# 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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