Question 5
An n-dragon is a set of n consecutive positive integers. The first two-thirds form the tail; the remaining one-third form the head. The sum of the numbers in the tail equals the sum in the head. For example, the nine consecutive integers 2,3,4,5,6,7,8,9,10 form a 9-dragon:
- Its tail is 2,3,4,5,6,7: six numbers with sum 27.
- Its head is 8,9,10: three numbers with sum 27.
(1) Find a 21-dragon. (3 points)
(2) Find the sum of the tail of a 99999-dragon. (5 points)
- Its tail is 2,3,4,5,6,7: six numbers with sum 27.
- Its head is 8,9,10: three numbers with sum 27.
(1) Find a 21-dragon. (3 points)
(2) Find the sum of the tail of a 99999-dragon. (5 points)