# Project Euler/16

Project Euler Problem 16 is a problem related to the powers of 2. The task is to find out the "digit sum" (sum of all digits in decimal expansion) of 21000.

## Implementations

### Aheui

This pattern works on both AheuiChem[citation needed] and Try It Online. It uses the "decimal multiplication calculator" algorithm which theoretically works for an arbitrarily large number multiplied by a non-zero digit. It also contains some weird parts, for example, a path branches into two and then the two branches joins up immediately, or paths that branches immediately back to itself.

```밣발발발따따따밣밣발따따뿌터너벌
ㅇㅇㅇㅇㅇㅇㅇ쑥너벌벌머차바싹볼
ㅇㅇㅇㅇㅇㅇㅇ뿌터너벌벌서
ㅇㅇㅇ아더뭉셕차숙머어ㅇ오쎤너더벊벌아셕어
ㅇㅇㅇㅇㅇ희무선빠박따빠발발다라싼샨오더오
ㅇㅇㅇㅇ먀썩뻐ㅇㅇㅇㅇㅇ요```

### C

```#include <stdio.h>
int a={1},k,l,r;

void flow(int d[]){
int i;
for(i=0;i<319;++i){
d[i+1]+=d[i]/10;
d[i]%=10;
}
}
int main(){
for(k=1;k<=1000;++k){
for(l=0;l<320;++l){
a[l]*=2;
}
flow(a);
}
for(l=0;l<320;++l){
r+=a[l];
}
printf("%d",r);
return 0;
}```

### Gofe

`/1000/&t/10/&q/2/Pt[&sQq>At<#sGqF]>#t.`

The language has no interpreter to test whether this program is correct so if you found it incorrect please revise it.

### I fuck, you fuck

```There's a fucker named a
Fuck a 2000 times
There's a fucker named b
Fuck b 2 times
b fucks a over and over
b unfucks b
There's a fucker named c
while a is fucked
c unfucks c
Fuck c 10 times
a unfucks c over and over
c fucks b
c unfucks c
Fuck c 10 times
a unfucks c again
a unfucks a
c fucks a
end fuck
b fucks you
```

### Python

```#Euler Problem 16
#by Europe2048

def sumdigits(n):
sum = 0
for i in str(n):
sum = sum + int(i)
return sum
print(sumdigits(2**1000))```

Alternate implementation (shorter), by None1:

```print(sum(map(int,str(2**1000))))
```

## External resources

• A001370, a related sequence on OEIS. The 1001st term is the solution.
• Problem 16 on Project Euler Official Website (not available)
• Problem 16 on Project Euler Mirror