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On epiphany 1735, Sir Zettler, who was a great publisher from the old continent, promised to issue a "Great Universal Encyclopedia of Collectible Wisdom". It was meant to be affordable for everybody: Each issue would cost only one shilling and contain sixteen pages of very precious information. A new issue would be published every third week to enhance people's enlightenment.

However, Zettler was also a businessman. His plan was to increase the price by one shilling from issue 10 on, then by another shilling from issue 100, and so on. And at the same time, he would cut the number of pages on each price increase by half.

The business prospered, but Zettler unfortunately did not finish the encyclopedia during his lifetime, as he died in the night after issue 255 had been published. Anna, his beloved 31 year old daughter and his only heir, took over her father's business.

When Anna was going through the accounts, she found out that her father had already calculcated the total price of the encyclopedia. Each client would have paid a total of 6,893 shillings when the encyclopedia was complete. She did not reveal any more details, but can you find out how many issues were planned in total?

Bonus questions:

  1. How old was Anna when the last issue was published? Around which day would that be? (use Gregorian years)
  2. After each 20th issue, a supplementary leaflet with corrigenda is published for free. Including these supplementaries, how many pages does the whole encyclopedia contain?

(inspired by Fritsche/Mischak/Krome 2007)

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The total number of planned issues was

2000
9 * 1 + 90 * 2 + 900 * 3 + 1001 * 4 = 6893
9 + 90 + 900 + 1001 = 2000

When the last issue was published, Anna was

131 years old.
(2000 - 255) * 3 weeks / 52 weeks per year = 100.67 and she was already 31.

Assuming the leaflets are two pages each, the total number of pages is

6666
9 * 16 + 90 * 8 + 900 * 4 + 1001 * 2 + 2000 / 20 * 2 = 6666

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  • $\begingroup$ a leaflet always has two sides (pages) $\endgroup$
    – friedemann_bach
    Commented Jan 31, 2022 at 22:20
  • $\begingroup$ it seems this one was way too easy ;-) $\endgroup$
    – friedemann_bach
    Commented Jan 31, 2022 at 22:22
  • $\begingroup$ @friedemann_bach The math for the first part is kinda tricky but I just used a spreadsheet and adjusted the total count until the price was right. $\endgroup$
    – caPNCApn
    Commented Jan 31, 2022 at 22:24
  • $\begingroup$ yes, a spreadsheet helps. I interpreted one year as 365.25 days, but that does not make much of a difference in this case. $\endgroup$
    – friedemann_bach
    Commented Jan 31, 2022 at 22:29

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