IMSO 2008 Mathematics – Taiwan Selection – Exploration Question 2

The diagram shows a 3 × 3 × 3 frame with 27 holes in which marbles can be placed. A–B–C, L–M–N and X–Y–Z are some possible lines of three marbles.



(a) From A, how many different lines of three marbles are possible? (3 points)

(b) What is the total number of different possible lines of three marbles in this frame? (5 points)