This basically means if she can catch you ... you're hers! It all started with a foot race and has evolved from there.

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According to Wikipedia In Li'l Abner, Sadie Hawkins was the daughter of one of Dogpatch's earliest settlers, Hekzebiah Hawkins. The "homeliest gal in all them hills", she grew frantic waiting for suitors to come a-courtin'. When she reached the age of 35, still a spinster, her father was even more frantic—about Sadie living at home for the rest of her life. In desperation, he called together all the unmarried men of Dogpatch and declared it "Sadie Hawkins Day". Specifically, a foot race was decreed, with Sadie in hot pursuit of the town's eligible bachelors—and matrimony as the consequence.

Before 1937 it was unheard of for a woman to be so bold as to ask a man lout on a date. Now (thanks to a comic strip character) it is acceptable everyday but especially on Sadie Hawkins day. So ladies now is your chance. I can remember my mom telling me that it was my fault "some pretty girl is sitting at home" because I was too shy to ask girls out (OK I was a wee bit more shy in high school.) Ladies ... don;t let it be your fault that some nice guy is sitting at home alone tonight.