Q$3(4$ marks$)$

Two students are playing a Nim game with piles of sizes $2,3,4,5,$ and $6.$ Explain why the first

player can guarantee a win. List all possible $($first$)$ moves the first player can make if they are

required to leave the game in a state with a nim$-$sum of $0.$

${?}^1$ Nim is a two player game. There are $n1$ piles of objects where pile i contains $k_{i}in{Z}^{+}$objects $($for $1in).$

On each turn, a player chooses a pile and removes at least one object from it $($they may remove any number of

objects provided they all come from the same pile$).$ The player who takes the last object is the winner of the game.