In this lesson, we are going to solve another fun math problem that asks us to solve the problem:

What is the index of the first term in the Fibonacci sequence to contain 1000 digits?

In case your college algebra is a little rusty: Fibonacci sequence is a series where you add the next number to the previous number in that series. These numbers can get massive quickly because of the addition to the previous value creates a mathematical snowball effect.

Though the problem sounds daunting, it can be solved easily in Ruby.

We are going to start by creating a method called fibonacci_digit_counter and define some variables:

def fibonacci_digit_counter
  num1, num2, i = -1, 0, 1
end

Next, we will create a while loop inside of the fibonacci_digit_counter method and iterate over the digit value of i.

while i.to_s.length < 1000
  num1 += 1

  i, num2 = num2, num2 + i
end

In this code, we are converting the value of i to string and calling the length method on it, and we want the loop to run as long as this length is less than 1000. Inside the loop, num1 is the counter that will keep adding the count every time we iterate, and this value is also the final answer to the problem. However, this variable has nothing to do with the Fibonacci number, as that is managed by the variables i and num2.

Also note that we are setting the value of i to num2 and num2 to the sum of num2 +1. This is exactly how the Fibonacci series is calculated.

Finally, we are going to return the variable num1 and print the fibonacci_digit_counter method.

If you run the program, the output is 4782, which is the correct answer.

The full the code is:

def fibonacci_digit_counter
  num1, num2, i = -1, 0, 1

  while i.to_s.length < 1000
    num1 += 1

    i, num2 = num2, num2 + i
  end

  num1
end

p fibonacci_digit_counter