>>27229892I did a statistical analysis of the type distribution of gyms/e4 once and constructed a set that was maximally "fresh". Here it is (1/2):
>Gen IRock, Water, Electric, Grass, Poison, Psychic, Fire, Ground
Ice, Fighting, Ghost, Dragon
>Gen IIFlying, Bug, Normal, Ghost, Fighting, Steel, Ice, Dragon
Psychic, Poison, Fighting, Dark
>Gen IIIRock, Fighting, Electric, Fire, Normal, Flying, Psychic, (Water/Water)
Dark, Ghost, Ice, Dragon
>Gen IVRock, Grass, Fighting, Water, Ghost, Steel, Ice, Electric
Bug, Ground, Fire, Psychic
>Gen V(Fire/Grass/Water/Normal), (Normal/Poison), Bug, Electric, Ground, Flying, (Ice/Dragon), (Dragon/Water)
Ghost, Dark, Psychic, Fighting
>Gen VIBug, Rock, Fighting, Grass, Electric, Fairy, Psychic, Ice
Steel, Fire, Dragon, Water
Bug 4 - 3/1 (2, E1, 3, 1)
Dark 3 - 0/3 (E4, E1, E2)
Dragon 6 - 3/3 (E4, 8, E4, 8, 7, E3)
Electric 5 - 5/0 (3, 3, 8, 4, 5)
Fairy 1 - 1/0 (6)
Fighting 6 - 4/2 (E2, 5, 2, 3, E4, 3)
Fire 5 - 3/2 (7, 4, E3, 1, E2)
Flying 3 - 3/0 (1, 6, 6)
Ghost 5 - 2/3 (E3, 4, E2, 5, E1)
Grass 4 - 4/0 (4, 2, 1, 4)
Ground 3 - 2/1 (8, E2, 5)
Ice 6 - 4/2 (E1, 7, E3, 7, 7, 8)
Normal 4 - 4/0 (3, 5, 2, 1)
Poison 3 - 2/1 (5, E2, 2)
Psychic 6 - 3/3 (6, E1, 7, E4, E3, 7)
Rock 4 - 4/0 (1, 1, 1, 2)
Steel 3 - 2/1 (6, 6, E1)
Water 6 - 5/1 (2, 8, 8, 4, 1, E4)