Question 166
In a box there are $50$ cards on which the first $100$ positive integers are written as follows: on the first card there are $1$ (on one side) and $2$ (on the other side), on the second card there are $3$ (on the one side) and $4$ (on the other side) and so on, up to the $50$th card, on which the numbers $99$ (on one side) and $100$ (on the other side) are written. Eliza pulls out four cards from the box and calculates the sum of the $8$ numbers written on the four cards. How many distinct sum can Eliza get?