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Did Pete take a cab ride to Madison Avenue, key himself into Sterling Cooper in the middle of the night (assuming he even had that privilege), drunkenly mess around Joan’s desk until he magically uncovered Peggy’s address?
One theory that I’ve long been intrigued with is that Pete and Peggy actually knew each other before she arrived at Sterling Cooper. It would explain, perhaps, why Pete treats Peggy quite cruelly the first time we see them meet on screen (and why Peggy willingly invites him into her apartment later that night). It may even provide some color on why Peggy made an advance on Don near the end of her first day at Sterling Cooper.
Another possibility, which is plausible (if barely) is that Pete “somehow” found his way to her apartment based on the knowledge that Peggy lives in Brooklyn. After all, Kurt in Season Two finds his way there by use of ‘neighbors.’
I held out some hope that this question would be addressed at some point but alas it was not to be.