PokéBase - Pokémon Q&A
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Not cheats

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Sorry Pokemaster, but shininess hasn’t been determined by IVs since Gen 2. I found several sources saying that no, it’s not possible to get a shiny through the Pokéwalker.

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Everybody points to this Smogon post that shows how Pokewalker PID generation works. If it's accurate, it does prove that Pokewalker Pokemon cannot be Shiny (among other things): https://www.smogon.com/forums/threads/61090/page-10#post-2634864
5 votes

Yes it should be possible since a shiny is determined by the random IVs (hidden pokemon data). It will be the same chance as normal, 1 in 8192.

But you won't be able to tell until you send it back to the game, because the Pokewalker is monochrome.

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I guess you might as well catch every pokemon you find on the Pokewalker then...