Question 133
A quadruplet of distinct positive integers $(a, b, c, d)$ is called $k$-good if the following conditions hold:
1. Among $a, b, c, d$, no three form an arithmetic progression.
2. Among $a + b, a + c, a + d, b + c, b + d, c + d$, there are $k$ of them, forming an arithmetic progression.
a) Find a 4-good quadruplet.
b) What is the maximal $k$, such that there is a $k$-good quadruplet?
1. Among $a, b, c, d$, no three form an arithmetic progression.
2. Among $a + b, a + c, a + d, b + c, b + d, c + d$, there are $k$ of them, forming an arithmetic progression.
a) Find a 4-good quadruplet.
b) What is the maximal $k$, such that there is a $k$-good quadruplet?