MathDB

2016 LMT Individual #16

Source:

April 10, 2016

Problem Statement

Let

N

be the number of functions

f:\{1,2,3,4,5,6,7,8,9,10\} \rightarrow \{1,2,3,4,5\}

that have the property that for

1\leq x\leq 5

it is true that

f(f(x))=x

. Given that

N

can be written in the form

5^a\cdot b

for positive integers

a

and

b

with

b

not divisible by

5

, find

a+b

.
Proposed by Nathan Ramesh

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