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Composite Magic Number

ISC 2014 Computer Science Practical, Question 1 · Number programs

The question

A Composite Magic number is a positive integer which is composite as well as a magic number.

Composite number: A composite number is a number that has more than two factors. For example: 10, factors are: 1, 2, 5, 10

Magic number: A magic number is a number in which the eventual sum of the digits is equal to 1. For example: 28=2+8=10=1+0=1

Accept two positive integers m and n, where m is less than n as user input. Display the number of Composite Magic integers that are in the range between m and n (both inclusive) and output them along with the frequency, in the format specified below. Example 1:

Input:  m=10
        n=100
Output: THE COMPOSITE INTEGERS ARE:
        10, 28, 46, 55, 64, 82, 91, 100
FREQUENCY OF COMPOSITE MAGIC INTEGERS IS: 8

Example 2:

Input:  m=1200
        n=1300
Output: THE COMPOSITE INTEGERS ARE:
        1207, 1216, 1225, 1234, 1243, 1252, 1261, 1270, 1288
FREQUENCY OF COMPOSITE MAGIC INTEGERS IS: 9

Example 3:

Input:  m = 120
        n=99
Output: INVALID INPUT

Question: ISC 2014 Computer Science Paper 2 (Practical), Question 1, set by the Council for the Indian School Certificate Examinations (CISCE). Solution and video: Vinay Singh.

Java solution

ISC2014Q1.java Download GitHub

import java.util.*;

class CompositeMagicNumber {
    private int m, n, frequency;
    String output;

    public CompositeMagicNumber(int m, int n) {
        this.m = m;
        this.n = n;
    }

    public void process() {
        frequency = 0;
        output = "THE COMPOSITE INTEGERS ARE:\n\t";
        for (int i = m; i <= n; i++) {
            if (isMagicNumber(i) && isCompositeNumber(i)) {
                frequency++;
                output+=i+", ";
            }
        }
        output=output.substring(0,output.length()-2);
    }

    public String toString() {
        return output;
    }

    public int getFrequency() {
        return frequency;
    }

    private static boolean isPrimeNumber(int n) {
        if (n < 2)
            return false;
        else if (n == 2)
            return true;
        else if (n % 2 == 0)
            return false;
        else {
            // number is odd
            int limit = (int) Math.sqrt(n);
            for (int divisor = 3; divisor <= limit; divisor += 2) {
                if (n % divisor == 0)
                    return false;
            }
        }
        return true;
    }

    private static boolean isCompositeNumber(int n) {
        return !isPrimeNumber(n);
    }

    private static boolean isMagicNumber(int n) {
        return n % 9 == 1;
    }
}

class ISC2014Q1 {
    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        System.out.print("INPUT:\tm = ");
        int m = in.nextInt();
        System.out.print("\tn = ");
        int n = in.nextInt();
        System.out.print("OUTPUT:\t");
        if (m < n) {
            CompositeMagicNumber obj = new CompositeMagicNumber(m, n);
            obj.process();
            System.out.println(obj);
            System.out.println("FREQUENCY OF COMPOSITE MAGIC INTEGERS IS: " + obj.getFrequency());
        } else {
            System.out.println("INVALID INPUT");
        }
        in.close();
    }
}

Composite Magic Number

The question

Java solution

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