12x12 Queens Puzzle #88
Difficulty: hard. 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 23-step reasoning is written out below.
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Step-by-step solution for puzzle #88
What follows is a complete solve of puzzle #88, worked the way a person works it rather than the way a computer does. It runs to 23 deductions — 12 queen placements and 11 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: last square in a region, region confined to one line, region shadow, pairing argument on columns, pairing argument on rows, last square in a row.
Show the full walkthrough (16 steps) — contains the solution
Step 1. Only row 10, column 7 is still open in sea green, and since each colour must take a queen, that settles it. That clears row 10, column 7, the rest of the sea green region and every square adjacent to it — diagonals included.
Step 2. All of the indigo region's remaining squares (3 open squares) lie in column 1. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 9 squares come off.
Step 3. The red region has 5 squares left, spread across rows 6–9, columns 11 and 12. 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.
Step 4. Wherever pale yellow ends up among its 6 squares, the same squares fall within reach of it — 1 square in total, impossible regardless of how the colour resolves.
Step 5. Teal is down to 5 candidates in rows 9, 11, and 12, columns 10–12, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about teal itself.
The board after step 5 — 1 of 12 queens placed. Step 6. The rose region has 4 squares left, spread across rows 11 and 12, columns 8–10. You do not need to know which of them takes the queen: every one of those options attacks the same 1 square, so they can be crossed out now.
Step 7. Red and teal are now boxed into columns 11 and 12 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 10 squares at once.
Step 8. Here is the pairing argument. The blue, slate, and rose regions have no open squares outside columns 8–10 — 3 colours confined to 3 columns. Between them they must take one column each, in some order, so every other colour is shut out of all of them: 4 squares come off in one stroke.
Step 9. 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: 11 squares in all.
Step 10. Wherever red 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 11. 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 9 squares at once.
The board after step 11 — 1 of 12 queens placed. Step 12. The orange region is down to one open square, at row 9, column 5. Every colour holds exactly one queen, so that square is forced. Row 9 and column 5 are now spoken for, along with the squares touching that queen.
Step 13. Only row 7, column 6 is still open in pale yellow, and since each colour must take a queen, that settles it. That clears row 7, column 6, the rest of the pale yellow region and every square adjacent to it — diagonals included.
Step 14. The amber region is down to one open square, at row 2, column 4. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 2 and column 4, the remaining amber squares, and the ring of neighbours around row 2, column 4.
Step 15. The mint region has 8 squares left, spread across rows 1, 3, 4, 5, 6, and 8, columns 2 and 3. You do not need to know which of them takes the queen: every one of those options attacks the same 1 square, so they can be crossed out now.
Step 16. 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: khaki has one square left, so its queen takes row 8, column 3; red has one square left, so its queen takes row 6, column 11; row 5 is down to one square, putting a queen on row 5, column 9; row 4 is down to one square, putting a queen on row 4, column 2; indigo has one square left, so its queen takes row 1, column 1; blue has one square left, so its queen takes row 3, column 10; rose has one square left, so its queen takes row 12, column 8; teal has one square left, so its queen takes row 11, column 12. 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 11, column 12.
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 #88
This is puzzle number 88 in the 12x12 collection, rated hard. The grid holds 144 squares split between twelve colored regions, and a finished board carries twelve 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, #88 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 #88 are: sea green (1 square), indigo (3 squares), red (5 squares), teal (9 squares), rose (9 squares), pale yellow (10 squares), amber (15 squares), orange (15 squares), blue (17 squares), mint (18 squares), slate (20 squares), khaki (22 squares). An even split would hand every color 12 squares, so the sea green region is running 11 squares under that average while the khaki region is the roomiest area on the grid with 22 squares.
Every color takes one queen and one only, whatever its size — which is why the 21 square difference between sea green and khaki 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.
Square count is only half the story — how a color is arranged counts too. Indigo is the tidiest shape on #88, packing 100% of its 3×1 bounding box, whereas pale yellow straggles across its 5×4 box at just 50%. Tidy blocks are easy to work around; scattered ones touch more lines and resist resolution.
Region by region
Below is every color on #88 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.
Sea green covers 1 square, spanning 1 row and 1 column (rows 10–10, columns 7–7). It never leaves row 10, so its queen is locked to that row.
Indigo occupies 3 squares within rows 1–3, columns 1–1. It sits wholly inside column 1, so its queen must be in that column.
Red: 5 squares across rows 6–9, columns 11–12.
Teal covers 9 squares, spanning 5 rows and 3 columns (rows 8–12, columns 10–12).
Rose occupies 9 squares within rows 10–12, columns 7–11.
Pale yellow: 10 squares across rows 4–8, columns 5–8.
Amber covers 15 squares, spanning 6 rows and 4 columns (rows 1–6, columns 4–7).
Orange occupies 15 squares within rows 8–12, columns 3–7.
Blue: 17 squares across rows 1–6, columns 8–12.
Mint covers 18 squares, spanning 9 rows and 3 columns (rows 1–9, columns 2–4).
Slate occupies 20 squares within rows 2–10, columns 7–10.
Khaki: 22 squares across rows 4–12, columns 1–4.
Where to start on this board
The most constrained color is where a solve should begin, and on #88 that is sea green with 1 square. It reaches from row 10 to row 10 and from column 7 to column 7 — 1 row 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 sea green never leaves row 10, its queen must be in that row — and that instantly settles row 10 for everyone else. Sweep along it and X out every square that is not sea green. 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.
No region here is pinned to a shallow band of rows, so turn the same idea sideways: red spans only two columns. Two narrow regions sharing the same two columns take one column each and lock everyone else out of both, which is usually enough to crack a board that offers no free opening.
The tightest lines on puzzle #88
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 1, 11 and 12 are the narrowest, touched by only 4 colors. Columns 1 and 2 are the tightest columns, with 2 colors.
Count colors per line and you have a ranking of where to look. The narrowest rows here see only 4 colors, so one of that handful must take the row and the rest are squeezed into the other 11 rows. Row 8 sits at the far end with 7 colors crossing it; it will almost certainly be among the last to settle.
Working through the middle game
The middle of #88 is where careless play costs time. Every queen you place kills a row, a column and the eight surrounding squares; if you do not mark all of that immediately, you will later "discover" a move that was available several turns ago. Mark first, then look.
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.
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 #88 is rated hard
What earns a board its rating is the shape of its opening. Here that opening offers three single-line regions, a 1-square smallest color, a tightest row touched by 4 colors, and a region-size spread of 21. Lopsided grids with flat regions fall quickly; balanced ones like this take more patience.
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 #88 is column 1.
Use this as a rough check on your progress: the completed board has 3 queens around the border and 9 queens in the middle, including 1 in a corner. Solutions spread out; if yours is bunching up in one region of the grid, retrace a few moves.
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 #88?
Puzzle #88 is rated hard. Its smallest color region holds 1 square, its tightest row is touched by 4 colors, and three of its regions are confined to a single row or column, which gives you a forced move early.
Does 12x12 puzzle #88 have only one solution?
Yes. Every puzzle in the 12x12 collection, including #88, 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 #88?
Start with the sea green region — the most constrained color on this board, with 1 square spanning rows 10–10 and columns 7–7. Narrowing the smallest region first removes the most squares elsewhere on the grid.