Ok, after categorizing all the guesses into their respective equivalence classes (first and last letter) I've come to the following conclusion which holds for all the guesses that have been made up to now:
A koan has the buddha nature iff the difference of its first and last letters' numeric value modulo 4 equals zero.
In other (simpler) words, the first letter of the koan must be a multiple of 4 letters away from the last letter (within the alphabet), the rest of the letters within the koan are irrelevant.