The Hearthome Gym in Pokémon Diamond and Pearl, was the 5th gym, but in Pokémon Platinum, this was changed to the 3rd gym. This is evident by the significant level change of Fantina's Pokémon.
The Hearthome Gym is a giant, five-story building constructed of gray stone blocks. It is illuminated by eerie gray-blue torches. On every floor, there is a mathematical puzzle and three doors corresponding with the answers. Picking the correct door leads to the next elevator up. Picking the wrong door leads to a dead end and a trainer to fight. The Gym Leader waits in the final room on the fifth floor, which has stain-glass windows and resembles a cathedral.
In Platinum
In Pokémon Platinum, Hearthome Gym has become much like Dewford Gym, in Generation III; it is dark and there is only limited light source. The player must navigate their way around the gym using a torch. Duskull lamps are used as visible walls, to guide the player around. There are other trainers with torches the player must battle, in order to make their way to Fantina.
She is third gym leader in this game, able to be battled on the first visit to Hearthome. Fantina uses similar Pokémon, at different levels, although she no longer has Drifblim, her original signature Pokémon.
The math questions are mostly basic addition and subtraction questions, which becomes somewhat of a running joke among the trainers faced, some of which mention that the questions should have been impossible to get wrong with use of the Pokétch's Calculator App.
Although the Hearthome Gym is considered the third in Platinum it still shows up as the fifth badge on the trainer card and Fantina's face is on the fifth slot.