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How many join avenue berries do I need my Pokemon to eat to reduce its EVs to 0, from 252?

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you need 11

If you have over 100 EVs in a stat, the first berry will reduce them to 100, while further berries will decrease the EVs by 10. Therefore if you want to remove all EVs you will need 11 berries for the stat. This applies to Gen 4.

Source: The Pokemon DB

*EDIT: Thanks to Pokemaster, I realized that Berries in Gen 5 work differently. They only reduce 10 EV's per berry. So that means...
252 / 10 = 25.2 berries. 26 berries should do.

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Quite Right  LeBoss
I think that the EV berries work a bit differently in generation 5, they just lower by 10 each time instead of reducing to 100.
Pokemaster is correct, LeBoss.
ok... edited
What about Gen 6?