How many possible paths through Norman's gym are there?

Question

assuming the player only moves forward, fighting only the minimum three required gym trainers to reach Norman, how many possible paths are there through the branching gym layout?

Answer 1

There are a total of 6 possible paths through Norman's gym, the following is every path you can path and which rooms you go through to get to Norman:

1. Speed Room (left door), Zero Reduction Room/Confusion Room* (left door), Strength Room (right door), Gym leader's room (right door)
2. Speed Room (left door), Defense Room (right door), Strength Room (left door), Gym Leader's room (right door)
3. Speed Room (left door), Defense Room (right door), One-Hit KO Room (right door), Gym Leader's Room (left door)
4. Accuracy Room (right door), Defense Room (left door), Strength Room (left door), Gym Leader's Room (right door)
5. Accuracy Room (right door), Defense Room (left door), One Hit KO Room (right door), Gym Leader's Room (left door)
6. Accuracy Room (right door), Recovery Room (right door), One Hit KO Room (left door), Gym Leader's Room (left door)
   *the Zero Reduction Room is in Ruby/Sapphire Omega Ruby/Alpha Sapphire and the Confusion Room is in Emerald.

And Here's a map for reference. Hope this helps!