Hello, ramanujam!

If I interpret the problem correctly, the answer is EIGHT.A word is a combination of 8 letters, each either A or B.

Letxandybe 2 words differing in exactly 3 places.

How many words differ from each ofxandyin 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

. . inat leastfive digits.