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1. A fast combination of punches.

2. A powerful combination of two people or things.
It's believed that this phrase originates from boxing, where there is a whole lot of punching that happens, and the 'old one two' is a quick combination of punches in boxing.

The earliest that I could find of this phrase in writing is during the early 1900s. For example, in the Oakland Tribune newspaper, printed June 1919, the expression is used in relation to boxing: 

    "The fans will see a big difference in Frankie. He is far stronger than he was before going to France, 
     and he is hitting much harder. He has the old one-two punch down to perfection and he stings every 
     time he lands."

By the looks of it, this idiom later began to not only refer to a strong combination of punches in boxing, but also to things or people that are considered to be a strong combination. An example of this term being used in such a way, outside the context of boxing, is seen in the Lowell Sun newspaper, 1949:

    "And maybe that's the way the old team of Stalin and Molotov figured in the first place, since they've 
     been working together for 35 years: The old one-two, with Molotov being tough and Stalin being soft 
     if he had to."
* For a simple lunch, the old one-two ingredients I like to put on a slice of bread are peanut butter and jelly.

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Note: The origins for many common expressions are not clear. In cases like this, what may be provided on the page instead is a theory as to how a phrase may have originated. Or, if no theory is mentioned, then I'll at least try to include a quote on the expression's page to give you an idea for a old a phrase is, at minimum. These quotes are typically the oldest known citations of an expression being used in writing, and most of the time they come from newspapers, books, or poems. It's possible that older citations exist and I have overlooked them.