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no of tidy 3n-tables

Source: Norwegian Mathematical Olympiad 2021 - Abel Competition p1a

May 29, 2021
combinatoricsnumbers in a tabletable

Problem Statement

A 3n3n-table is a table with three rows and nn columns containing all the numbers 1,2,,3n1, 2, …, 3n. Such a table is called tidy if the nn numbers in the first row appear in ascending order from left to right, and the three numbers in each column appear in ascending order from top to bottom. How many tidy 3n3n-tables exist?