Question 172
Find $2^{2006}$ positive integers satisfying the following conditions.
(a) Each positive integer has $2^{2005}$ digits.
(b) Each positive integer only has 7 or 8 in its digits.
(c) Among any two chosen integers, at most half of their corresponding digits are the same.
(a) Each positive integer has $2^{2005}$ digits.
(b) Each positive integer only has 7 or 8 in its digits.
(c) Among any two chosen integers, at most half of their corresponding digits are the same.