Problem $1.$ Pebbles Game. Two players play a game, starting with three piles of $n$ pebbles each. Players

alternate turns. On each turn, a player may do one of the following:

take one pebble from any pile

take two pebbles each from two different piles

The player who takes the last pebble$($s$)$ wins the game.

Write an algorithm that, given $n,$ determines whether the first player can "force" a win. That is$,$ can the

first player choose moves such that, regardless of what the other player does, they will always win.

In addition, write a procedure that tells a player which move $($if any$)$ they should make to force a win given

the current triple of pebbles in each pile.

What is the complexity of your solution?