Given two sets A = {x_j} and B = {y_j} of N points in R^2, there is of course the set of points {(x_j, y_j)} in R^4 that has A and B as its two projected images. Problem solved! (The earlier problem that Michael Kleber solved was whether there are 36 points in R^3 (not R^4) with suitable projections.) *This* is the possibly interesting question: ----- Given two sets A and B of N points in R^2, when is there a set X in R^3 and 2-planes P, Q in R^3 with the orthogonal projections of X onto P, Q having images congruent to A and B, respectively? More generally, replace R^2 with R^k, and R^3 with R^n for n < 2k. —Dan ----- ..... When there is an integer like 169 that belongs to two figurate numbers (H_7 = 169 = 13^2), I wonder if there is a set of 169 points in R^4 = R^2 x R^2 whose projection by p_12 onto one R^2 factor is the first figure and onto the other by p_34 is the second figure. I seem to recall asking this here some years ago for T_8 = 6^2, and that Michael Kleber showed that there's no set X of 36 points in R^4 with p_12(X) = triangle of side 8 and p_34(X) = square of side 6. Maybe there's a general statement about when such a thing can exist? -----