Prom numbers

Computer Science Level 3

A $b$ -prom number is a positive integer which is the concatenation of the product of its digits and the sum of its digits in base $b$ . For example, $3612$ is a 10-prom number, since the product of its digits is $36$ and the sum of its digits is $12$ , and $3612$ is the concatenation of $36$ and $12$ . Note that $1236$ is not a 10-prom number; the concatenation must be the product before the sum. Also note that $01$ is not a 10-prom number; prom numbers may not begin with $0$ .

What is the only 3-digit 10-prom number?

The answer is 911.

3 solutions

Bill Bell
Aug 2, 2015

def is10Prom(n):
    return str(n)==str(reduce(lambda a,b: a*b,map(int,list(str(n))),1))+str(sum(map(int,list(str(n)))))

for n in range(100,1000):
    if is10Prom(n):
        print n

Ankush Tiwari
Apr 8, 2014

In java:

public class prom

{

void main()

{

    for(int i=100;i<=999;i++)

    {

        int a=i;

        int p=1; int s=0;

        while(a>0)

        {

            int d=a%10;

            p*=d;

            s+=d;

            a/=10;

        }

        String x= ""+p+s;

        String y = ""+i;

        if(x.equalsIgnoreCase(y))

        System.out.println(i);

    }

}

}

Pebrudal Zanu
Jan 14, 2014

Suppose the number are $a,b,c$

Case I, If $a \times b\times c$ two digit and $a+b+c$ only one digit.

    for a in range (1,10):

for b in range (1,10):

    for c in range (1,10):

        d=a*b*c

        e=a+b+c

        if 10*d+e==100*a+10*b+c and e<10:

            print a,b,c

There is no result.

Case II. If $a \times b\times c$ only one digit and $a+b+c$ two digit.

    for a in range (1,10):

for b in range (1,10):

    for c in range (1,10):

        d=a*b*c

        e=a+b+c

        if 100*d+e==100*a+10*b+c and d<10:

            print a,b,c

The result is 9 1 1

So the answer $\fbox{911}$

Prom numbers

The answer is 911.

3 solutions

0 pending reports