MathDB

Kawaii Permutations

Source: Bangladesh Mathematical Olympiad 2020 Problem 8

February 19, 2022

combinatorics

Problem Statement

We call a permutation of the numbers

1

2

3

\dots

n

'kawaii' if there is exactly one number that is greater than its position. For example:

1

4

3

2

is a kawaii permutation (when

n=4

) because only the number

4

is greater than its position

2

. How many kawaii permutations are there if

n=14