10x10 Queens Puzzle #238

Difficulty: easy. 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 #238

What follows is a complete solve of puzzle #238, 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 line confined to one region.

Techniques this board needs: region confined to one line, last square in a region, region shadow, line confined to one region, last square in a row.

Show the full walkthrough (11 steps) — contains the solution

  1. Step 1. Amber cannot leave row 2 — every one of its open squares (2 open squares) sits there. That row belongs to amber, so every square on it owned by another colour is dead: 12 squares in all.

  2. 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: 6 squares come off.

  3. Step 3. Only row 3, column 7 is still open in blue, and since each colour must take a queen, that settles it. Everything else in row 3, in column 7, in blue and in the ring around that square is now dead.

  4. Step 4. The amber region is down to one open square, at row 2, column 5. Every colour holds exactly one queen, so that square is forced. Row 2 and column 5 are now spoken for, along with the squares touching that queen.

    Puzzle #238 after step 4: 2 of 10 queens placed
    The board after step 4 — 2 of 10 queens placed.

  5. Step 5. Pale yellow is down to 3 candidates in rows 7 and 8, columns 3 and 4, and they overlap enough to cover 2 squares elsewhere. Cross those out without deciding anything about pale yellow itself.

  6. Step 6. All of the khaki region's remaining squares (2 open squares) lie in row 8. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 9 squares come off.

  7. Step 7. Pale yellow cannot leave row 7 — every one of its open squares (2 open squares) sits there. That row belongs to pale yellow, so every square on it owned by another colour is dead: 5 squares in all.

    Puzzle #238 after step 7: 2 of 10 queens placed
    The board after step 7 — 2 of 10 queens placed.

  8. Step 8. Orange is down to 3 candidates in rows 9 and 10, columns 9 and 10, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about orange itself.

  9. Step 9. Column 6 has only red squares left (4 open squares). The column needs a queen and only red can provide one, which pins that colour to this column and kills its squares elsewhere: 5 squares.

  10. Step 10. Every open square left in column 8 (2 open squares) belongs to the slate region. Since that column must contain a queen, slate is the colour that supplies it — so slate squares anywhere else on the board are out, 6 squares in all.

  11. Step 11. From here the board cascades. Keep alternating the region sweep and the line sweep and 8 queens fall out in order without any new idea being needed: row 4 is down to one square, putting a queen on row 4, column 1; 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 4; sea green has one square left, so its queen takes row 10, column 3; orange has one square left, so its queen takes row 9, column 10; indigo has one square left, so its queen takes row 1, column 9; slate has one square left, so its queen takes row 5, column 8; red has one square left, so its queen takes row 6, column 6. 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 6, column 6.

    Puzzle #238 after step 11: 10 of 10 queens placed
    The board after step 11 — 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 #238

Board #238 of the 10x10 bank carries a easy 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.

There is exactly one way to finish #238, 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 #238 are: amber (2 squares), khaki (3 squares), orange (3 squares), indigo (4 squares), blue (4 squares), pale yellow (7 squares), sea green (9 squares), slate (22 squares), mint (23 squares), red (23 squares). An even split would hand every color 10 squares, so the amber region is running 8 squares under that average while the red region is the roomiest area on the grid with 23 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 amber, with 2 squares, is under far more pressure than red with 23. 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 2×2 box that encloses it, while red is the most scattered at 37% of its 9×7 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 easy board.

Amber covers 2 squares, spanning 1 row and 2 columns (rows 2–2, columns 5–6). It never leaves row 2, so its queen is locked to that row.

Khaki occupies 3 squares within rows 8–8, columns 1–3. It never leaves row 8, so its queen is locked to that row.

Orange: 3 squares across rows 9–10, columns 9–10.

Indigo covers 4 squares, spanning 2 rows and 2 columns (rows 1–2, columns 9–10).

Blue occupies 4 squares within rows 1–3, columns 7–8.

Pale yellow: 7 squares across rows 5–8, columns 3–5.

Sea green covers 9 squares, spanning 2 rows and 5 columns (rows 9–10, columns 1–5).

Slate occupies 22 squares within rows 3–9, columns 7–10.

Mint: 23 squares across rows 1–7, columns 1–7.

Red covers 23 squares, spanning 9 rows and 7 columns (rows 2–10, columns 2–8).

Where to start on this board

The most constrained color is where a solve should begin, and on #238 that is amber with 2 squares. It reaches from row 2 to row 2 and from column 5 to column 6 — 1 row by 2 columns. 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 amber never leaves row 2, its queen must be in that row — and that instantly settles row 2 for everyone else. Sweep along it and X out every square that is not amber. 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. Khaki, indigo, sea green and orange 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 #238

A quick way to find the next move is to count how many different colors touch each line. On this board, rows 1, 4 and 10 are the narrowest, touched by only 3 colors. Columns 1, 6, 8, 9 and 10 are the tightest columns, with 3 colors.

The fewer colors a line touches, the sooner it surrenders its queen. A row meeting just 3 colors has to be claimed by one of them, which pushes every remaining region into the other 9 rows. Row 2, meeting 5 colors, is the opposite case — the busiest line on #238 and the last one you should expect to crack.

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.

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.

Say the reason out loud: "this region has one square left", "this column has one square left". If no such sentence is available, the eliminating is not finished. One more pass of X marks is almost always quicker than committing to a placement you cannot defend.

Why puzzle #238 is rated easy

The easy label comes out of four measurable things about #238: two of its regions are locked to one row or column, its smallest color spans 2 squares, its least crowded row meets 3 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.

Stuck on #238 despite the easy 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.

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 #238, start hunting for it near row 1.

Here is a shape check that gives nothing away: when #238 is solved, 4 queens sit on the outer edge of the grid and 6 sit inside it, and no queen lands in a corner. A work-in-progress board that clusters its queens in one quadrant while leaving others bare is usually carrying a mistake.

How to play Queens

  1. The board is an N×N grid divided into N colored regions.
  2. Place exactly one queen (♛) in each row, each column, and each colored region.
  3. No two queens may touch each other — not horizontally, vertically, or diagonally.
  4. 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.
  5. 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 #238?

Puzzle #238 is rated easy. 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 #238 have only one solution?

Yes. Every puzzle in the 10x10 collection, including #238, 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 #238?

Start with the amber region — the most constrained color on this board, with 2 squares spanning rows 2–2 and columns 5–6. Narrowing the smallest region first removes the most squares elsewhere on the grid.