I have an L-shaped hallway with:

a ceiling light in the middle of each leg
a light switch at the end of each leg
a light switch at the intersection.

Several years ago, I used to be able to turn the lights on and off
from any switch. But now the lights can be turned on and off by only
one switch (at the end of one leg).

In previous attempts to resolve this problem, I replaced all of the
switches but I didn't record what wires went to each terminal.

Question: What kind of new switches do I need (single-pole, 3-way, 4-
way) and how many of each?

How do I determine what wire connects to each terminal of each switch?