Problem 4 Angel has a warehouse. which initially contains 100 piles of 100 pieces of rubbish each. Each moming. Angel performs exact!y 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. everv 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?