All three of them are in the Pokemon World Tournament. It is free and does not require any shards.
It is located to the south of Driftveil City. Prominent Trainers from previous games gather here to participate in battles in an eight person single-elimination tournament. Single Battles, Double Battles, Triple Battles, and Rotation Battles are held here. Special Trainers can be downloaded via Nintendo Wi-Fi Connection. It also contains both the move relearner and Move Deleter, as they are no longer located at Mistralton City. -Bulbepedia
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