First Round, January 2019

There are $13$ distinct multiples of $7$ that consist of two digits. You want to create a longest possible chain consisting of these multiples, where two multiples can only be adjacent if the last digit of the left multiple equals the first digit of the right multiple. You can use each multiple at most once. For example, $21$ – $14$ – $49$ is an admissible chain of length $3$. What is the maximum length of an admissible chain? A) $6$ B) $7$ C) $8$ D) $9$ E) $10$