#! /usr/bin/env python3
#
import numpy as np

def simulate_many ( n ):

# simulate_many estimates the average distance.
#
#  Input:
#
#    integer n, the number of simulations.
#
#  Output:
#
#    real average, the average distance between two flies in the
#    unit square, after n simulations.
#
  average = 0.0
  for test in range ( 0, n ):
    p1 = np.random.rand(2)
    p2 = np.random.rand(2)
    d = np.linalg.norm ( p1 - p2 )
    average = average + d

  average = average / n

  return average