/sci/ - Science & Math

Lets say you have letters A-F. They are paired in groups of two across 6 rows.
group 1 is row 1-2 group 2 is row 3-4 group 3 is row 5-6.
There are 5 columns
In the first column the letters A B C D E F are there in order
In each group, one of the first two Letters that appear in column 1 have to appear in every column in one of those two rows.
In each column there cant be any repeat letters
In each group, the remaining 4 spaces must come from the remaining 4 letters not in its column 1 group. Each group cannot have more than 1 letter from outside its group.

This seems impossible. am I just retarded and cant figure it out?
no sudoku solver is able to check this for me because it wont be able to recognize that only repeats vertically are wrong. repeats horizontally are fine.

An example of all possible values is something like
AA_A_
B_B_B
CC_C_
D_D_D
EE_E_
F_F_F
its possible the letters may need to be moved to different spaces though