Question: I have sixteen students in my class who sit in four rows of four. Each week they sit in a different order. 

After a number of weeks every student has sat next to every other student, next meaning side by side, one behind the other, or sitting diagonally together. What is the fewest number of weeks in which this can happen?

How many if my students were 25?

Answer: 
Here's 16 students in

> 
> 4
> 
> 
> 

weeks.

> 
> 
> ```
> 
> 0123 A8B9 CAD0 135E
> 4567 2031 B179 A2BC
> 89AB ECFD 58E4 94D0
> CDEF 6475 F263 7F68
> 
> ```
> 
> 
> 
>
As a starting point for Question 2, here it is done in

> 
>  7 weeks
> 
> 
> 

Solution

> 
> 
> ```
> 
> 01234   IG968   HCFA1   97HEP   BA92H   HDCE0   EB095
> 56789   B1HKJ   3P4JD   MF8AK   L3CJ8   8K1F2   GN46H
> ABCDE   P4307   E20BM   N3LI4   KDGN7   GMBNI   3IACK
> FGHIJ   D5MAL   7698K   J50D6   50461   P6LJA   DF712
> KLMNP   NF2CE   GILN5   1CG2B   IEMPF   93475   JM8PL
> 
> ```
> 
> 
> 
>