MathDB

Problem 4. Angel has a warehouse, which initially contains

100

piles of

100

pieces of rubbish each. Each morning, Angel performs exactly one of the following moves: (a) He clears every piece of rubbish from a single pile. (b) He clears one piece of rubbish from each pile.
However, every evening, a demon sneaks into the warehouse and performs exactly one of the following moves: (a) He adds one piece of rubbish to each non-empty pile. (b) He creates a new pile with one piece of rubbish.
What is the first morning when Angel can guarantee to have cleared all the rubbish from the warehouse?

Problem Statement