MathDB
5 questions, each options each , 2000 candidates

Source: Mathcenter Contest / Oly - Thai Forum 2008 R3 p10 https://artofproblemsolving.com/community/c3196914_mathcenter_contest

November 9, 2022
combinatoricsthis problem is a nightmare

Problem Statement

One test is a multiple choice test with 55 questions, each with 44 options, 20002000 candidates, each choosing only one answer for each item.Find the smallest possible integer nn that gives a student's answer sheet the following properties: In the student's answer sheet nn, there are four sheets in it. Any two of the four tiles have exactly the same three answers.
(tatari/nightmare)