After finishing a very boring book, Fred notices that the page numbers contained exactly zeros and exactly ones. The book started with page . How many pages were in the book?
Source: NCTM Mathematics Teacher, December 2005
We arrange the numbers in rows of numbers as follows
Each row starting from row contains zero except row which contains zeros. The number of rows containing zero is . The total number of zeros from page to page is
Thus, the book has at most pages.
On the other hand, rows have one, rows have ones, while row has ones. The total number of ones from page to page is
Since the book has ones, the last page must be . The book has pages.