Question

The Funny Book has its pages numbered the following way:

1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5 ... That is, there is one 1, two 2s, three 3s, four 4s, five 5s, and so on.
What is the greatest number of pages that the Funny Book can have if it contains a page that is
numbered “20” but not any that are numbered “21”?

Answer 1

Answer: We can use the formula for the sum of an arithmetic series to find the number of pages in the Funny Book. The formula is:

S = n/2 (2a + (n-1)d)

Where S is the sum of the series, n is the number of terms, a is the first term, and d is the common difference.

In this case, the series is the page numbers, a = 1, d = 1, and we know that there is no page numbered "21" but the page numbered "20" is there.

The number of pages numbered 20 is 20, and the number of pages numbered 19 is 19. So n = 20 + 19 = 39

By substituting the values into the formula

S = 39/2 (2*1 + (39-1)1) = 3920 = 780

The greatest number of pages that the Funny Book can have if it contains a page numbered 20 but not any that are numbered 21 is 780.

Explanation: