MathDB

9.1

Part of 2021 Kyiv City MO Round 1

Problems(1)

Birthday paradox

Source: Kyiv City MO 2021 Round 1, Problem 9.1

12/21/2023
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 1717."
Can Dmitro determine the day and month of Olena's birth?
Proposed by Olena Artemchuk and Mykola Moroz
Birthday