One of Professor Stirringstone's most brilliant inventions is the Cuppedia Multi charm, which charms a baking pie such that every slice is a different variety of pie. Since eight students (Alan, Elsath, Faralene, Gregory, Hoshi, Karen, Neal, and Rina) were staying at HOL over the Christmas holiday, Professor Stirringstone generously baked a pie with eight slices (each of a different flavor or variety of pie).

The pie was divided into eight identical sections, as seen (numbered one through eight) on the diagram below. Can you determine which student had which slice of pie, and which flavor or variety each student chose?

1. Of apple, cherry, pumpkin, and shepherd's pie - no two of these slices are adjacent to one another.
   
   
2. The slice of mince pie has a number that is one more than the slice of pumpkin's number, and twice the number of the blueberry slice.
   
   
3. The slices of apple and cherry aren't directly across the pie from one another.
   
   
4. Karen (who didn't take the blueberry slice) took the slice directly across from the slice of steak-and-kidney pie.
   
   
5. Neal's pie slice is adjacent to both the slice that Hoshi took and the slice of shepherd's pie.
   
   
6. The slice of pecan pie is not slice #6.
   
   
7. Karen's slice of pie is adjacent to both Alan's and Rina's - neither of whom chose the apple slice.
   
   
8. The slice of pie directly across from Rina's slice has a number one more than Elsath's slice, and one less than Gregory's.