#Playing with numbers-4.

Computer Science Level 3

A number is said to have a property Z b Z_b if that number is divisible by the number of segments needed to display the number in a 7-segment display after converting the number in base b. For example : ( 57 ) 10 = ( 2010 ) 3 (57)_{10}=(2010)_3 and 2010 needs 19 segments to be displayed so 57 has the property Z 3 Z_3 . If the lowest 5-digit numbers having properties Z 3 Z_3 and Z 9 Z_9 are respectively x 3 x_3 and x 9 x_9 , enter x 9 − x 3 x_9-x_3 .

For the previous problem : #Playing with numbers-3


The answer is 2.

Rafsan Rcc by Rafsan Rcc , 17, Bangladesh

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2 solutions

Rafsan Rcc
May 10, 2021 
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#include<stdio.h>
#include<math.h>

unsigned long int convert(unsigned long int number,int base);
unsigned long int segment(unsigned long int number);

int main()
{
    unsigned long int i;
    i=10000;
    do
    {i+=1;
    }while(i%segment(convert(i,3))!=0);
    printf("x3=%lu\n",i);
    i=10000;
    do
    {i+=1;
    }while(i%segment(convert(i,9))!=0);
    printf("x9=%lu",i);
 }
//segment returns the number of segments to display number
unsigned long int segment(unsigned long int number)
{   unsigned long int result,n;
    int s[10]={6,2,5,5,4,5,6,4,7,6};
    n=number;
    do
    {result+=s[n%10];
     n-=n%10;
     n/=10;
    }while(n>0);
    return result;
}

unsigned long int convert(unsigned long int number,int base)
{
    unsigned long int n,result;
    int i;
    i=0;
    n=number;
    result=0;
    do{result+=(n%base)*pow(10,i);
    n-=(n%base);
    n/=base;
    i+=1;}
    while(n>0);
    return result;
}


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def segment(x):
    seg=[6,2,5,5,4,5,6,4,7,6]
    result=0
    for i in x:
        result+=seg[int(i)]
    return result

def convert(number,base):
    result=[]
    n=number
    while n>0:
        result.append(n%base)
        n//=base
    result.reverse()
    r=""
    for i in result:
        r+=str(i)
    return r

i=10000
while i%segment(convert(i,3))!=0:
    i+=1
print("x3=",i)
i=10000
while i%segment(convert(i,9))!=0:
    i+=1
print("x9=",i)

0 Helpful 1 Interesting 0 Brilliant 0 Confused
Kunal Gupta
May 16, 2021 
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def get_segments(x):
    arr = [6, 2, 5, 5, 4, 5, 6, 4, 7, 6]
    return arr[x]

def convert_to_base_b_and_return_sum(x, b):
    ans = 0
    while x!=0:
        ans+=get_segments(x%b)
        x = x//b
    return ans

def getzb(b):
    x = 10000
    while True:
        if(x%convert_to_base_b_and_return_sum(x, b)==0):
            return x
        x+=1

print (getzb(9)-getzb(3))

0 Helpful 0 Interesting 0 Brilliant 0 Confused

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