#Playing with numbers-2

Computer Science Level 3

A positive integer has a property Y Y if the sum of the squares of its digits is coprime with the number. The probability that a number not more than 2 × 1 0 6 2\times10^6 will have that property is x % x\% . Enter x x .

Here is #Playing with numbers-1


The answer is 62.16125.

Rafsan Rcc by Rafsan Rcc , 17, Bangladesh

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2 solutions

Fletcher Mattox
May 10, 2021

The correct answer is 62.01115, not what the author of the problem specified. 

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from math import gcd

count = 0
for n in range(1, 2*10**6 + 1):
    count += gcd(n, sum(list(map(lambda i:i**2, list(map(int,list(str(n)))))))) == 1
print(count/(2*10**6) * 100)


1
 
62.01115

1 Helpful 0 Interesting 0 Brilliant 0 Confused

Even I got the same number!

Kunal Gupta - 3 weeks, 6 days ago

His answer is wrong. But it's close enough to the correct answer that Brilliant rounding conveniently honors the correct answer as well.

Fletcher Mattox - 3 weeks, 6 days ago
Rafsan Rcc
May 9, 2021

Here are the codes that I used. 

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#include<stdio.h>
#include<math.h>

unsigned long int coprime(unsigned long int x,unsigned long int y);
unsigned long int sum(unsigned long int x);

int main()
{ unsigned long int result,i;
  result=0;
  for(i=1;i<=2000000;i++)
  {result+=sum(i);}
  printf("\nTotal : %lu",result);
}

//coprime(x,y) returns 1 if x and y are coprime,otherwise 0
unsigned long int coprime(unsigned long int x,unsigned long int y)
{int i;
 int result=1;
 for(i=2;i<=x;i++)
 {if(x%i==0 && y%i==0) {result=0;break;};}
 return result;}

 //sum finds the sum of the squares of the digits of x and returns 1 if that sum is coprime with x,otherwise returns 0
unsigned long int sum(unsigned long int x)
{ unsigned long int s,n,i;
    s=0;
    n=x;
    for(i=0;i<=log(x);i++)
    {s+=pow(n%10,2);
    n-=n%10;
    n/=10;}
    if (coprime(s,x)==1) return 1;
    else return 0;
}


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#coprime(x,y) returns 1 if x and y are coprime,otherwise 0
def coprime(x,y):
    r=1
    for i in range(2,x+1):
        if(x%i==0 and y%i==0) :
            r=0
            break
    return r

#sum finds the sum of the squares of the digits of x and returns 1 if that sum is coprime with x,otherwise returns 0
def sum(x):
    result=0
    for i in str(x):
        result+=int(i)**2
    if coprime(result,x)==1 : return 1
    else : return 0

a=0
for i in range(1,2000001):
    a+=sum(i)
print("\nTotal : ",a)

1 Helpful 1 Interesting 1 Brilliant 1 Confused

@Rafsan Rcc I think your coprime function is broken. For example, it claims 2 and 4 are coprime. 

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def coprime(x,y):
    r=1
    for i in range(2,x//2+1):
        if(x%i==0 and y%i==0) :
            r=0
            break
    return r

print(coprime(2, 4))


1
 
1

Fletcher Mattox - 1 month ago

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