Starting in the top left corner of a 22 grid, there are 6 routes (without backtracking) to the bottom right corner.

How many routes are there through a 2020 grid?

+-%factorial
factorial(0)->1;
factorial(N)->
	lists:foldl(fun(A,B)->A*B end, 1, lists:seq(1,N)).

+-%pow
pow(_,0)->1;
pow(1,_)->1;
pow(A,B)->pow(A,B,1).
pow(_,0,Res)->Res;
pow(Mult,B,Res) when B band 1 == 1 ->
	pow(Mult*Mult,B bsr 1, Res*Mult);
pow(Mult,B,Res)->pow(Mult*Mult,B bsr 1, Res).

p15()->io:format("~w~n",[factorial(40) div pow(factorial(20),2)]).

+-#factorial
def factorial(n)
  return 1 if n<2
  (2..n).inject{|u,v|u*v}
end

def p15
  puts factorial(40)/(factorial(20)**2)
end