Let's say that you save 10'000 $ in an account with 5% interest, then you'll have 500 $ a year to spend on presents. If every child has two children the amount children in a generation is 2^n. When they grow up we stop giving them presents for mathematical simplicity. Then it's possible to give every child in the 9th generation a $1 gift a year. Which is quite neat. If we have a generation length of between 25 and 30 years this will be between 225 and 270 years in the future.
In the long run, it is highly likely that you will either be an ancestor of every single human, or none of them. (http://www.bbc.co.uk/news/magazine-19331938) You don't need to give every single one of your descendants a gift. Give 2-5 gifts a year, randomized after filtering out undesirables using a naughty/nice algorithm.
Assuming total population remains roughly the same, if enough people did this, it would actually work. Most kids would get gifts from grand^n Santa.
Nice idea and an interesting article. If the goal is to be remembered for as long as possible giving more presents is obviously better. After 9 generations only a small part
But some might feel that a enormous list of children with ratings of their behavior would be questionable.
