9x9 Queens Puzzle #89

Difficulty: easy. Place 9 queens on this 9x9 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 21-step reasoning is written out below.

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Step-by-step solution for puzzle #89

What follows is a complete solve of puzzle #89, worked the way a person works it rather than the way a computer does. It runs to 21 deductions — 9 queen placements and 12 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: region shadow, region confined to one line, line confined to one region, pairing argument on rows, pairing argument on columns, last square in a region.

Show the full walkthrough (13 steps) — contains the solution

  1. Step 1. Wherever khaki 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.

  2. Step 2. All of the orange 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: 9 squares come off.

  3. Step 3. Mint cannot leave column 8 — every one of its open squares (3 open squares) sits there. That column belongs to mint, so every square in it owned by another colour is dead: 5 squares in all.

  4. Step 4. Every open square left in row 1 (7 open squares) belongs to the indigo region. Since that row must contain a queen, indigo is the colour that supplies it — so indigo squares anywhere else on the board are out, 10 squares in all.

    Puzzle #89 after step 4: 0 of 9 queens placed
    The board after step 4 — 0 of 9 queens placed.

  5. Step 5. Khaki and orange are now boxed into rows 8 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 10 squares at once.

  6. Step 6. All of the pale yellow region's remaining squares (2 open squares) lie in row 7. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 6 squares come off.

  7. Step 7. Red cannot leave row 6 — every one of its open squares (3 open squares) sits there. That row belongs to red, so every square on it owned by another colour is dead: 4 squares in all.

  8. Step 8. All of the mint region's remaining squares (2 open squares) lie in column 8. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 1 square come off.

  9. Step 9. Mint and slate are now boxed into rows 4 and 5 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 6 squares at once.

    Puzzle #89 after step 9: 0 of 9 queens placed
    The board after step 9 — 0 of 9 queens placed.

  10. Step 10. All of the amber region's remaining squares (2 open squares) lie in column 7. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 1 square come off.

  11. Step 11. Blue is down to 3 candidates in rows 2 and 3, columns 1 and 2, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about blue itself.

  12. Step 12. Here is the pairing argument. The blue and khaki regions have no open squares outside columns 1 and 2 — 2 colours confined to 2 columns. Between them they must take one column each, in some order, so every other colour is shut out of all of them: 3 squares come off in one stroke.

  13. Step 13. From here the board cascades. Keep alternating the region sweep and the line sweep and 9 queens fall out in order without any new idea being needed: red has one square left, so its queen takes row 6, column 3; slate has one square left, so its queen takes row 5, column 6; mint has one square left, so its queen takes row 4, column 8; amber has one square left, so its queen takes row 2, column 7; blue has one square left, so its queen takes row 3, column 1; pale yellow has one square left, so its queen takes row 7, column 5; indigo has one square left, so its queen takes row 1, column 4; khaki has one square left, so its queen takes row 8, column 2; orange has one square left, so its queen takes row 9, column 9. 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 9.

    Puzzle #89 after step 13: 9 of 9 queens placed
    The board after step 13 — 9 of 9 queens placed.

That completes the board: 9 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 9x9 Queens puzzle #89

Puzzle #89 is one of the easy-rated boards in the 9x9 set. Nine colors divide its 81 squares, and you win by placing nine queens so that each row, each column and each color holds exactly one, with no two queens adjacent in any direction.

As with every puzzle in this collection, #89 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 #89 are: orange (2 squares), khaki (3 squares), blue (6 squares), mint (6 squares), red (9 squares), amber (12 squares), slate (12 squares), pale yellow (14 squares), indigo (17 squares). An even split would hand every color 9 squares, so the orange region is running 7 squares under that average while the indigo region is the roomiest area on the grid with 17 squares.

Every color takes one queen and one only, whatever its size — which is why the 15 square difference between orange and indigo 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.

A region's outline can constrain it more than its size does. Here mint is the most solid, filling 100% of its 3×2 box, and amber the most diffuse at 48% of its 5×5 box. Solid blocks give clean eliminations; diffuse ones spread across the board and stay open longer.

Region by region

Below is every color on #89 with its exact reach, smallest region first. It is worth a slow read: the spans reveal which rows and columns several regions are fighting over.

Orange occupies 2 squares within rows 8–9, columns 9–9. It sits wholly inside column 9, so its queen must be in that column.

Khaki: 3 squares across rows 8–9, columns 1–2.

Blue covers 6 squares, spanning 4 rows and 2 columns (rows 2–5, columns 1–2).

Mint occupies 6 squares within rows 4–6, columns 8–9.

Red: 9 squares across rows 6–9, columns 1–3.

Amber covers 12 squares, spanning 5 rows and 5 columns (rows 1–5, columns 5–9).

Slate occupies 12 squares within rows 4–7, columns 2–7.

Pale yellow: 14 squares across rows 7–9, columns 4–9.

Indigo covers 17 squares, spanning 4 rows and 7 columns (rows 1–4, columns 1–7).

Where to start on this board

The most constrained color is where a solve should begin, and on #89 that is orange with 2 squares. It reaches from row 8 to row 9 and from column 9 to column 9 — 2 rows 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 orange stays inside column 9, its queen belongs to that column and no other region may use it. Cross out the rest of column 9 straight away. Any color that was relying on those squares now has a visibly smaller footprint, and that shrinkage is where your second deduction comes from.

Work outward to the other flat regions next. Khaki 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 #89

A quick way to find the next move is to count how many different colors touch each line. On this board, row 1 is the narrowest, touched by only 2 colors. Columns 3, 4 and 8 are the tightest columns, 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 8 rows. By contrast row 4 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.

The whole middle game reduces to two sweeps. Sweep the nine colors looking for one with a single square left; sweep the nine rows and nine columns looking for the same. Each sweep feeds the next, and switching between them deliberately — rather than drifting — is what separates a fast 9x9 solve from a stalled one.

Resist the plausible-looking queen. On #89 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 #89 is rated easy

What earns a board its rating is the shape of its opening. Here that opening offers one single-line region, a 2-square smallest color, a tightest row touched by 2 colors, and a region-size spread of 15. Lopsided grids with flat regions fall quickly; balanced ones like this take more patience.

Difficulty in Queens is never arithmetic and never luck. Every board has one solution and none require guessing. What varies is the length of the chain you must follow before the next queen becomes certain — one or two steps on an easy board, five or six on a hard one, sometimes with several partial eliminations held in play at once.

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 9x9

At 9x9 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 #89 is row 1.

As a sanity check rather than a spoiler: the finished solution to #89 puts 3 queens on the outer border and 6 queens in the interior, 1 of them in an actual 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

  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 9x9 Queens puzzle #89?

Puzzle #89 is rated easy. Its smallest color region holds 2 squares, its tightest row is touched by 2 colors, and one of its regions is confined to a single row or column, which gives you a forced move early.

Does 9x9 puzzle #89 have only one solution?

Yes. Every puzzle in the 9x9 collection, including #89, has been verified to have exactly one valid arrangement of nine queens, and it can always be reached by logic alone — no guessing or backtracking needed.

Where should I place my first queen on puzzle #89?

Start with the orange region — the most constrained color on this board, with 2 squares spanning rows 8–9 and columns 9–9. Narrowing the smallest region first removes the most squares elsewhere on the grid.