Question 93
Given the set of $N$ four-digit numbers formed from the digits $1$, $2$, $3$, $4$, $5$, $6$, $7$, $8$. Find the smallest possible value of $N$ if the set satisfies the following condition:
a) For any two different digits from $1$, $2$, $3$, $4$, $5$, $6$, $7$, $8$ there exists a number from the set which contains both of them;
b) For any two different digits from $1$, $2$, $3$, $4$, $5$, $6$, $7$, $8$ there exist no greater than two numbers from the set which contain both of them.
(E. Barabanov)
a) For any two different digits from $1$, $2$, $3$, $4$, $5$, $6$, $7$, $8$ there exists a number from the set which contains both of them;
b) For any two different digits from $1$, $2$, $3$, $4$, $5$, $6$, $7$, $8$ there exist no greater than two numbers from the set which contain both of them.
(E. Barabanov)