Patches #55 Hints & Answer

Patches #55 is solved by covering the whole board with rectangles, one clue per block. We split it into 7 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 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.

2. Step 2

   Work the tall clue around row 2, col 2. With 3 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 3, col 1. 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.

4. Step 4

   The wide clue at row 1, col 6 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.

5. Step 5

   Work the tall clue around row 2, 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.

6. Step 6

   Look at the square clue near row 5, 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.

7. Step 7

   The tall clue at row 6, col 6 can only be filled one way: a rectangle of area 12 that matches its proportions. Place it now — once it is down, the cells beside it stop being ambiguous.