Question 72
Bob's Rice ID number has six digits, each a number from $1$ to $9$, and any digit can be used any number of times. The ID number satisfies the following property: the first two digits is a number divisible by $2$, the first three digits is a number divisible by $3$, etc., so that the ID number itself is divisible by $6$. One ID number that satisfies this condition is $123252$. How many different possibilities are there for Bob's ID number?