Optimize day 24 part two with sympy reducing to smaller system.

adventofcode/2023/day/24/never_tell_me_the_odds_part_two.py

@@ -16,16 +16,21 @@ def __init__(self, x0, y0, z0, vx, vy, vz):
     vx, vy, vz = [int(x) for x in tail.strip().split(', ')]
     hailstones.append(Hailstone(x0, y0, z0, vx, vy, vz))
 
-n = len(hailstones)
+symbols_str = 'x y z vx vy vz'
+num_symbols = len(symbols_str.split())
 eqs = []
-for i in range(n):
-    h = hailstones[i]
-    x, y, z, vx, vy, vz = sympy.symbols('x y z vx vy vz')
-    eqs.append((h.vy - vy)*(x - h.x0) - (h.vx - vx)*(y - h.y0))
-    eqs.append((h.vz - vz)*(y - h.y0) - (h.vy - vy)*(z - h.z0))
+i = -1
+for n in range(3, len(hailstones)):
+    for i in range(i + 1, n):
+        h = hailstones[i]
+        x, y, z, vx, vy, vz = sympy.symbols(symbols_str)
+        eqs.append((h.vy - vy)*(x - h.x0) - (h.vx - vx)*(y - h.y0))
+        eqs.append((h.vz - vz)*(y - h.y0) - (h.vy - vy)*(z - h.z0))
+    i = n - 1
+    solution = sympy.solve(eqs)
+    if len(solution) == 1 and len(solution[0].keys()) == num_symbols:
+        break
 
-solution = sympy.solve(eqs)
-
-assert(len(solution) == 1)
+print(solution)
 solution = solution[0]
 print('Part Two:', solution[x] + solution[y] + solution[z])