Consider the set A of all integers from 0 to 399 inclusively; all numbers are written in three-digit format (so instead of 0 we write
000, instead of 17 we write 017 etc.). Two distinct numbers from A
are said to be neighbors if they differ at exactly one place (so 007
and 017 are neighbors because they differ at exactly one place, the
tens place). What is the maximum number of different numbers
from A such that no two of them are neighbors?