Problem #PRU-100620

Problems Set theory and logic Algorithm Theory Game Theory Winning and loosing positions

Problem

This time, Sally and Fatima have some number of books on a shelf. Every turn, each of them is allowed to take 1, 3 or 4 books from the shelf. The girl that takes the last book wins, Sally goes first. Who will win if there are: a) 14, b) 16, c) 19 books on the shelf?