MathDB
What have the Mayas ever done for us?

Source: All-Russian MO 2024 11.3

April 22, 2024
combinatoricscombinatorics proposedgameilostthegame

Problem Statement

Yuri is looking at the great Mayan table. The table has 200200 columns and 22002^{200} rows. Yuri knows that each cell of the table depicts the sun or the moon, and any two rows are different (i.e. differ in at least one column). Each cell of the table is covered with a sheet. The wind has blown aways exactly two sheets from each row. Could it happen that now Yuri can find out for at least 1000010000 rows what is depicted in each of them (in each of the columns)? Proposed by I. Bogdanov, K. Knop