If I interpret the problem correctly, the answer is EIGHT.A word is a combination of 8 letters, each either A or B.
Let x and y be 2 words differing in exactly 3 places.
How many words differ from each of x and y in at least 5 places?
and differ in exactly three places.
. . Which three places? .It doesn't matter.
Suppose they differ in their first three letters.
They may look like this:
. . . . .
The word cannot differ from and in the first three places.
. . The first three places can filled in: ways.
The last five letters of must be the opposites of those in and .
. . There is one way to do this.
Therefore, there are ways that can differ from and
. . in at least five digits.