The game of Nim is a game that involves two players and two piles of matches on atable or other flat surface. The players take turns removing a non-zero number of matchesfrom one pile. For example, if there are two piles of matches, one with 2 matches, theother one with 7 matches, and it’s Jason’s turn to play, Jason can removeat most7matches; he isnotallowed to pick 8 or 9 matches by also snatching matches from the pilethat has 2 matches! He is alsonotallowed to pick, say, one match from one pile and onefrom another. It has to be thesamepile each time. Unfortunately for Jason, removing either the 7 matches that make up the large pile orthe 2 that make up the small pile, thus "emptying" one of the two piles, would be aterribleidea, since in our variant of Nim (there are several) the player who takes thelastmatchonthe entire tablewins the game! The teaching staff makesno claimas to this game beingactual fun. Suppose that both piles have thesamenon-zero number of matches, which we willcalln(son≥1). Usingstrong inductiononn, prove that, in this special case where thepiles have the same size, the player who playssecondcanalways win. Put differently, the second players always has astrategy to winno matterhow many matchesthe firstplayer picks atanygiven point in the game.