A leaf is torn from a novel. The sum of the numbers on the remaining pages is 15000. What are the page numbers on the torn leaf?
I know the answers.
(i found it out using the n(n+1)/2 formula and finding n for 15000 ,which yielded a non-whole value, and finding sum for the next greater whole value. The sum obtained i.e 15051 minus 15000 yielded 51 and since the torn leaf has consecutive page numbers, i got 25 and 26)
I would say the above method is extremely crude and wouldn't be accepted as a solution at all.Does anybody know the proper solution to this problem using number theory(as the question was listed in a number theory question bank)??
(not only does the removed leaf have one odd and one even number the odd number must be one less than the even.