project_euler_45.rb

# Triangular, pentagonal, and hexagonal
# Problem 45
# Triangle, pentagonal, and hexagonal numbers are generated by the following formulae:
#
# Triangle    Tn=n(n+1)/2   1, 3, 6, 10, 15, ...
# Pentagonal  Pn=n(3n−1)/2  1, 5, 12, 22, 35, ...
# Hexagonal   Hn=n(2n−1)    1, 6, 15, 28, 45, ...
# It can be verified that T285 = P165 = H143 = 40755.
#
# Find the next triangle number that is also pentagonal and hexagonal.
#
def t(n)
  n * (n + 1) / 2
end

def p(n)
  n * (3 * n - 1) / 2
end

def h(n)
  n * (2 * n - 1)
end

i = 285

p_offset = 0
h_offset = 0

p_found = false
h_found = false

loop do
  i += 1
  triangle = t(i)

  loop do
    pentagonal = p(p_offset)
    if pentagonal > triangle
      break
    elsif pentagonal == triangle
      p_found = true
      break
    else
      p_offset += 1
    end
  end

  loop do
    hexgonal = h(h_offset)
    if hexgonal > triangle
      break
    elsif hexgonal == triangle
      h_found = true
      break
    else
      h_offset += 1
    end
  end

  if p_found && h_found
    puts triangle
    break
  else
    p_found = false
    h_found = false
  end
end