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diff --git a/2.1.py b/2.1.py
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+#!/usr/bin/pytnon2
+
+## You are given a list of "pegs" with their location (positive integers, asc order).
+## these pegs can accept gears with radius > 1
+## the goal is the last gear to be spinning twice as fast as the 1st one for any given list
+## if it's possible return the first gear's radius in a list [a,b] where the ratio is a/b
+## if not return [-1,-1]
+
+from fractions import gcd
+from functools import reduce
+
+# test
+from random import seed
+from random import random
+
+def simplify(ratio_nums):
+    return list(map(reduce(gcd, ratio_nums).__rfloordiv__, ratio_nums))
+
+def solution(pegs):
+    if len(pegs) == 2:
+        r1_by_three = 2 * (pegs[1] - pegs[0])
+        nums = [r1_by_three, 3]
+        return simplify(nums)
+    S = pegs[-1] - pegs[0]
+    if len(pegs) % 2 == 0:
+        C = 0
+        for i in range (1, len(pegs) - 1):
+            C += (-1)**i * pegs[i]
+        r1_by_three = 2 * S - 4 * C
+
+        r = [r1_by_three/3]
+        for i in range(len(pegs) -1):
+          r.append(pegs[i+1]-pegs[i]-r[i])
+          if r[-1] < 1:
+            return [-1, -1]
+        if (r[0]) < 1 or (r[0]) > pegs[1]-pegs[0]-1:
+            return [-1, -1]
+        return simplify([r1_by_three, 3])
+    else:
+        K = 0
+        for i in range (1, len(pegs) - 2):
+            K += (-1)**i * pegs[i]
+        r1 = 2*S - 4*K - 4*pegs[-1] + 4*pegs[-2]
+        if r1 < 1:
+            return [-1, -1] 
+        return [r1, 1]
+
+seed(1)
+
+def ran():
+  return int(random() * 1000)
+
+for i in range(1,1000):
+  a=[ran(),ran(),ran(),ran(),ran(),ran()]
+  a.sort()
+  print(a)
+  print(solution(a))
+  print("")