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find_k4_solution.py

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+import itertools
+
+def verify(m, k, r, p0, p1):
+    def get_p(x):
+        s = sum(x) % m
+        return p0 if s == 0 else p1
+
+    all_edges = set()
+    for color in range(k):
+        visited_set = set()
+        curr = tuple([0]*k)
+        edges = set()
+        for _ in range(m**k):
+            if curr in visited_set: return False
+            visited_set.add(curr)
+            p = get_p(curr)
+            dim = p[color]
+            edges.add((curr, dim))
+            nx = list(curr)
+            nx[dim] = (nx[dim] + r[dim]) % m
+            curr = tuple(nx)
+        if curr != (0,0,0,0): return False
+        if len(visited_set) != m**k: return False
+        if all_edges.intersection(edges): return False
+        all_edges.update(edges)
+    return True
+
+perms = list(itertools.permutations(range(4)))
+r = [1, 1, 1, 1]
+# Limit search
+for p0 in perms[:5]:
+    for p1 in perms:
+        if verify(2, 4, r, p0, p1):
+            print(f"Found solution: p0={p0}, p1={p1}")
+            import sys
+            sys.exit(0)