I'm working on a website for some firefighters that want to be able to
sign-up for overtime and I need some help figuring out a date related
problem.

Here's the scenario:

Four groups of firefighters (group1, group2, group3, group4). Each
group works a 24 hr shift. So group1 works April 1, group2 works April
2, group3 works April 3, group4 works April 4, group 1 works April 5,
etc. It just keeps rolling like this forever into next year, etc.

I need to come up with a methodology for the following:

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