# Impossible Sum

Number Theory Level pending

N= $$(2014!)^{1}$$ + $$(2013!)^{2}$$ + $$(2012!)^{3}$$ + ................. + $$(1!)^{2014}$$
Let,
$$x_{1}$$ = Sum of digits of N
$$x_{2}$$ = Sum of digits of $$x_{1}$$
$$x_{3}$$ = Sum of digits of $$x_{2}$$
. .
. .
. .
$$x_{n}$$ = Sum of digits of $$x_{n-1}$$ ,such that $$x_{n}$$ < 10 & $$x_{n-1}$$ >= 10

Find $$x_{n}$$ .

Example :-
if N = 2345678
$$x_{1}$$ = 2+3+4+5+6+7+8 = 35
$$x_{2}$$ = 3+5 =8 <10
Thus, Answer is 8 in this case.

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