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Problem 7 of Second round - "multicolored" figures

Source: VI International Festival of Young Mathematicians Sozopol, Theme for 10-12 grade

December 19, 2019
combinatoricstableChessboardColoring

Problem Statement

A corner with arm nn is a figure made of 2n−12n-1 unit squares, such that 2 rectangles 11 x (n−1)(n-1) are connected to two adjacent sides of a square 11 x 11, so that their unit sides coincide. The squares or a chessboard 100100 x 100100 are colored in 15 colors. We say that a corner with arm 8 is “multicolored”, if it contains each of the colors on the board. What’s the greatest number of corners with arm 8 which could be “mutlticolored”?
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