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Unicyclist

Let's analyze the information given:

1) The magician is a male.
2) Mary is not a unicyclist.
3) Peter is not a magician.

From statement 1, we know the magician is a male.
So, Peter and Mary cannot be the magician.

From statement 3, Peter is not a magician.
So, Peter is either the unicyclist or the juggler.

From statement 2, Mary is not a unicyclist.
So, Mary is either the magician or the juggler.

Now, let's put it together:
- Peter is not a magician, so he must be either the unicyclist or the juggler.
- Mary is not a unicyclist, so she must be either the magician or the juggler.
- The magician is a male, so Mary cannot be the magician.
Therefore, Mary must be the juggler.
- Since Peter is not the magician, he must be the unicyclist.

So, the professions are:
- Peter is the unicyclist.
- Paul (since Mary is the juggler) is the magician.
- Mary is the juggler.

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