Why does my sink drain keep clogging up?

What people tried

Every workaround mentioned in the threads below. We haven’t tested any of them — and nobody here is claiming they worked.

1. 1
   Trying to manually fix the plumbing setup oneself
2. 2
   Replacing the accordion trap with a normal one and modifying the dishwasher tailpiece extension
3. 3
   Cleaning out the drain stopper and pipe
4. 4
   Placing a hollow cylinder over the drain holes to test for air lock
5. 5
   Drilling out holes in the drain strainer to create a vent
6. 6
   Unclogging or replacing the pipe
7. 7
   Getting the line snaked to remove roots
8. 8
   Modifying the PVC pipe to create a clean out
9. 9
   Detaching the downspout from the underground system and using an above-ground extension
10. 10
    Digging up and replacing the pipe with a shovel
11. 11
    Hiring a plumber

In their words

Unedited, most upvoted first, each linked to the thread it came from.