo and in the ring around that square is now dead.
Step 4. All of the amber region's remaining squares (4 open squares) lie in row 2. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 3 squares come off.
The board after step 4 — 2 of 10 queens placed. Step 5. Mint cannot leave row 4 — every one of its open squares (2 open squares) sits there. That row belongs to mint, so every square on it owned by another colour is dead: 8 squares in all.
Step 6. The slate region is down to one open square, at row 5, column 1. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 5 and column 1, the remaining slate squares, and the ring of neighbours around row 5, column 1.
Step 7. Only row 4, column 3 is still open in mint, and since each colour must take a queen, that settles it. Everything else in row 4, in column 3, in mint and in the ring around that square is now dead.
Step 8. All of the khaki region's remaining squares (3 open squares) lie in column 4. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 4 squares come off.
The board after step 8 — 4 of 10 queens placed. Step 9. Only row 10, column 2 is still open in sea green, and since each colour must take a queen, that settles it. That clears row 10, column 2, the rest of the sea green region and every square adjacent to it — diagonals included.
Step 10. Wherever red ends up among its 3 squares, the same squares fall within reach of it — 2 squares in total, impossible regardless of how the colour resolves.
Step 11. Khaki cannot leave column 4 — every one of its open squares (2 open squares) sits there. That column belongs to khaki, so every square in it owned by another colour is dead: 1 square in all.
Step 12. 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: orange has one square left, so its queen takes row 9, column 6; amber has one square left, so its queen takes row 2, column 7; 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 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 #236
This is puzzle number 236 in the 10x10 collection, rated medium. The grid holds 100 squares split between ten colored regions, and a finished board carries ten queens — one in every row, one in every column, one in every color, and never two of them touching, diagonals included.
There is exactly one way to finish #236, and it has been verified. More importantly, you can reach it without ever gambling: at every stage some square is provably right or provably wrong. Boards differ only in how deep you must dig before that proof appears, and the geometry of these ten regions is what sets the depth.
How the colors divide this board
From smallest to largest, the regions on puzzle #236 are: indigo (2 squares), blue (2 squares), slate (3 squares), khaki (4 squares), orange (5 squares), mint (8 squares), sea green (10 squares), amber (13 squares), red (18 squares), pale yellow (35 squares). An even split would hand every color 10 squares, so the indigo region is running 8 squares under that average while the pale yellow region is the roomiest area on the grid with 35 squares.
Every color takes one queen and one only, whatever its size — which is why the 33 square difference between indigo and pale yellow 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.
Look at arrangement as well as area. Indigo is the densest region on this grid at 100% of a 1×2 frame; red is the loosest, occupying only 45% of its 8×5 frame. The loose one reaches into more rows and columns, which is exactly why it usually settles last.
Region by region
Here is the full footprint of every color on puzzle #236, smallest first. Reading these spans before you place anything is the quickest way to see which parts of the grid are genuinely contested.
Indigo occupies 2 squares within rows 1–1, columns 9–10. It never leaves row 1, so its queen is locked to that row.
Blue: 2 squares across rows 2–3, columns 10–10. It sits wholly inside column 10, so its queen must be in that column.
Slate covers 3 squares, spanning 2 rows and 2 columns (rows 4–5, columns 1–2).
Khaki occupies 4 squares within rows 7–9, columns 3–4.
Orange: 5 squares across rows 8–10, columns 5–6.
Mint covers 8 squares, spanning 4 rows and 3 columns (rows 1–4, columns 1–3).
Sea green occupies 10 squares within rows 6–10, columns 1–4.
Amber: 13 squares across rows 1–3, columns 2–8.
Red covers 18 squares, spanning 8 rows and 5 columns (rows 2–9, columns 2–6).
Pale yellow occupies 35 squares within rows 2–10, columns 6–10.
Where to start on this board
Indigo is the natural opening on #236: it is the smallest region on the grid at 2 squares, boxed into rows 1–1 and columns 9–10. Since one of those squares must hold a queen, that block of 1 row and 2 columns is the most contested part of 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. Blue and slate 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 #236
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 1, 5, 6 and 10 are the narrowest, touched by only 3 colors. Columns 7, 8 and 9 are the tightest columns, with 2 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 9 is the crowded extreme at 5 colors — worth revisiting later, not now.
Working through the middle game
After the first few queens the puzzle becomes bookkeeping. A placed queen wipes its row, its column and every square it touches — as many as eight neighbours — so the space collapses quickly. Record those eliminations on the board instead of carrying them in your head, and the next forced move tends to announce itself.
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 #236 is rated medium
The rating reflects how much the board concedes up front. Puzzle #236 has two regions confined to a single row or column, its smallest color holds 2 squares, its tightest row meets just 3 colors, and the gap between its largest and smallest regions is 33 squares. Flat, lopsided boards open quickly; even, sprawling ones make you earn the first placement.
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.
Stuck on #236 despite the medium rating? The odds strongly favour a bookkeeping error over a hard chain of logic. Re-check each placed queen for its complete set of eliminations, paying particular attention to the four diagonal squares — those are the ones that get overlooked, and one of them is usually sitting on the answer.
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.
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 #236 is column 7.
A non-spoiling distribution check: solved, #236 carries 4 queens on the perimeter against 6 queens inside, with the corners empty. 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 #236?
Puzzle #236 is rated medium. Its smallest color region holds 2 squares, its tightest row is touched by 3 colors, and two of its regions are confined to a single row or column, which gives you a forced move early.
Does 10x10 puzzle #236 have only one solution?
Yes. Every puzzle in the 10x10 collection, including #236, 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 #236?
Start with the indigo region — the most constrained color on this board, with 2 squares spanning rows 1–1 and columns 9–10. Narrowing the smallest region first removes the most squares elsewhere on the grid.