gym 1: falkner, violet city
gym 2: bugsy azelea town
gym 3: Whitney goldenrod city
you now need to get the squirt bottle from the flower shop up near the top right of goldenrod city to get sudowoodo to move.
gym 4: morty ecruteak city
gym 5:chuck cianwood city
gym 6:jasmine olivine city
gym 7: pryce mahogany town
gym 8: Claire blackthorn city
now to advance you have to beat the elite 4 and lance.
elite trainer 1: will
elite trainer 2: koga
elite trainer 3: Bruno
elite trainer 4: Karen
league champion: dragon master lance
gym 9: lt. surge vermillion city
at this point you have to go to cerulean city and solve the machine part side quest to advance, to do this you have to go up the bridge, encounter the rocket then go into mistys gym, go to the 2x2 pool in the gym and press a while in the water to find the machine part and now you go to the power plant (go east from cerulean city, and then south , down on the water talk to the power plant manager, give him the part and he will fix his previously broken generator.He will give TM 07 (zap cannon) and then the magnet train will be running again, and misty will return to her gym after you speak to her up at cerulean cape (north of cerulean city.
gym 10: misty cerulean city
gym 11: Sabrina saffron city
gym 12: erika celadon city
gym 13:brock pewter city
gym 14: janine fuchia city
gym 15: blaine seafoam islands
gym 16: blue viridian city
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in total 16 badges
in every game except gold and silver and crystal there are 8 badges, gold silver and crystal have 16 cause you can fight the kanto and johto leaders.
You are in jhoto first then when you have all the 8 gym badges you can go to kanto and get 8 more badges which will be all 16 badges then you can challenge the pokemon league. Hope that helped.
There is only 8.
there is 16 badges... 8 in kanto and 8 in johto