1000 cards are placed in a row on a table. A card has two sides, one colored red and the other blue. Initially the first 500 cards are red side up and last 500 are blue side up. Someone comes and flips every second card. Someone else comes and flips every third card.
People keep coming until the last person flips every hundredth card.
You CAN'T know the sum. I still don't know the sum. Now I know the sum.