at least 11 new mistakes were made - VI Soros Olympiad 1999-00 Round 1 9.10
Source:
May 21, 2024
combinatorics
Problem Statement
The schoolboy wrote a homework essay on the topic “How I spent my summer.” Two of his comrades from a neighboring school decided not to bother themselves with work and rewrote his essay. But while rewriting they made several mistakes - each their own. Before submitting their work, both students gave their essays to four other friends to rewrite (each gave them to two acquaintances). These four schoolchildren do the same, and so on. With each rewrite, all previous mistakes are saved and, possibly, new ones are made. It is known that on some day each new essay contained at least errors. Prove that there was a day when at least new mistakes were made in total.