game with stach of 100 cards, spliting into smaller piles
Source: Dutch NMO 2004 p3
September 21, 2019
combinatorics
Problem Statement
Start with a stack of cards.
Now repeat the following: choose a stack of at least cards and split them into two smaller piles (at least card of each). Continue this until there are finally stacks of card each. Every time you split a pile into two stacks you get a number of points that is equal to the product of the number of cards in the two new stacks.
What is the maximum number of points that you can earn in total?