With 2000 index cards, each having a single number on it, I am tasked with the job of finding the grand total of all numbers. In order to do so, I have 1000 people, each who sit at a desk in a room that has 25 rows with 40 desks. Each person can pass a stack of cards to their neighbor front, back, right and left. Given that I am only allowed to give the entire stack to one person, it takes 3 seconds for a person to pass a stack (regardless of size) to their neighbor. It takes 1 second to add 2 numbers and the person allowed to write the sum on the card to pass to the neighbor.
What's the fastest means of obtaining the sum of all numbers on the card if I am required to gather all subtotals to give to the original person I passed the entire stack to?
I'm wondering whether it's fastest to utilize all 1000 or whether there's a faster way of getting the sum without having to use all.
EDIT: I feel like the best thing to do is to give the initial stack to the person in the middle so that it'll be quickest to have everything passed back to him/her