Ever since I was a kid, the concept of a seven day week threw me. Way back then I came up with a ten day week, three weeks a month, 13 months a year, and five non-month "holidays" calendar in my head. The five non-month holidays were (if I recall correctly) summer and winter solstice, spring and fall equinox, and New Year's Day.

I never could get around the 1/4 day problem, and still had to account for leap years with a sixth non-month day every four years. It was a fun thought experiment as a teenager interested in math and science though.