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Completing 7-Day Field Research Tasks: By diligently doing your daily Field Research tasks for a week, you'll get a Research Breakthrough encounter. This breakthrough has a chance of rewarding you with a Sinnoh Stone.
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Defeating Team Go Rocket Leaders: Taking down those villainous Team Go Rocket Leaders is not just for saving the Pokemon they captured, you can also get a Sinnoh Stone as a reward after defeating them.
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Winning Trainer Battles: Challenge other trainers to PvP battles and emerge victorious. Winning these battles grant you a chance of getting a Sinnoh Stone.
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Winning Go Battle League Battles: Participate in the Go Battle League and win matches. Earning a "Mystery Item" reward after victories in the league has a possibility of being a Sinnoh Stone.
These are the main methods to acquire Sinnoh Stones. Remember, they aren't guaranteed rewards so persistence is key!