Birthday paradox
Source: Kyiv City MO 2021 Round 1, Problem 9.1
December 21, 2023
Birthday
Problem Statement
Before the math competition, Dmytro overheard Olena and Mykola talking about their birthdays.О: "The day and month of my birthday are half as large as the day and month of Mykola's birthday."
М: "Also, the day of Olena's birth and the month of my birth are consecutive positive integers."
О: "And the sum of all these four numbers is a multiple of ."Can Dmitro determine the day and month of Olena's birth?Proposed by Olena Artemchuk and Mykola Moroz