several identical napkins on a table, hammering nails
Source: TOT 563 1997 Autumn S A4
September 11, 2024
geometrycombinatorial geometrycombinatoricsRegular
Problem Statement
(a) Several identical napkins, each in the shape of a regular hexagon, are put on a table (the napkins may overlap). Each napkin has one side which is parallel to a fixed line. Is it always possible to hammer a few nails into the table so that each napkin is nailed with exactly one nail? (b) The same question for regular pentagons.(A Kanel)