Patches #23 Hints & Answer
Patches #23 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
Work the square clue around row 1, col 5. 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 2
Look at the square clue near row 4, 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 3
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.
- Step 4
Work the tall clue around row 3, col 6. With 3 cells to cover and a fixed shape, only one rectangle fits without overlapping a neighbour. Commit to it and the board tightens.
- Step 5
Look at the tall clue near row 4, col 5. 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.
- Step 6
The tall clue at row 5, col 1 can only be filled one way: a rectangle of area 6 that matches its proportions. Place it now — once it is down, the cells beside it stop being ambiguous.
- Step 7
Work the tall clue around row 3, col 3. With 10 cells to cover and a fixed shape, only one rectangle fits without overlapping a neighbour. Commit to it and the board tightens.
- Step 8
Look at the wide clue near row 6, col 5. Its number 3 fixes the rectangle’s area, so draw the block that covers exactly 3 cells around it without touching another clue. Lock it in before moving on.
- Step 9
The tall clue at row 6, col 2 can only be filled one way: a rectangle of area 6 that matches its proportions. Place it now — once it is down, the cells beside it stop being ambiguous.