[Detailed Explanation of the Real Questions of the Blue Bridge Cup JavaB Group] Sliced Noodles (2014)

Title description

Cut noodles
One high-gluten ramen noodles, cut in the middle, you can get 2 noodles.
If you fold it in half and cut it in the middle, you can get 3 noodles.
If you fold in half twice and cut in the middle, you can get 5 noodles.
So, how many noodles will you get if you fold in half 10 times and cut in the middle?

The answer is a whole number, please submit the answer through the browser. Don't fill in any redundant content.

Problem solving ideas

We can easily get a sequence of a(0)=2, a(1)=3, a(2)=5, a(3)=9, a(4)=17...The

first method
we can think of This is an analogue geometric sequence, which can be considered a(n)=2 ⁿ +1, and then a(10)=2 ¹⁰ +1=1025

In the second method,
we can also find that a(1)=2a(0)-1, a(2)=2a(1)-1...to
sum up, a(n)=2a(n-1)-1

Reference Code

public class Test {
    
    
	 
	public static void main(String[] args) {
    
    
		int count = 2;
		int n=10;
		for (int i = 1; i < n+1; i++) {
    
    
			count=2*count-1;
		}
		System.out.println(count);
	}
}

Answer: 1025