A mule note is simply a Series of notes that uses back plates from a different Series. Mule notes can be produced by using back plates from a prior Series — The Series 1963 $1 Federal Reserve Note, for example, has new face plates, but uses back plates from Series 1957 B $1 Silver Certificates.
Mule notes can also be produced by using back plates from a newer Series — Series 1934 $5 Federal Reserve Notes with back plate numbers 939 are Series 1934 faces with Series 1934 A backs!
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I have a $1 serial number H433210050 and another with serial number K76761331 are either worth anything?