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Archive · Patches #31

Patches #31 (October 27, 2026): solution and step-by-step

The 6×6 medium board from Tuesday, October 27, 2026. Play it first; the placements and the solved board are folded below. Replays don't affect your streak.

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squaretallwideany shapenumber = that many cells

← #30Today's puzzle →

Patches #31 was the 6×6 medium board of Tuesday, October 27, 2026: 7 clues (3 squares, 3 talls and 1 wide), 4 of them with an area number, and 7 rectangles to draw so that every cell is covered exactly once. The patches run from 2 to 9 cells. Our deduction solver, the one behind the hint button, lays them all without guessing in 7 steps: 3 because only one rectangle fits a clue, 4 because some uncovered cell can be reached by only one clue. The tightest clue at the start is the tall 8 at row 1, column 1, with only 1 possible rectangle before anything is placed. A brute-force solver would face 3 branch points on the way to the unique answer.

Patches #31 in numbers

Board6×6, Medium
Clues7 (4 with a number)
Shapes3 square · 3 tall · 1 wide · 0 any
Patch sizes2 to 9 cells
Deduction steps7
“Only one rectangle fits” steps3
“Only one clue reaches this cell” steps4
Brute-force branch points3
How to start Patches #31: the first 7 patches

Each placement is what the hint button would say at that point, from the empty board. Rows and columns are counted from the top-left corner.

  1. Tall 8 clue at row 1, column 1 → 2×4 patch. Only one patch fits the tall rectangle (8) clue here: 2 wide × 4 tall. Every other rectangle would cross another clue, a placed patch or the edge.

  2. Tall 6 clue at row 1, column 6 → 1×6 patch. Only one patch fits the tall rectangle (6) clue here: 1 wide × 6 tall. Every other rectangle would cross another clue, a placed patch or the edge.

  3. Square 9 clue at row 3, column 5 → 3×3 patch. The outlined cell can only be reached by the square (9) clue — no other clue's patch can stretch to it — so it belongs to that patch. That fixes the patch: 3×3.

  4. Square clue at row 5, column 3 → 2×2 patch. The outlined cell can only be reached by the square clue — no other clue's patch can stretch to it — so it belongs to that patch. That fixes the patch: 2×2.

  5. Tall clue at row 5, column 5 → 1×3 patch. The outlined cell can only be reached by the tall rectangle clue — no other clue's patch can stretch to it — so it belongs to that patch. (Fill it in draws the whole patch: 1 wide × 3 tall.)

  6. Square clue at row 5, column 1 → 2×2 patch. The outlined cell can only be reached by the square clue — no other clue's patch can stretch to it — so it belongs to that patch. That fixes the patch: 2×2.

  7. Wide 2 clue at row 6, column 3 → 2×1 patch. Only one patch fits the wide rectangle (2) clue here: 2 wide × 1 tall. Every other rectangle would cross another clue, a placed patch or the edge.

Patches #31 solution

Each colour is one patch; the clue cell shows its shape (■ square, ▮ tall, ▬ wide, ✦ any) and area.

  • tall 8 at row 1, column 1: 2 wide × 4 tall, top-left row 1, column 1
  • square 9 at row 3, column 5: 3 wide × 3 tall, top-left row 1, column 3
  • tall 6 at row 1, column 6: 1 wide × 6 tall, top-left row 1, column 6
  • square at row 5, column 3: 2 wide × 2 tall, top-left row 4, column 3
  • tall at row 5, column 5: 1 wide × 3 tall, top-left row 4, column 5
  • square at row 5, column 1: 2 wide × 2 tall, top-left row 5, column 1
  • wide 2 at row 6, column 3: 2 wide × 1 tall, top-left row 6, column 3

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