12x12 Queens Puzzle #114

Difficulty: easy. 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 22-step reasoning is written out below.

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Step-by-step solution for puzzle #114

What follows is a complete solve of puzzle #114, worked the way a person works it rather than the way a computer does. It runs to 22 deductions — 12 queen placements and 10 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, last square in a region, pairing argument on rows, pairing argument on columns.

Show the full walkthrough (16 steps) — contains the solution

  1. Step 1. Wherever blue 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 slate region's remaining squares (2 open squares) lie in column 1. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 12 squares come off.

  3. Step 3. Only row 7, column 2 is still open in pale yellow, and since each colour must take a queen, that settles it. Everything else in row 7, in column 2, in pale yellow and in the ring around that square is now dead.

  4. Step 4. 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. Row 5 and column 1 are now spoken for, along with the squares touching that queen.

  5. Step 5. Red is down to 2 candidates in rows 6 and 9, columns 3 and 4, and they overlap enough to cover 3 squares elsewhere. Cross those out without deciding anything about red itself.

    Puzzle #114 after step 5: 2 of 12 queens placed
    The board after step 5 — 2 of 12 queens placed.

  6. Step 6. The teal region has 3 squares left, spread across rows 11 and 12, columns 5 and 6. You do not need to know which of them takes the queen: every one of those options attacks the same 2 squares, so they can be crossed out now.

  7. Step 7. Wherever rose ends up among its 2 squares, the same squares fall within reach of it — 4 squares in total, impossible regardless of how the colour resolves.

  8. Step 8. Teal is down to 2 candidates in rows 11 and 12, columns 5 and 6, and they overlap enough to cover 2 squares elsewhere. Cross those out without deciding anything about teal itself.

  9. Step 9. Teal and rose are now boxed into rows 11 and 12 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.

  10. Step 10. The sea green region is down to one open square, at row 10, column 3. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 10 and column 3, the remaining sea green squares, and the ring of neighbours around row 10, column 3.

  11. Step 11. Only row 6, column 4 is still open in red, and since each colour must take a queen, that settles it. Everything else in row 6, in column 4, in red and in the ring around that square is now dead.

    Puzzle #114 after step 11: 4 of 12 queens placed
    The board after step 11 — 4 of 12 queens placed.

  12. Step 12. All of the mint region's remaining squares (2 open squares) lie in row 4. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 8 squares come off.

  13. Step 13. Only row 3, column 12 is still open in blue, and since each colour must take a queen, that settles it. That clears row 3, column 12, the rest of the blue region and every square adjacent to it — diagonals included.

  14. Step 14. 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.

  15. Step 15. Mint and teal are now boxed into columns 5 and 6 and nothing else. That is 2 colours needing 2 columns, so they fill those columns between them — which locks every remaining colour out and removes 6 squares at once.

  16. Step 16. From here the board cascades. Keep alternating the region sweep and the line sweep and 7 queens fall out in order without any new idea being needed: orange has one square left, so its queen takes row 9, column 7; rose has one square left, so its queen takes row 12, column 8; amber has one square left, so its queen takes row 2, column 9; indigo has one square left, so its queen takes row 1, column 11; khaki has one square left, so its queen takes row 8, column 10; teal has one square left, so its queen takes row 11, column 6; mint has one square left, so its queen takes row 4, column 5. 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 4, column 5.

    Puzzle #114 after step 16: 12 of 12 queens placed
    The board after step 16 — 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 #114

Board #114 of the 12x12 bank carries a easy 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.

Like every board on this site, #114 has been verified to have exactly one valid solution, and that solution is reachable by deduction alone. You never have to guess and then unwind; every queen can be justified by something already visible on the grid. What changes from puzzle to puzzle is where the first certainty appears and how long the chain of reasoning runs before the next one — and that is entirely a product of how these particular colors are shaped.

How the colors divide this board

From smallest to largest, the regions on puzzle #114 are: slate (2 squares), blue (3 squares), teal (3 squares), rose (3 squares), pale yellow (4 squares), indigo (7 squares), red (9 squares), sea green (14 squares), orange (15 squares), amber (23 squares), mint (27 squares), khaki (34 squares). An even split would hand every color 12 squares, so the slate region is running 10 squares under that average while the khaki region is the roomiest area on the grid with 34 squares.

That imbalance is the first thing to read, because every region takes exactly one queen regardless of how much space it owns. Slate has only 2 places to put its queen; khaki has 34. The spread between them on this board is 32 squares, and the wider that spread runs, the more it pays to solve from the small end inward.

Look at arrangement as well as area. Slate is the densest region on this grid at 100% of a 2×1 frame; mint is the loosest, occupying only 56% of its 6×8 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.

Slate: 2 squares across rows 5–6, columns 1–1. It sits wholly inside column 1, so its queen must be in that column.

Blue covers 3 squares, spanning 2 rows and 2 columns (rows 3–4, columns 11–12).

Teal occupies 3 squares within rows 11–12, columns 5–6.

Rose: 3 squares across rows 11–12, columns 7–8.

Pale yellow covers 4 squares, spanning 3 rows and 2 columns (rows 7–9, columns 1–2).

Indigo occupies 7 squares within rows 1–3, columns 10–12.

Red: 9 squares across rows 6–9, columns 2–4.

Sea green covers 14 squares, spanning 5 rows and 4 columns (rows 8–12, columns 1–4).

Orange occupies 15 squares within rows 6–11, columns 5–8.

Amber: 23 squares across rows 1–5, columns 5–11.

Mint covers 27 squares, spanning 6 rows and 8 columns (rows 1–6, columns 1–8).

Khaki occupies 34 squares within rows 5–12, columns 7–12.

Where to start on this board

Slate is the natural opening on #114: it is the smallest region on the grid at 2 squares, boxed into rows 5–6 and columns 1–1. Since one of those squares must hold a queen, that block of 2 rows and 1 column is the most contested part of the board.

Because slate stays inside column 1, its queen belongs to that column and no other region may use it. Cross out the rest of column 1 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. Blue, teal and rose 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 #114

A quick way to find the next move is to count how many different colors touch each line. On this board, rows 1, 2, 4 and 10 are the narrowest, touched by only 3 colors. Column 9 is the tightest column, with 2 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 11 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.

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 #114 is rated easy

Ratings track how generous the opening is. On #114 you get one region pinned to a single row or column, a smallest color of 2 squares, a tightest row crossed by 3 colors, and a 32-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.

If #114 feels harder than its rating suggests, the usual culprit is incomplete marking rather than a difficult deduction. Check that every queen already on the grid has its full cross of eliminations recorded — including the diagonal neighbours, which are by far the easiest to miss. More stalled solves come from one forgotten diagonal X than from any genuinely deep chain of logic.

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.

One pattern is worth learning at every size, and it is available here. When two regions can only fit inside the same two rows, they must take one row each — which locks every other region out of both. The same argument works for columns, and for any matching count: three regions sharing three rows, four sharing four. Spotting these pairings turns a slow grind into a quick cascade, and on #114 the place to look for one is around column 9.

As a sanity check rather than a spoiler: the finished solution to #114 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

  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 12x12 Queens puzzle #114?

Puzzle #114 is rated easy. Its smallest color region holds 2 squares, its tightest row is touched by 3 colors, and one of its regions is confined to a single row or column, which gives you a forced move early.

Does 12x12 puzzle #114 have only one solution?

Yes. Every puzzle in the 12x12 collection, including #114, 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 #114?

Start with the slate region — the most constrained color on this board, with 2 squares spanning rows 5–6 and columns 1–1. Narrowing the smallest region first removes the most squares elsewhere on the grid.