Problem 68: Magic 5-gon Ring

eu068.c

@@ -0,0 +1,52 @@
+#include "euler.h"
+
+static int nodeorder[][3] = {
+  { 0, 5, 6 }, { 1, 6, 7}, { 2, 7, 8}, { 3, 8, 9 }, { 4, 9, 5}
+};
+
+#define VAL(k) ((k) == '0' ? 10 : (k) - '0')
+
+static int samesum(const char *a) {
+  int s1 = VAL(a[0]) + VAL(a[5]) + VAL(a[6]);
+  if (VAL(a[1]) + VAL(a[6]) + VAL(a[7]) != s1) return 0;
+  if (VAL(a[2]) + VAL(a[7]) + VAL(a[8]) != s1) return 0;
+  if (VAL(a[3]) + VAL(a[8]) + VAL(a[9]) != s1) return 0;
+  if (VAL(a[4]) + VAL(a[9]) + VAL(a[5]) != s1) return 0;
+  return 1;
+}
+
+void eu068(char *ans) {
+  // Encoding 10 as 0 so we can do string permutations with nextperm()
+  char *nval = "9876543210";
+  char nodes[11];
+  char buf[20];
+  ans[0] = 0;
+
+  strcpy(nodes, nval);
+
+  do {
+    // For a 16 digit sum, 10 must be in the outer 5 nodes.
+    if (index(nodes, '0') >= nodes + 5) continue;
+    if (!samesum(nodes)) continue;
+
+    int min = VAL(nodes[0]), mindex = 0;
+    for (int i = 1; i < 5; i++) {
+      if (VAL(nodes[i]) < min) {
+        min = VAL(nodes[i]);
+        mindex = i;
+      }
+    }
+
+    buf[0] = 0;
+    int pos = 0;
+    for (int i = 0; i < 5; i++) {
+      for (int j = 0; j < 3; j++) {
+        pos += sprintf(&buf[pos], "%d", VAL(nodes[nodeorder[(i+mindex) % 5][j]]));
+      }
+    }
+    if (strcmp(ans, buf) < 0) {
+      printf("%s\n", buf);
+      strcpy(ans, buf);
+    }
+  } while (prevperm(nodes));
+}

euler.c

@@ -252,6 +252,7 @@ struct puzzle puzzles[] = {
   { "065", &eu065, "272" },
   { "066", &eu066, "661" },
   { "067", &eu067, "7273" },
+  { "068", &eu068, "6531031914842725" },
 };
 
 #define NPUZZLES (sizeof puzzles / sizeof(puzzles[0]))