Fibonacci nim: The next move. Suppose 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. How many sticks should you take next to win?

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:

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.

8

step-by-step explanation: