lattice points game in 3D, n consecutive points on a line // to axes wanted
Source: Ukraine TST 2018 p3
April 29, 2020
combinatoricslattice pointscombinatorial geometrycollineargamegame strategy
Problem Statement
Consider the set of all integer points in . Sasha and Masha play such a game. At first, Masha marks an arbitrary point. After that, Sasha marks all the points on some a plane perpendicular to one of the coordinate axes and at no point, which Masha noted. Next, they continue to take turns (Masha can't to select previously marked points, Sasha cannot choose the planes on which there are points said Masha). Masha wants to mark consecutive points on some line that parallel to one of the coordinate axes, and Sasha seeks to interfere with it. Find all , in which Masha can achieve the desired result.