Problem:
The pages of a book are numbered through . When the page numbers of the book were added, one of the page numbers was mistakenly added twice, resulting in the incorrect sum of . What was the number of the page that was added twice?
Solution:
Let be the number of the page that was counted twice. Then, , and is between and . In other words, i.e.,
By trial and error (clearly, is a little larger than ) we find that . Thus .
The problems on this page are the property of the MAA's American Mathematics Competitions