problem0():
  Carry out the middle square random number sequence.

0 :  3647
1 :  3006
2 :  360
3 :  1296
4 :  6796
5 :  1856
6 :  4447
7 :  7758
8 :  1865
9 :  4782
10 :  8675

problem1():
  Estimate pi in two lines of code.
  pi_estimate =  3.13192

problem2():
  Given 0 <= d < 365, day of year
  print month and day of month.
  Use d=68 which should be March 10.

  The calendar date is March 10

problem3(): given card index c, identify rank and suit.
  Card index c =  29
  Card 29 is Four of Diamonds

problem4(): Newton-Pepys dice problem
  Process 1: 6 dice are rolled, does at least 1 six show?
  Process 2: 12 dice are rolled, does at least 2 sixes show?
  Process 3: 18 dice are rolled, does at least 3 sixes show?

  Process 1 probability estimate =  0.667
  Process 2 probability estimate =  0.635
  Process 3 probability estimate =  0.591

problem5():
  Probability of a straight in poker.

  Estimated probability of a straight is  0.00353
  Theoretical value is  0.003940037553482932

problem6():
  Probability of a flush in poker.

  Estimated probability of a flush is  0.00226
  Theoretical value is  0.001965401545233478

problem7(): shared birthdays among a group?

  There were  24  unique birthdays in group of  25 people.

problem8(): Stop having children after first boy.

  Total kids born =  1915
  Total girls born =  915
  Total boys born =  1000
  Maximum family size was  11
  Average family size was  1.915

problem9():
  How long does a random sequence stay monotone, on average?
  Tested  10000  sequences
  Average length of monotone sequence =  2.719
  Theoretical value is  2.718281828459045