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-Exercises
-=========
-
-1. Round a float to the nearest integer using ``int()``. 
-
-#. What does this do? round(amount * 10)/10.0. How to round it to the nearest
-   5 paise?
-
-#. Print out the fibonacci sequence less than 30
-
-#. Write a program that prints the numbers from 1 to 100. But for multiples
-   of three print "Fizz" instead of the number and for the multiples of five
-   print "Buzz". For numbers which are multiples of both three and five print
-   "FizzBuzz". This is famously known as the FizzBuzz test. 
-
-#. Write a program that displays all three digit numbers that are equal to
-   the sum of the cubes of their digits. That is, print numbers :math:`$abc$`
-   that have the property :math:`$abc = a^3 + b^3 + c^3$` These are called
-   :math:`$Armstrong$` numbers.
-
-#. Collatz sequence                                              
-                                                                 
-   #. Start with an arbitrary (positive) integer.                
-   #. If the number is even, divide by 2; if the number is odd multiply by 3
-      and add 1.
-   #. Repeat the procedure with the new number.                  
-   #. There is a cycle of 4, 2, 1 at which the procedure loops.  
-                                                                 
-   Write a program that accepts the starting value and prints out the Collatz
-   sequence.
-
-#. Kaprekar's constant                                             
-                                                                   
-   #. Take a four digit number–with at least two digits different. 
-   #. Arrange the digits in ascending and descending order, giving A and D
-      respectively.
-   #. Leave leading zeros in A!                                    
-   #. Subtract A from D.                                           
-   #. With the result, repeat from step 2.                         
-                                                                   
-   Write a program to accept a 4-digit number and display the progression to
-   Kaprekar’s constant.
-
-#. Write a program that prints the following pyramid on the screen.  
-
-   ::                                                                
-                                                                     
-       1                                                             
-       2  2                                                          
-       3  3  3                                                       
-       4  4  4  4                                                    
-                                                                     
-                                                                     
-   The number of lines must be obtained from the user as input. When can your
-   code fail?
-
-#. Write a function to return the gcd of two numbers.
-
-#. Write a program to find Primitive Pythagorean Triads A pythagorean triad
-   :math:`$(a,b,c)$` has the property :math:`$a^2 + b^2 = c^2$`. By primitive
-   we mean triads that do not ‘depend’ on others. For example, (4,3,5) is a
-   variant of (3,4,5) and hence is not primitive. And (10,24,26) is easily
-   derived from (5,12,13) and should not be displayed by our program. Write a
-   program to print primitive pythagorean triads. The program should generate
-   all triads with a, b values in the range 0—100
-
-#. Write a program that generates a list of all four digit numbers that have
-   all their digits even and are perfect squares. For example, the output
-   should include 6400 but not 8100 (one digit is odd) or 4248 (not a perfect
-   square).
-
-#. The aliquot of a number is defined as: the sum of the *proper* of the
-   number. 
-
-   For example, the ``aliquot(12) = 1 + 2 + 3 + 4 + 6 = 16``. 
-
-   Write a function that returns the aliquot number of a given number.
-
-#. A pair of numbers (a, b) is said to be *amicable* if the aliquot number of
-   a is b and the aliquot number of b is a. 
-
-   Example: ``220, 284`` 
-
-   Write a program that prints all five digit amicable pairs.
-
-#. Given an empty chessboard and one Bishop placed in any square, say (r, c),
-   generate the list of all squares the Bishop could move to.
-
-
-#. Write a program to display the following pyramid. The number of lines
-   in the pyramid should not be hard-coded. It should be obtained from
-   the user. The pyramid should appear as close to the centre of the
-   screen as possible.
-
-   ::
-
-                            *
-                           ***
-                          *****
-                         *******
-               
-
-#. Write a program to display the following pyramid. The number of lines
-   in the pyramid should not be hard-coded. It should be obtained from
-   the user. The pyramid should appear as close to the centre of the
-   screen as possible.
-
-   ::
-
-                            *
-                           * *
-                          * * *
-                         * * * *
-               
-
-#. Write a program to display the following pyramid. The number of lines
-   has to be a parameter obtained from the user. The pyramid must appear
-   aligned to the left edge of the screen.
-
-   ::
-
-               1
-               2 2
-               3 3 3
-               4 4 4 4
-               
-
-#. Write a program to display the following pyramid. The number of lines
-   has to be a parameter obtained from the user. The pyramid must appear
-   aligned to the left edge of the screen.
-
-   ::
-
-                 1
-                 2   4
-                 3   6   9
-                 4   8  12  16
-                 5  10  15  20  25
-               
-
-#. Write a program to display the following output. The last number
-   where the program will stop printing has to be a parameter obtained
-   from the user. The pyramid must appear aligned to the left edge of
-   the screen. Note that depending on the last number, the base of the
-   pyramid may be smaller than the line above it.
-
-   ::
-
-                 1
-                 2   3
-                 4   5   6
-                 7   8   9  10
-                11  12  
-               
-#. Given a string like, "1, 3-7, 12, 15, 18-21", produce the list
-   ``[1,3,4,5,6,7,12,15,18,19,20,21]``
-
-#. You are given date strings of the form “29, Jul 2009”, or “4 January
-   2008”. In other words a number a string and another number, with a comma
-   sometimes separating the items.Write a function that takes such a string
-   and returns a tuple (yyyy, mm, dd) where all three elements are ints.
-
-#. Count word frequencies in a file.
-
-#. Given a dictionary of the names of students and their marks, identify how
-   many duplicate marks are there? and what are these?
-
-#. Given a string of the form "4-7, 9, 12, 15" find the numbers missing in
-   this list for a given range.
-
-
-
-.. 
-   Local Variables:
-   mode: rst
-   indent-tabs-mode: nil
-   sentence-end-double-space: nil
-   fill-column: 77
-   End:
-