A3

Part of 2023 Simon Marais Mathematical Competition

Problems(1)

Minimum number of values in the union of sets

Source: Simon Marais Mathematics Competition 2023 Paper A Problem 3

For each positive integer

n

f(n)

denote the smallest possible value of

|A_1 \cup A_2 \cup \dots \cup A_n|

A_1, A_2, A_3 \dots A_n

are sets such that

A_i \not\subseteq A_j

|A_i| \neq |A_j|

i \neq j

f(n)

for each positive integer

n