Question

There are n holes on the drywall and these n holes are on one horizontal line. You are using patches (each patch is with length 1) to cover these holes. What is the minimum number of patches that you have to use? Provide your algorithm and the correctness analysis.

Answer 1

Solution:

Algorithm

Step (1) Outline the Damaged Area with a Carpenter’s Square-

Using a carpenter’s square and a pencil or marker, draw a line at least an inch or more above and below the damaged area.

Use a stud finder to find the nearest stud on either side of the hole and mark those.

Step (2) Cut the Sides with a Keyhole Saw or Utility Knife-

Use a saw blade or utility knife to cut along the lines you just drew. When you run into a stud, mark and measure a 3/4 inch farther in, which will be the center of the stud.

The edge of the patch should be directly over the stud so both the existing drywall and patch have support.

Cut along the lines carefully, making several passes with each cut slightly deeper than the previous cut.

Remove the damaged piece of drywall.

Step (3) Cut the Support and Install in the Wall-

Cut a 1 x 3-inch piece of scrap lumber or 3/4-inch piece of plywood approximately 2 to 4 inches longer than the height of the patch.

Screw these supports vertically behind the opening to keep the patch from cracking.

Hold the support in place and secure it with drywall screws without driving the screws through the drywall.

Step (4) Cut the Drywall Patch to Size

Using a 2 x 2-inch piece of drywall, measure the repair area.

Cut a piece of drywall to size using a drywall knife and carpenter's square.

Step(5) Install the Drywall Patch with Drywall Screws

Position the screws at least an inch from the edges to avoid spitting or crumbling the drywall.

Use a drill to affix the patch in place.

Step (6)

Complete the Drywall Patch

Run strips of self-adhesive fiberglass drywall tape around the patch, centering the tape on the seams.

Use a 6-inch drywall taping knife to spread drywall joint compound across the patch and tape to create a smooth, flat surface.

Let the compound dry overnight, and then sand until smooth. Repeat with a second coat.

For a very smooth drywall hole repair, spread a third coat with a 12-inch drywall taping knife and let dry overnight, then sand, wipe with a tack cloth and paint the area.