Answer:
1 stick.
Step-by-step explanation:
We have been given that you are playing a round of Fibonacci nim with a friend. The game begins with 15 sticks. You start by removing 02 stick(s); your friend then takes 4.
First of all, we will find the number of remaining sticks as shown below:
[tex]\text{Number of remaining sticks}=15-2-4[/tex]
[tex]\text{Number of remaining sticks}=9[/tex]
We know that 1st 15 Fibonacci numbers are 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610.
We can see that Fibonacci number next to 9 is 8, so you should take one more stick to get a Fibonacci number.
Therefore, you should take 1 stick to win the game.
