MathDB

normal counting problem in KJMO 2022

Source: KJMO 2022 number 2

January 19, 2023

combinatoricscounting

Problem Statement

For positive integer

n

(≥

3

), find the number of ordered pairs

(a_1, a_2, ... , a_n)

of integers that satisfy the following two conditions
1. For positive integer

i

such that

1

≤

i

≤

n

then

1

≤

a_i

≤

i

2. For positive integers

i,j,k

such that

1

≤

i

<

j

<

k

≤

n

, if

a_i = a_j

then

a_j

≥

a_k

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