project_euler_25.rb

# 1000-digit Fibonacci number
# Problem 25
# The Fibonacci sequence is defined by the recurrence relation:
#
# Fn = Fn−1 + Fn−2, where F1 = 1 and F2 = 1.
# Hence the first 12 terms will be:
#
# F1 = 1
# F2 = 1
# F3 = 2
# F4 = 3
# F5 = 5
# F6 = 8
# F7 = 13
# F8 = 21
# F9 = 34
# F10 = 55
# F11 = 89
# F12 = 144
# The 12th term, F12, is the first term to contain three digits.
#
# What is the first term in the Fibonacci sequence to contain 1000 digits?

f1, f2, i = 1, 1, 2

loop do
  f1, f2, i = f2, f1 + f2, i + 1
  break if f2.to_s.size >= 1000
end

puts i