Question 120
The sum of several (not necessarily different) positive integers not exceeding $10$ is equal to $S$.
Find all possible values of $S$ such that these numbers can always be partitioned into two groups with the sums of the numbers in each group not exceeding $80$.
Find all possible values of $S$ such that these numbers can always be partitioned into two groups with the sums of the numbers in each group not exceeding $80$.