10x10 Queens Puzzle #152

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 12-step reasoning is written out below.

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Step-by-step solution for puzzle #152

What follows is a complete solve of puzzle #152, worked the way a person works it rather than the way a computer does. It runs to 12 deductions — 10 queen placements and 2 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 confined to one line.

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

Show the full walkthrough (9 steps) — contains the solution

  1. Step 1. Only row 3, column 1 is still open in blue, and since each colour must take a queen, that settles it. That clears row 3, column 1, the rest of the blue region and every square adjacent to it — diagonals included.

  2. Step 2. The orange region is down to one open square, at row 9, column 2. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 9 and column 2, the remaining orange squares, and the ring of neighbours around row 9, column 2.

  3. Step 3. Only row 6, column 3 is still open in red, and since each colour must take a queen, that settles it. Everything else in row 6, in column 3, in red and in the ring around that square is now dead.

    Puzzle #152 after step 3: 3 of 10 queens placed
    The board after step 3 — 3 of 10 queens placed.

  4. Step 4. 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: 7 squares come off.

  5. Step 5. 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: amber has one square left, so its queen takes row 2, column 10; mint has one square left, so its queen takes row 4, column 4; indigo has one square left, so its queen takes row 1, column 5; khaki has one square left, so its queen takes row 8, 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 8, column 6.

  6. Step 6. Slate cannot leave row 5 — every one of its open squares (2 open squares) sits there. That row belongs to slate, so every square on it owned by another colour is dead: 1 square in all.

    Puzzle #152 after step 6: 7 of 10 queens placed
    The board after step 6 — 7 of 10 queens placed.

  7. Step 7. The pale yellow region is down to one open square, at row 7, column 8. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 7 and column 8, the remaining pale yellow squares, and the ring of neighbours around row 7, column 8.

  8. Step 8. Only row 5, column 7 is still open in slate, and since each colour must take a queen, that settles it. Everything else in row 5, in column 7, in slate and in the ring around that square is now dead.

  9. Step 9. 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.

    Puzzle #152 after step 9: 10 of 10 queens placed
    The board after step 9 — 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 #152

This is puzzle number 152 in the 10x10 collection, rated easy. 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.

As with every puzzle in this collection, #152 has a single verified solution and needs no guesswork. Each queen follows from something already visible. What the board controls is tempo — how soon the first forced move shows up and how far apart the rest are spaced — and that is a direct consequence of how these colors are cut.

How the colors divide this board

From smallest to largest, the regions on puzzle #152 are: blue (1 square), indigo (3 squares), amber (3 squares), orange (4 squares), pale yellow (8 squares), red (9 squares), khaki (11 squares), sea green (11 squares), mint (19 squares), slate (31 squares). An even split would hand every color 10 squares, so the blue region is running 9 squares under that average while the slate region is the roomiest area on the grid with 31 squares.

One queen per color, regardless of acreage: that is what turns this uneven split into a solving order. Blue is working with 1 square while slate has 31 to spare, a gap of 30. Attack the cramped end and the roomy regions tend to resolve themselves.

Look at arrangement as well as area. Indigo is the densest region on this grid at 100% of a 1×3 frame; mint is the loosest, occupying only 48% 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

The complete breakdown of each region on this board follows, ordered from tightest to roomiest. Skimming the spans first tells you where the board is crowded and where it has slack.

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

Indigo: 3 squares across rows 1–1, columns 3–5. It never leaves row 1, so its queen is locked to that row.

Amber 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.

Orange occupies 4 squares within rows 8–10, columns 1–2.

Pale yellow: 8 squares across rows 5–9, columns 7–9.

Red covers 9 squares, spanning 5 rows and 3 columns (rows 4–8, columns 1–3).

Khaki occupies 11 squares within rows 8–10, columns 2–6.

Sea green: 11 squares across rows 7–10, columns 6–10.

Mint covers 19 squares, spanning 8 rows and 5 columns (rows 1–8, columns 1–5).

Slate occupies 31 squares within rows 1–7, columns 5–10.

Where to start on this board

Blue is the natural opening on #152: it is the smallest region on the grid at 1 square, boxed into rows 3–3 and columns 1–1. Since one of those squares must hold a queen, that block of 1 row and 1 column is the most contested part of the board.

Because blue never leaves row 3, its queen must be in that row — and that instantly settles row 3 for everyone else. Sweep along it and X out every square that is not blue. 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 is no more than two rows tall, so its queen is 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 #152

A quick way to find the next move is to count how many different colors touch each line. On this board, rows 2, 4 and 10 are the narrowest, touched by only 3 colors. Columns 4, 6, 7, 8, 9 and 10 are the tightest columns, with 3 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 8 is the crowded extreme at 6 colors — worth revisiting later, not now.

Working through the middle game

Past the opening, treat this as an elimination exercise rather than a placement exercise. Each queen takes out a row, a column and its eight neighbours, and the value of a move is measured by how much it removes. Cross everything out as you go and let the board do the remembering.

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 #152 is rated easy

Ratings track how generous the opening is. On #152 you get four regions pinned to a single row or column, a smallest color of 1 square, a tightest row crossed by 3 colors, and a 30-square gap between the largest and smallest regions. Those four numbers largely explain the easy label.

The scale has nothing to do with maths or luck — every puzzle here is solvable by deduction and has exactly one answer. It measures reasoning depth: how many eliminations must stack up before a placement becomes provable. That depth is what separates a easy board from the rest.

A board that feels above its rating is nearly always a board with a missing X. Audit every queen on the grid: full row cleared, full column cleared, all eight touching squares cleared. Diagonals are the common omission, and missing one is far more often the cause of a stall than any genuine difficulty in the puzzle.

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 row 2 on this board.

A non-spoiling distribution check: solved, #152 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

  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 #152?

Puzzle #152 is rated easy. 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 #152 have only one solution?

Yes. Every puzzle in the 10x10 collection, including #152, 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 #152?

Start with the blue region — the most constrained color on this board, with 1 square spanning rows 3–3 and columns 1–1. Narrowing the smallest region first removes the most squares elsewhere on the grid.