Discussion: This is a simplification of a Putnam problem from several years ago. The student solves it making use of the pigeonhole principle. It is observed that if the parity of two points is the same, ie in every place they are identical then the midpoint of the line segment joining the points is also a lattice point. Since there are four possible configurations and five points two have the same parity.

Written response: Now that we have introduced the notion of equivalence relation try to show that the relation between two lattice points in R^n given by (x_1,x_2,...,x_n) equivalent to (y_1,y_2,...,y_n) if and only if all the differences x_i - y_i are even, is an equivalence relation.

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