five_digits_numbers_divisible_by_12.c

/*

    five_digits_numbers_divisible_by_12.c

    Task:
    How many 5-digit numbers can be formed by using digits 0,1,2,3,4,5
    (without repetition) that are divisible by 12?

A number is divisible by 12 if the number formed by the last two digits in the number
is divisible by 4 AND the sum of the digits in the number is divisible by 3.

For example, for 123,456 the last two digits (56) is divisible by 4, AND
1 + 2 + 3 + 4 + 5 + 6 = 21. 21 is divisible by 3.
Thus, 123,456 is divisible by 12.

However, 123,458 is not divisible by 12 for two reasons:
The last two digits (58) is not divisible by 4 and
1 + 2 + 3 + 4 + 5 + 8 = 23 and 23 is not divisible by 3.

Remember, both conditions must be met for the number to be divisible by 12.

https://divisible.info/Divi.../Divisibility-rule-for-12.html


Divisibility rule for 3

If the sum of the digits of a number is divisible by 3,
then the number is divisible by 3.


Divisibility rule for 4

If the number formed by the last two digits in a number is divisible by 4,
or if the last two digits are 00,
the original number is divisible by 4.


    You can find all my C programs at Dragan Milicev's pastebin:

    https://pastebin.com/u/dmilicev

*/

#include <stdio.h>

// returns 1 if all elements are distinct (unique, different from each other)
// otherwise returns 0
int all_array_elements_are_distinct( int arr[], int size )
{
    int i, j;

    for (i=0; i<size; i++)
        for (j=i+1; j<size; j++)
            if (arr[i] == arr[j])
                return 0;

    return 1;
}

// If the sum of the digits of a number is divisible by 3, returns 1,
// otherwise returns 0
int is_divisible_by_3( int d1, int d2, int d3, int d4, int d5 )
{
    if( (d1 + d2 + d3 + d4 + d5) % 3 == 0 )
        return 1;

    return 0;
}

// If the number formed by the last two digits is divisible by 4
// or the last two digits are 00, returns 1,
// otherwise returns 0
int is_divisible_by_4(int d4, int d5)
{
    int n = d4*10 + d5;

    if( n%4==0 || (d4==0 && d5==0) )
        return 1;

    return 0;
}


int main(void)
{
    int d1, d2, d3, d4, d5, counter=0;
    int arr_num[5];

    for(d1=1; d1<6; d1++)
        for(d2=0; d2<6; d2++)
            for(d3=0; d3<6; d3++)
                for(d4=0; d4<6; d4++)
                    for(d5=0; d5<6; d5++)
                    {
                        arr_num[0] = d1;
                        arr_num[1] = d2;
                        arr_num[2] = d3;
                        arr_num[3] = d4;
                        arr_num[4] = d5;

                        // if all 5 digits are different from each other
                        if( all_array_elements_are_distinct(arr_num, 5) )
                            if( is_divisible_by_3(d1,d2,d3,d4,d5) )
                                if( is_divisible_by_4(d4,d5) )
                                {
                                    counter++;
                                    printf(" %d %d %d %d %d \n", d1, d2, d3, d4, d5);
                                }
                    }

    printf("\n The computer says that there are %d such numbers that are divisible by 12. \n", counter);


    return 0;

} // main()