Post History

First, the fussiness of the people has absolutely no bearing on how their solar system ended up.  It is what it is, whether they like it or not.

As for the physics, you are basically asking for rotations of the planet and its orbit around the star to be integer multiples.  Yes, that can happen, but realistically only for small integers.  Look up something called "tidal locking" or "tidal resonance".  For example, our moon is tidally locked to the earth.  In this case its spin and orbit have a ratio of 1:1.

Mercury has a spin to orbit ratio of 3:2.  That's only possible because Mercury is so close to the very massive sun.

Tidal locking and resonance rely on the difference in gravity of the body being orbited between the near and far side of the orbiting body.  The forces keeping a body in resonance decrease at higher ratios.  Therefore, most resonances out there are 1:1, which is full tidal locking.  Anything more requires orbiting close to something massive.

If you're looking for something like earth orbiting the sun with a resonance of 365:1, that's not going to happen.  First, earth is too far from the sun so that even 1:1 resonance is unlikely.  Venus is not tidally locked or in any resonance with the sun, and it's closer to the sun than earth.  Second, 365:1 is so extreme that it's not going to happen.