I find this whole thing a bit odd. I've been to professional cocktail and dinner parties (while in Texas) and it was never required for me to have a male counterpart with me. I mingled amongst the people I knew and left when I was ready, on my own.

But if you must have a date, consider a friend, relative (brother, cousin....), neighbor, any male you feel comfortable enough to spend a formal evening with. Or even, another co-worker who isn't invited to attend (woops! I guess I assumed this is a work event).

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When you get to the end of your rope, tie a knot and swing.