7.4. Toma thought of a positive integer and found the remainders when it is divided by 3, 6, and 9. It is known that the sum of these three remainders is 15. Try to find the remainder when the number is divided by 18.
7.4. The remainder when this number is divided by 18 is 17.

Since the remainders when divided by $3$, $6$, and $9$ do not exceed $2$, $5$, and $8$ respectively, the sum of these three remainders is always no more than $2+5+8=15$. Since their sum is equal to 15, these three remainders must be $2$, $5$, and $8$. Furthermore, since the remainder when the number is divided by 9 is 8, the remainder when it is divided by 18 can only be 8 or 17. If the remainder were 8, then the number would be even. Thus, the remainder when it is divided by 6 could not be 5, leading to a contradiction.