12x12 Queens Puzzle #294
Difficulty: medium. Place 12 queens on this 12x12 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 15-step reasoning is written out below.
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Step-by-step solution for puzzle #294
What follows is a complete solve of puzzle #294, worked the way a person works it rather than the way a computer does. It runs to 15 deductions — 12 queen placements and 3 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, pairing argument on rows, last square in a region, pairing argument on columns.
Show the full walkthrough (5 steps) — contains the solution
Step 1. Wherever amber ends up among its 3 squares, the same squares fall within reach of it — 1 square in total, impossible regardless of how the colour resolves.
Step 2. Here is the pairing argument. The indigo, amber, and blue regions have no open squares outside rows 1–3 — 3 colours confined to 3 rows. Between them they must take one row each, in some order, so every other colour is shut out of all of them: 12 squares come off in one stroke.
Step 3. Only row 4, column 5 is still open in mint, and since each colour must take a queen, that settles it. Everything else in row 4, in column 5, in mint and in the ring around that square is now dead.
The board after step 3 — 1 of 12 queens placed. Step 4. Here is the pairing argument. The amber and pale yellow 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: 8 squares come off in one stroke.
Step 5. From here the board cascades. Keep alternating the region sweep and the line sweep and 11 queens fall out in order without any new idea being needed: rose has one square left, so its queen takes row 12, column 3; teal has one square left, so its queen takes row 11, column 6; sea green has one square left, so its queen takes row 10, column 12; khaki has one square left, so its queen takes row 8, column 11; indigo has one square left, so its queen takes row 1, column 10; amber has one square left, so its queen takes row 2, column 1; blue has one square left, so its queen takes row 3, column 8; pale yellow has one square left, so its queen takes row 7, column 2; orange has one square left, so its queen takes row 9, column 7; red has one square left, so its queen takes row 6, column 4; slate has one square left, so its queen takes row 5, 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 5, column 9.
The board after step 5 — 12 of 12 queens placed.
That completes the board: 12 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 12x12 Queens puzzle #294
Board #294 of the 12x12 bank carries a medium rating. Its 144 squares are shared between twelve colored regions, and the solution places twelve queens: one per row, one per column, one per region, none of them side by side or corner to corner.
As with every puzzle in this collection, #294 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 #294 are: amber (3 squares), khaki (5 squares), indigo (6 squares), rose (7 squares), mint (8 squares), pale yellow (8 squares), teal (8 squares), sea green (12 squares), blue (14 squares), orange (17 squares), red (26 squares), slate (30 squares). An even split would hand every color 12 squares, so the amber region is running 9 squares under that average while the slate region is the roomiest area on the grid with 30 squares.
Every color takes one queen and one only, whatever its size — which is why the 27 square difference between amber and slate 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. Khaki is the densest region on this grid at 83% of a 3×2 frame; slate is the loosest, occupying only 47% of its 8×8 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 #294, smallest first. Reading these spans before you place anything is the quickest way to see which parts of the grid are genuinely contested.
Amber: 3 squares across rows 1–2, columns 1–2.
Khaki covers 5 squares, spanning 3 rows and 2 columns (rows 7–9, columns 11–12).
Indigo occupies 6 squares within rows 1–3, columns 10–12.
Rose: 7 squares across rows 9–12, columns 1–3.
Mint covers 8 squares, spanning 4 rows and 4 columns (rows 1–4, columns 2–5).
Pale yellow occupies 8 squares within rows 5–10, columns 1–2.
Teal: 8 squares across rows 11–12, columns 3–7.
Sea green covers 12 squares, spanning 3 rows and 6 columns (rows 10–12, columns 7–12).
Blue occupies 14 squares within rows 1–3, columns 4–9.
Orange: 17 squares across rows 6–10, columns 5–11.
Red covers 26 squares, spanning 8 rows and 6 columns (rows 3–10, columns 1–6).
Slate occupies 30 squares within rows 2–9, columns 5–12.
Where to start on this board
Amber is the natural opening on #294: it is the smallest region on the grid at 3 squares, boxed into rows 1–2 and columns 1–2. Since one of those squares must hold a queen, that block of 2 rows and 2 columns is the most contested part of the board.
With 2 rows and 2 columns of room, amber needs narrowing rather than solving outright. Test its 3 squares against the neighbours: a candidate that would strand another color is dead, and eliminating even two of them tightens the whole corner of the board around rows 1–2.
Work outward to the other flat regions next. Teal 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 #294
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 4, 5, 11 and 12 are the narrowest, touched by only 3 colors. Columns 1, 3, 4, 8, 9, 10 and 12 are the tightest columns, with 4 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 11 rows. By contrast row 9 meets 6 colors — the most crowded line here, and the one least likely to resolve early. Spend your attention accordingly.
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.
With twelve queens to seat and twelve regions competing over 144 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 12x12 boards quickly and players who stall halfway.
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 #294 is rated medium
The rating reflects how much the board concedes up front. Puzzle #294 has no region confined to a single row or column, its smallest color holds 3 squares, its tightest row meets just 3 colors, and the gap between its largest and smallest regions is 27 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.
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 12x12
At 12x12 you are managing 144 squares, and holding the whole board in your head will not work. Split it into quadrants and solve locally. Most useful deductions on a grid this large are regional — a color pinched between two placed queens, or a band of rows that two regions must share. Trust the marks on the board over your memory.
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 #294 is row 4.
As a sanity check rather than a spoiler: the finished solution to #294 puts 4 queens on the outer border and 8 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 12x12 Queens puzzle #294?
Puzzle #294 is rated medium. Its smallest color region holds 3 squares, its tightest row is touched by 3 colors, and no region is confined to a single row or column, so the opening move takes some hunting.
Does 12x12 puzzle #294 have only one solution?
Yes. Every puzzle in the 12x12 collection, including #294, has been verified to have exactly one valid arrangement of twelve queens, and it can always be reached by logic alone — no guessing or backtracking needed.
Where should I place my first queen on puzzle #294?
Start with the amber region — the most constrained color on this board, with 3 squares spanning rows 1–2 and columns 1–2. Narrowing the smallest region first removes the most squares elsewhere on the grid.