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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:
+