problem 1) Count the number of zeros in 69!.

problem 2) A magic square is the square matrix of integers such that sum of every row, the sum of every column and sum of each of the diagonal are same. Such a magic square is given below:

8 1 6
3 5 7
4 9 2

prepare a program to show a magic square.

problem 3) Find out a appropriate representation for polynomials in the single variable based on arrays. A polynomial p(x) is of the form: 5 x 3 - 10 x + 23. prepare the program that given p(x) and a point, say x = 1, determine the value of p(x) at that point. Like, the value of the polynomial 5 x 3 - 10 x + 23 at x = 1 is 18.

Given two polynomials, prepare different functions for performing polynomial arithmetic involving operations of +, - and *. Or, prepare the complete definitions of the following function prototypes:

void add ( float *p, degp, float *q, degq, float *res, degres );
void sub ( float *p, degp, float *q, degq, float *res, degres );
void mult ( float *p, degp, float *q, degq, float *res, degres );

where p, q and polynomials with degrees 'degp' and 'degq' respectively and res is resulting polynomial of degree degres that holds after the polynomial arithmetic +, -, *

problem 4) This assignment deals with creating data structure for large numbers (nonnegative). You have to read from an input file, say, "input", data of the following type:

980089673400089200098129823 # 120006734009867453400 #

23457689020#

1000000000000000000209 #

34567892 #

Note that every big number is followed by hash(#) symbol as shown above. Furthermore digits of the big number are consecutive ( you may suppose this to be always true in the input if which simplifies the design ). Neither the number of digits in a big number is known apriori nor is the number of such large numbers in the input file.

Program must read such input file and produce output file of the following form:

/* Output From Program */

Big Number 1 : 27 digits : 980089673400098200098129893

Big Number 2 : .......................................

Note that representation selected for a big number is to be a linked list each of whose node must contain certain fragments of the large number. A possible representation is outlined below but you may select a different one if you so please. A node may be defined as:

i) a short integer and a

ii) link.

Data of the first node must hold the no. of digits in the number; data of remaining nodes would store 4 consecutive digits of the large number. The internal representation for the first input number would be:

27 -> 9800 -> 8967 -> 3400 -> 982 -> 9 -> 8129 -> 893

Though, when you generate back the number, you have to account for the missing zeros in the above representation. You may select to read the input as a character array, convert to numbers as you proceed and assemble the linked list.