Problem

Source: 46th International Tournament of Towns, Senior A-Level P7, Fall 2024

Tags: combinatorics



Several napkins of equal size and of shape of a unit disc were placed on a table (with overlappings). Is it always possible to hammer several point-sized nails so that all the napkins will be thus attached to the table with the same number of nails? (The nails cannot be hammered into the borders of the discs). Vladimir Dolnikov, Pavel Kozhevnikov