Exactly six different essays will appear in a coming issue of a magazine. Three of the essays- G, I, and Jare by the writer K, and the other three essays-M, N, and P-are by the writer Y. Each essay will appear exactly once in the issue, and an essay must appear on each of the pages 3, 6, 9, 12, 15, and 18. The order in which the essays appear in the issue will be governed by the following conditions: The essays on pages 3, 9, and 15 must all be by the same writer. I must precede P. M must precede J. If N appears on page 6, which of the following essays must appear on page 12?

Explanation: The six pages are 3, 6, 9, 12, 15, 18. Essays by K: G, I, J. Essays by Y: M, N, P. Rules: (1) Pages 3, 9, 15 have the same writer. (2) I < P (I precedes P). (3) M < J (M precedes J). Given: N is on page 6. N is by writer Y. Case 1: Writer K is on pages 3, 9, 15. The K essays are G, I, J. So, {G, I, J} must be on {3, 9, 15}. The remaining pages are {6, 12, 18}, which must be the Y essays {M, N, P}. Given N is on 6. So, {M, P} must be on {12, 18}. Rule (2) is I < P. I is on 3, 9, or 15. P is on 12 or 18. Rule (3) is M < J. M is on 12 or 18. J is on 3, 9, or 15. For M < J, M must be before J. If J is on 3 or 9, M must be on 12. If J is on 15, M can be on 12 or 18. If M is on page 12, then P must be on page 18. This is a possible, complete arrangement: Page 3: K, Page 6: N (Y), Page 9: K, Page 12: M (Y), Page 15: K, Page 18: P (Y). Given that M < J and I < P. If M is on 12, J must be on 15. If P is on 18, I must be on 3 or 9. Thus, M must appear on page 12.