MathDB
2003 integers from 1 to 2003 on blackboard

Source: Argentina 2003 OMA L3 p2

May 12, 2024
combinatoricsnumber theoryalgebra

Problem Statement

On the blackboard are written the 20032003 integers from 11 to 20032003. Lucas must delete 9090 numbers. Next, Mauro must choose 3737 from the numbers that remain written. If the 3737 numbers Mauro chooses form an arithmetic progression, Mauro wins. If not, Lucas wins. Decide if Lucas can choose the 9090 numbers he erases so that victory is assured.