Question 10
Andy constructed the smallest subset $S$ of positive integers that satisfies the following properties:
- If number $t$ is in $S$, then the numbers $6t$ and $6t+1$ are also in $S$.
- The number $1$ is in $S$, but the numbers $2,3,4$ and $5$ are not in $S$.
Then, Andy calculates the sum of two distinct numbers in $S$, where the two numbers are both less than $2022$. How many different possible sums can Andy obtain?
- If number $t$ is in $S$, then the numbers $6t$ and $6t+1$ are also in $S$.
- The number $1$ is in $S$, but the numbers $2,3,4$ and $5$ are not in $S$.
Then, Andy calculates the sum of two distinct numbers in $S$, where the two numbers are both less than $2022$. How many different possible sums can Andy obtain?