22 lines
622 B
Python
22 lines
622 B
Python
from math import factorial
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def get_number_of_routes(n):
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"""
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There are n down and n right moves which means 2 * n moves
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in total. All permutations are calculated with (2n)!. Next redundant
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moves have to be canceled out. The combinations for only down moves
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or only right moves would (if they were different symbols) be n!.
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Hence, the denominator is (n!)^2.
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"""
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return factorial(2 * n) // (factorial(n) * factorial(n))
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def euler_015():
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return get_number_of_routes(20)
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assert(get_number_of_routes(2) == 6)
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assert(euler_015() == 137846528820)
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print("e015.py: {}".format(euler_015()))
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