15 players are seated around a circular table.
Palo Alto Networks technical mcq question, verified with a worked answer. Free to practise - no sign-up.
15 players are seated around a circular table. The first player tears off the first page of a book of 100 pages, the second player tears off the next two pages, the third the next three and so on until all pages are torn off. Which player tears off the last page?
Note that the sum of the numbers from 1 to n is given by ______
Select any one of the following options
Show answer & explanation
Player k tears k pages. The cumulative sum for 13 players is 13*14/2 = 91 pages. The 14th player must tear 14 pages (pages 92 to 105), which includes the final 100th page.
Step-by-step Derivation:
Step 1: Sum of pages torn after k turns S_k = k(k+1)/2.
Step 2: For k = 13: S_13 = 13 * 14 / 2 = 91 pages.
Step 3: For k = 14: S_14 = 14 * 15 / 2 = 105 pages.
Step 4: Since the book has 100 pages, the 100th page is torn during the 14th turn.
Step 5: Turn 14 corresponds to player 14 (14 mod 15 = 14).