2015
05-23

# Hexagram

A Hexagram is a 6-pointed star, sometimes called the Star of David. Given these numbers:
3 17 15 18 11 22 12 23 21 7 9 13

There are four unique ways of assigning the numbers to vertices of the hexagram such that all of the sets of four numbers along the lines have the same sum (57 in this case). All other ways may be obtained from these by rotation and/or reflection.

Given 12 distinct numbers, in how many ways, disregarding rotations and reflections, can you assign the numbers to the vertices such that the sum of the numbers along each of 6 straight lines passing through 4 vertices is the same?

There will be several test cases in the input. Each test case will consist of twelve unique positive integers on a single line, with single spaces separating them. All of the numbers will be less than 1,000,000. The input will end with a line with twelve 0s.

There will be several test cases in the input. Each test case will consist of twelve unique positive integers on a single line, with single spaces separating them. All of the numbers will be less than 1,000,000. The input will end with a line with twelve 0s.

3 17 15 18 11 22 12 23 21 7 9 13
1 2 3 4 5 6 7 8 9 10 11 13
0 0 0 0 0 0 0 0 0 0 0 0

4
0

//============================================================================
// Name        : B.cpp
// Author      :
// Version     :
// Description : Hello World in C++, Ansi-style
//============================================================================

#include <iostream>
#include<stdio.h>
#include<algorithm>
using namespace std;
int a[13], p[13];
int sum, i, ans;
bool use[13];
void dfs(int k) {
int i;
if (k == 12) {
ans++;

return;
}
//for (i = 0; i < 12; i++)
//	printf("%d ", p[i]);
//printf("\n");
for (i = 0; i < 12; i++) {
if (i > 0 && !use[i - 1] && p[k - 1] == a[i])
continue;
if (!use[i]) {
p[k] = a[i];
if (k == 3) {
if (p[0] + p[1] + p[2] + p[3] != sum) {
//	use[i] = 0;
continue;
}
}
if (k == 6) {
if (p[3] + p[4] + p[5] + p[6] != sum) {
//	use[i] = 0;
continue;
}
}

if (k == 8) {
if (p[0] + p[8] + p[7] + p[6] != sum) {
//	use[i] = 0;
continue;
}
}
//			if (k == 9) {
//				if (p[0] + p[8] + p[7] + p[6] != sum) {
//					//	use[i] = 0;
//					return;
//				}
//			}
if (k == 10) {
if (p[10] + p[1] + p[8] + p[9] != sum) {
//	use[i] = 0;
continue;
}
}
if (k == 11) {
if (p[10] + p[2] + p[4] + p[11] != sum) {
//	use[i] = 0;
continue;
}
if (p[9] + p[7] + p[5] + p[11] != sum) {
//use[i] = 0;
continue;
}
}
use[i] = 1;
dfs(k + 1);
use[i] = 0;
}
}
}
int main() {
while (1) {
sum = 0;
for (i = 0; i < 12; i++) {
scanf("%d", &a[i]);
sum += a[i];
}
sort(a, a + 12);
//	printf("%d\n", sum);
if (!sum)
break;
if (sum % 3) {
printf("0\n");
continue;
}
ans = 0;
sum /= 3;
dfs(0);
printf("%d\n", ans / 12);
}
return 0;
}
/*
3 17 15 18 11 22 12 23 21 7 9 13
1 2 3 4 5 6 7 8 9 10 11 13
1 1 1 1 1 1 1 1 1 1 1 1
0 0 0 0 0 0 0 0 0 0 0 0
*/