Another way to get free gems is to complete quests in Clash of Clans

However, you don’t actually need to spend any real gems to get through anything in the tutorial,

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 aside from building a second builder’s home. With everything else in the tutorial, you can wait it out and watch them complete after the given amount of time, instead of spending your gems to speed up the tasks. Some tasks will take up to 15 minutes to complete, while others will take only 3 minutes at the most.

Another way to get free gems is to complete quests in Clash of Clans. Every single quest rewards you with free gems for completing them, and while most of them only offer you up to 5 gems at a time,

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these 5 gems at a time really add up by the time you get around to completing around 10 quests.