Discussion
A printer numbers the pages of a book starting with 1A. If 4S is the last page of the book, then how many pages are in the book ?
Answer: C
The book has 97 pages.
The pages are labelled with a number followed by a letter: 1A, 1B, ... 1Z, then 2A to 2Z, then 3A to 3Z, then 4A onward. Each number therefore covers 26 pages, one for each letter.
\[ \begin{aligned} 1A \text{ to } 3Z &= 3 \times 26 = 78 \\ 4A \text{ to } 4S &= 19\ (\text{S is the 19th letter}) \\ \text{total} &= 78 + 19 = 97 \end{aligned} \]
104 would be four full sets of 26 (up to 4Z), and 98 and 95 miscount the letters of the last set.
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