Here is the problem set:

1. Imagine an innite chess board of square tiles as in the Figure below. You start with one whole piece of pie in the lower left hand corner, as you see in the rst diagram. At each stage you cut the amount of pie in half in one of the squares and distribute the two equal pieces to the squares to the immediate right and to next square above, if those two squares are unoccupied. You can see a few operations performed below. Problem: With legal moves as above, can you get all the crumbs out of all of the nine yellow squares in the lower left corner as in the last diagram below? Explain your answer. Hint: Think about how much pie could appear in each square. 2. Calculate the innite sum 00 n + 1 2\" ' n=0 Hint: Look about how much pie could appear in each square as in Problem 1