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Project Euler - problem 030

August 1st, 2007 by Daniel

Surprisingly there are only three numbers that can be written as the sum of fourth powers of their digits:

1634 = 14 + 64 + 34 + 44
8208 = 84 + 24 + 04 + 84
9474 = 94 + 44 + 74 + 44

As 1 = 14 is not a sum it is not included.

The sum of these numbers is 1634 + 8208 + 9474 = 19316.

Find the sum of all the numbers that can be written as the sum of fifth powers of their digits.

1
2
3
4
5
6
7
8
9
10
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14
15
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21
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27
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34
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44
45
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70

 
#include <iostream>
using namespace std;
 
#define ANT 7
#define opp 5
 
int opphoyd(int num1, int num2){
int res =1;
for(int i = 0 ; i < num2; i++){
res *= num1;
}
return res;
}
 
bool number (int arg[], int length) {
int num1 = 0;
for (int n=0; n<length; n++){
num1 += opphoyd(10, length-n-1) * arg[n];
}
 
int num2= 0;
for (int n=0; n<length; n++){
num2 += opphoyd(arg[n], opp);
}
 
return num1 == num2;
 
}
 
int main ()
{
int res = 0;
int temp= 0;
int tab[ANT];
int pos = (ANT-1);
 
while(true){
 
tab[pos]++;
 
while(tab[pos]>9){
tab[pos]=0;
pos--;
tab[pos]++;
}
 
if(pos < 0){
break;
}
 
if(number(tab, ANT)){
temp = 0;
for (int n=0; n<ANT; n++){
temp += opphoyd(tab[n], opp);
}
res += temp;
}
pos= ANT - 1;
 
//   cout << res ;
//   cout << " n";
 
}
 
res --;
cout << res ;
cout << " n";
return 0;
}

2 Responses to “Project Euler - problem 030”

  1. Harsh

    What’s weird in this question is that no upper limit has been mentioned? Or does this kinda narcissity not occur over a billion digits at all?

    Dec 11th, 2007    3:55 pm   
  2. Daniel

    Harsh: This occur not over 6 digits, but you need to prove that mathematical or test it.

    Dec 11th, 2007    5:57 pm   

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