Question 17
Given a set $S=\{1,2,3,\ldots,199,200\}$. The subset $A=\{a,b,c\}$ of $S$ is said to be “nice” if $a+c=2b$. How many “nice” subsets does $S$ have?
(Note: The order of the elements inside the set does not matter. For example, we consider $\{a,b,c\}$ or $\{a,c,b\}$ or $\{c,b,a\}$ to be the same set.)
(Note: The order of the elements inside the set does not matter. For example, we consider $\{a,b,c\}$ or $\{a,c,b\}$ or $\{c,b,a\}$ to be the same set.)