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To play the game, we have to mix up boys and girls.

Hi,

Does the bolded part make sense to you? Thanks.
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Hello.

"To play the game, we have to mix up boys and girls."
I think this is okay.

"Boys and girls have to be mixed up to start the game."
How about this?
Oh no! This sounds very wrong to my ear. IIs it just me? It sounds like to play this game you need to confuse theirsexuality maybe by dressing some boys like girls and some girls like boys. I'm sure somebody won't be happy. I use mix up like this:

Our mailman mixed up our mail again! Can you believe that? 3 times in one week?