MathDB
2012 PUMaC Combinatorics A4 / B6

Source:

October 5, 2019
combinatorics

Problem Statement

How many (possibly empty) sets of lattice points {P1,P2,...,PM}\{P_1, P_2, ... , P_M\}, where each point Pi=(xi,yi)P_i =(x_i, y_i) for xi,yi{0,1,2,3,4,5,6}x_i , y_i \in \{0, 1, 2, 3, 4, 5, 6\}, satisfy that the slope of the line PiPjP_iP_j is positive for each 1i<jM1 \le i < j \le M ? An infinite slope, e.g. PiP_i is vertically above PjP_j , does not count as positive.