1 \documentclass[11pt]{article}

     2 \title{Basic Python Problem Set 1}

     3 \author{Asokan Pichai}

     4 \date{}

     5 \begin{document}

     6 \maketitle

     7 \section{Pyramids}

     8 \begin{enumerate}

     9     \item Write a program to display the following pyramid. The number of lines in the pyramid should not be hard-coded.

    10         It should be obtained from the user.  The pyramid should appear as close to the centre of the screen as possible.

    11         \begin{verbatim}

    12                      *

    13                     ***

    14                    *****

    15                   *******

    16         \end{verbatim}

    17     \item Write a program to display the following pyramid. The number of lines in the pyramid should not be hard-coded.

    18         It should be obtained from the user.  The pyramid should appear as close to the centre of the screen as possible.

    19         \begin{verbatim}

    20                      *

    21                     * *

    22                    * * *

    23                   * * * *

    24         \end{verbatim}

    25     \item Write a program to display the following pyramid. The number of lines has to be a parameter obtained from the

    26         user. The pyramid must appear aligned to the left edge of the screen.

    27         \begin{verbatim}

    28         1

    29         2 2

    30         3 3 3

    31         4 4 4 4

    32         \end{verbatim}

    33     \item Write a program to display the following pyramid. The number of lines has to be a parameter obtained from the

    34         user. The pyramid must appear aligned to the left edge of the screen.

    35         \begin{verbatim}

    36           1

    37           2   4

    38           3   6   9

    39           4   8  12  16

    40           5  10  15  20  25

    41         \end{verbatim}

    42     \item Write a program to display the following output. The last number where the program will stop printing has to

    43         be a parameter obtained from the user. The pyramid must appear aligned to the left edge of the screen. Note that

    44         depending on the last number, the base of the pyramid may be smaller than the line above it.

    45         \begin{verbatim}

    46           1

    47           2   3

    48           4   5   6

    49           7   8   9  10

    50          11  12  

    51         \end{verbatim}

    52 \end{enumerate}

    53 \section{Some mathematics}

    54 \begin{enumerate}

    55     \item Write a program to calculate the gcd of two numbers.

    56     \item Write a program to generate all the Armstrong numbers: three numbers that are equal to the sum of the cubes of

    57         their digits: that is $abc = a^3 + b^3 + c^3$

    58     \item Write a program that lists all four digit numbers that are perfect squares \emph{and} have all their digits

    59         even. An example is $6400$ which is $80^2$. Note that in order to be listed a four digit number must satisfy

    60         both criteria. For example, $5625$ is a square, it does not have all digits even and

    61         $4842$ is not a square and hence they should not appear in the output. You can assume that two functions

    62         $areDigitsEven()$ and $isSquare()$ are available. (Please ask the instructor for the exact location of these

    63         functions and copy them to your area.)

    64 \end{enumerate}

    65 \section{Code}

    66 \begin{verbatim}

    67 #-------------------------------- #

    68 # Accepts an integer and returns  #

    69 # True if all digits are even     #

    70 # False otherwise                 #

    71 #-------------------------------- #

    72 def areDigitsEven( n ):

    73     while n > 0:

    74         if (n % 10) %2 != 0:

    75             return False

    76         n = n / 10

    77     return True

    78 #-------------------------------- #

    79 # Accepts an integer and returns  #

    80 # True if it is a perfect square  #

    81 # False otherwise                 #

    82 #-------------------------------- #

    83 def isSquare( n ):

    84     i = 1

    85     while i * i < n:

    86         i += 1

    87     return i * i == n

    88     

    89 \end{verbatim}

    90 \end{document}

    91