Final answer:
Fibonacci nim is a mathematical game where players take turns removing sticks from a pile. The number of sticks a player can take follows the Fibonacci sequence.
Step-by-step explanation:
Fibonacci nim is a mathematical game played with sticks. In each turn, a player can remove one or more sticks from the pile. The goal is to avoid taking the last stick. The number of sticks a player can take in a turn follows the Fibonacci sequence: 1, 1, 2, 3, 5, 8, 13, ... The sequence continues with each number being the sum of the two previous numbers.
In this game, since the game begins with 90 sticks, the next move depends on how many sticks are left and how many the opponent has already taken in their turn. You can determine the next move by subtracting the previous number of sticks taken from the current number of sticks remaining to find the next number in the Fibonacci sequence. For example, if the opponent took 3 sticks in the previous turn and there are 78 sticks remaining, the next number in the Fibonacci sequence is 90 - 3 = 87. Therefore, you should take 87 sticks in your turn.