MathDB

3

Part of 2004 Dutch Mathematical Olympiad

Problems(1)

game with stach of 100 cards, spliting into smaller piles

Source: Dutch NMO 2004 p3

9/21/2019
Start with a stack of 100100 cards. Now repeat the following: choose a stack of at least 22 cards and split them into two smaller piles (at least 11 card of each). Continue this until there are finally 100100 stacks of 11 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?
combinatorics