To place 3 non-consecutive positions: let the positions be $ x_1 < x_2 < x_3 $, with $ x_i+1 \ge x_i + 2 $. Let $ y_i = x_i - (i-1) $, then $ y_1 < y_2 < y_3 $ in $ \1,\dots,6\ $. So number is $ \binom63 = 20 $. - Groen Casting