Patches #31 Hints & Answer
Patches #31 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
- Step 1
The square clue at row 4, col 2 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.
- Step 2
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.
- Step 3
Look at the square clue near row 6, col 6. 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.
- Step 4
The wide clue at row 4, col 4 can only be filled one way: a rectangle of area 4 that matches its proportions. Place it now — once it is down, the cells beside it stop being ambiguous.
- Step 5
Work the wide clue around row 1, col 3. With 5 cells to cover and a fixed shape, only one rectangle fits without overlapping a neighbour. Commit to it and the board tightens.
- Step 6
Look at the tall clue near row 4, col 1. Its number 6 fixes the rectangle’s area, so draw the block that covers exactly 6 cells around it without touching another clue. Lock it in before moving on.
- Step 7
The wide clue at row 2, col 3 can only be filled one way: a rectangle of area 10 that matches its proportions. Place it now — once it is down, the cells beside it stop being ambiguous.
- Step 8
Work the wide clue around row 5, 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.
- Step 9
Look at the wide clue near row 6, col 2. Its number 4 fixes the rectangle’s area, so draw the block that covers exactly 4 cells around it without touching another clue. Lock it in before moving on.