2011 UNCO Math Contest II Problems/Problem 6

Problem

What is the remainder when $1! + 2! + 3! + \cdots + 2011!$ is divided by $18$ ?

Solution

Since all the terms past $5!$ are divisible by $18$ , it is only necessary to look at the remainder resulted from the first 5 terms. $1!+2!+3!+4!+5!=153\equiv 9\pmod{18}$

2011 UNCO Math Contest II (Problems • Answer Key • Resources)
Preceded by Problem 5	Followed by Problem 7
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All UNCO Math Contest Problems and Solutions

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2011 UNCO Math Contest II Problems/Problem 6

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