Problem

Source: Tournament of Towns, Junior A-Level , Fall 2019 p7

Tags: grid, Coloring, combinatorics



Peter has a wooden square stamp divided into a grid. He coated some 102 cells of this grid with black ink. After that, he pressed this stamp 100 times on a list of paper so that each time just those 102 cells left a black imprint on the paper. Is it possible that after his actions the imprint on the list is a square 101×101 such that all the cells except one corner cell are black? (Alexsandr Gribalko)