MathDB

With

28

points, a “triangular grid” of equal sides is formed, as shown in the figure. One operation consists of choosing three points that are the vertices of an equilateral triangle and removing these three points from the grid. If after performing several of these operations there is only one point left, in what positions can that point remain? Give all the possibilities and indicate in each case the operations carried out. Justify why the remaining point cannot be in another position. https://cdn.artofproblemsolving.com/attachments/f/c/1cedfe0e1c5086b77151538265f8e253e93d2e.gif

Problem Statement