4 distinct integers p, q, r and s are chosen from the set {1,2,3,…,16,17}. The minimum possible value of p/q+r/s can be written as ab, where a and b are positive, coprime integers. What is the value of a+b?

To find the minimum possible value of p/q + r/s, we need to minimize both fractions individually.

First, let's consider the fraction p/q. Since p and q are distinct integers chosen from the set {1, 2, 3, ..., 16, 17}, we want to minimize p and maximize q. Therefore, p should be 1, and q should be the largest number in the set, which is 17.

Next, let's consider the fraction r/s. Following the same logic, we want to minimize r and maximize s. So, we set r as the next smallest number after 1, which is 2. Finally, s should be the largest remaining number in the set, which is 16.

Therefore, the minimum value of p/q + r/s is 1/17 + 2/16 = 1/17 + 1/8.

To add fractions, we need a common denominator. The least common multiple of 17 and 8 is 136. Therefore, we rewrite the fractions with the common denominator:

1/17 = 8/136
1/8 = 17/136

Now, we can add the fractions:

8/136 + 17/136 = 25/136

The value of a is 25, and the value of b is 136.

To find the sum of a and b, we calculate 25 + 136 = 161.

Therefore, the value of a + b is 161.