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diff --git a/gearing-up-for-destruction/matthieu/solution.py b/gearing-up-for-destruction/matthieu/solution.py
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+++ b/gearing-up-for-destruction/matthieu/solution.py
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+# coding=utf-8
+from fractions import Fraction
+
+def solution(pegs):
+    # This function is based on the formulat I figured out on paper
+    # using what I could find online about gears, I used the 
+    # (number of gears entraining one other) / (number of gears entraned by one other)
+    # Using the distances, I can express the sizes of all gears from the first one
+    # and then, using the formula, I can find x
+
+    # The developed formula shows that the signs + / - are present half of the time
+    # However, the x present in the last part changes if the number is event/pair
+    # (because of the signs, when n is pair, it adds up to the one present in the other branch
+    # of the equation, if n is impair, it removes 2x from the single x on the other branch, resulting
+    # in a negative x in the other branch
+
+    sm = 0
+    # Avoid .append by creating a sized array
+    distances = [pegs[0]] + [0] * (len(pegs) - 1)
+
+    # We calculate the points between the pegs, (except the first one)
+    for i, v in enumerate(pegs):
+        if i != 0:
+            distances[i] = pegs[i] - pegs[i - 1]
+
+    # Derived from the formula
+    for i, v in enumerate(distances[1:]):
+        sm += (-1) ** (i) * (2 * v)
+    
+    denom = 1
+
+    # If the number of pegs is pair, we divide by 3
+    if len(pegs) % 2 == 0:
+        denom = 3
+
+    # Avoid .append by creating a sized array
+    sizes = [sm / denom] + [0] * (len(pegs) - 1)
+
+    # calculate all the gear sizes
+    for i, v in enumerate(distances):
+        if v == distances[0]:
+            continue
+        
+        size = v - sizes[i - 1]
+        sizes[i] = size
+
+        # all gears must be >=
+        if size < 1:
+            return [-1, -1]
+
+    # used to simplify the fraction
+    f = Fraction(sm, denom)
+
+    # the first gear must be >= 1
+    if f < 1:
+        return [-1, -1]
+    
+    return [f.numerator, f.denominator]
+
+
+assert solution([4, 17, 50]) == [-1, -1], "invalid"
+assert solution([4, 30, 50]) == [12, 1], "invalid"