Patches #1 Hints & Answer

Patches #1 is solved by covering the whole board with rectangles, one clue per block. We split it into 8 steps below: fix the constrained clues first, and the flexible any-shape clues fall into place last.

Step-by-step solution

1. Step 1

   The square clue at row 1, col 1 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.

2. Step 2

   Work the square clue around row 1, 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.

3. Step 3

   Look at the tall clue near row 4, col 6. 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.

4. Step 4

   The wide clue at row 6, col 4 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.

5. Step 5

   Work the wide clue around row 2, col 4. With 6 cells to cover and a fixed shape, only one rectangle fits without overlapping a neighbour. Commit to it and the board tightens.

6. Step 6

   Look at the wide clue near row 3, col 2. Its number 15 fixes the rectangle’s area, so draw the block that covers exactly 15 cells around it without touching another clue. Lock it in before moving on.

7. Step 7

   The tall clue at row 6, col 6 can only be filled one way: a rectangle of area 2 that matches its proportions. Place it now — once it is down, the cells beside it stop being ambiguous.

8. Step 8

   Work the wide clue around row 1, col 2. With 4 cells to cover and a fixed shape, only one rectangle fits without overlapping a neighbour. Commit to it and the board tightens.