Patches #72 Hints & Answer

Here is the full answer to Patches puzzle #72. You fill every cell with rectangles, each holding exactly one clue. The solve falls into 7 stages — start from the clues whose size and shape leave only one option, then chain the deductions.

Step-by-step solution

1. Step 1

   Look at the square clue near row 1, col 2. 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 tall clue at row 3, col 6 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.

3. Step 3

   Work the wide clue around row 6, col 3. With 6 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 square clue near row 2, col 5. Its number 9 fixes the rectangle’s area, so draw the block that covers exactly 9 cells around it without touching another clue. Lock it in before moving on.

5. Step 5

   The tall clue at row 3, col 2 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.

6. Step 6

   Work the tall clue around row 3, col 1. With 3 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

   Finally resolve the dashed any-shape clue near row 5, col 3. Its rectangle can be any proportion, so fill it last — the surrounding blocks now leave only one valid placement that covers every remaining cell.