Patches #3 Hints & Answer

Patches #3 is solved by covering the whole board with rectangles, one clue per block. We split it into 9 steps below: fix the constrained clues first, and the flexible any-shape clues fall into place last.

Step-by-step solution

1. Step 1

   Look at the square clue near row 3, col 1. Its number 1 fixes the rectangle’s area, so draw the block that covers exactly 1 cells around it without touching another clue. Lock it in before moving on.

2. Step 2

   The square clue at row 4, col 6 can only be filled one way: a rectangle of area 1 that matches its proportions. Place it now — once it is down, the cells beside it stop being ambiguous.

3. Step 3

   Work the square clue around row 5, col 6. With 1 cells to cover and a fixed shape, only one rectangle fits without overlapping a neighbour. Commit to it and the board tightens.

4. Step 4

   Look at the wide clue near row 4, col 3. Its number 5 fixes the rectangle’s area, so draw the block that covers exactly 5 cells around it without touching another clue. Lock it in before moving on.

5. Step 5

   The wide clue at row 5, col 3 can only be filled one way: a rectangle of area 5 that matches its proportions. Place it now — once it is down, the cells beside it stop being ambiguous.

6. Step 6

   Work the wide clue around row 2, col 4. With 10 cells to cover and a fixed shape, only one rectangle fits without overlapping a neighbour. Commit to it and the board tightens.

7. Step 7

   Look at the tall clue near row 1, col 1. Its number 2 fixes the rectangle’s area, so draw the block that covers exactly 2 cells around it without touching another clue. Lock it in before moving on.

8. Step 8

   The wide clue at row 3, col 2 can only be filled one way: a rectangle of area 5 that matches its proportions. Place it now — once it is down, the cells beside it stop being ambiguous.

9. Step 9

   Finally resolve the dashed any-shape clue near row 6, col 2. Its rectangle can be any proportion, so fill it last — the surrounding blocks now leave only one valid placement that covers every remaining cell.