Your friend will pick a $4$-letter word and you will make guesses in order to find it.
-A word can contain only the letters $A, B, C,\:\text {and} \:D$, and they can be used more than once. $(AAAA-DDDD)$.
-In your guess if at least three letters are in their correct places you will win a prize. What is the minimum number of guesses in order to guarantee to win the prize?
You are looking for the covering code number $K_4(4,1)$. Finding such numbers are very hard problems in general.
This particular one can be found in this paper, and it is equal to 24.
The covering table is also given, I reproduce it here:
AAAA AABB ABAB ABBA ACCC ADDD CACD CCDA CDAC DDCA DADC DCAD BAAB BABA BBAA BBBB BCCC BDDD CBCD CCDB CDBC DDCB DBDC DCBD
Reference: Covering theorems for vectors with special reference to the case of four and five components. R. G. Stanton, J. D. Horton and J. G. Kalbfleisch