Chapter 5.2, Problem 11E

sider this variation of the game of Nim. The game begins withnmatches. Two players take turns removing matches, one, two, or three at a time. The player removing the last match loses. Use strong induction to show that if each player plays the best strategy possible, the first player wins ifn=4j+2, or4j+3 for some nonnegative integerjand the second player wins in the remaining case whenn=4j+1 for some nonnegative integerj.