Question 8
Proceeding through a sequence of numbers term by term, we calculate a running tally as follows. The tally starts at zero. Starting with the first term, a term is subtracted from the running tally if the result is non-negative, otherwise it is added to the tally. When we arrive at the end of the sequence, the resulting tally is called the roman sum of the sequence. For instance, the roman sum of the sequence $2,4,3,3,1,5$ is $0+2+4-3-3+1+5=6$.
For a sequence consisting of the numbers $1,2,3,\ldots,100$ in some order, what is its largest possible roman sum?
For a sequence consisting of the numbers $1,2,3,\ldots,100$ in some order, what is its largest possible roman sum?