What is the number of fives used in numbering a 260-page book?
What is the number of fives used in numbering a 260-page book?
55
56
57
60
Solution
The digit 5 appears 20 times in each hundred (1-100, 101-200, 201-300). For 1 to 260, full hundreds 1-100 and 101-200 contribute 20 + 20 = 40. The block 201-300 has 20 fives, but numbers above 260 (265, 275, 285, 295 = 4 numbers) must be excluded. So 1-260 has $(20 + 20 + 20) - 4 = 56$ fives.