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Enoncé du problème

gears = [20,20,30,35,36,40,40,40,42,45,48,50,50,54,57,60,60,70,80,80]

def calculate_pitch(na, nb, nc, nd):
    p = na / nb * nc / nd * 1.5
    e = abs(p - target_pitch) / target_pitch
    return (p, e)

target_tpi = float(input("tpi : "))
target_pitch = 25.4 / target_tpi
sol = []
t = len(gears)

for a in range(t):
 r = set(range(t))
 r.remove(a)
 na = gears[a]
 for b in r:
  s = set(r)
  s.remove(b)
  nb = gears[b]
  if (na + nb) >= 75 and (na + nb) <= 160:
   for c in s:
    nc = gears[c]
    u = set(s)
    u.remove(c)
    for d in u:
     nd = gears[d]
     if (nc + nd) >= 85 and (nc + nd) <= 140:
      pitch, error = calculate_pitch(na, nb, nc, nd)
      if error <= 0.005:
       v = (na,nb,nc,nd)
       if v not in sol:
        sol.append(v)
        print("Engrenages : {}".format(v))
        print("Pas obtenu : {:.3f} mm".format(pitch))
        print("Erreur : {:.3f}%".format(error * 100))
        input()  

print("Nb solutions :", len(sol))