Gfyuki

A few days ago, as I was delving into the mess in my grand parents' attic, I found an impressive ancient book that was written in a language that I had never seen before.

"This book is a collection of riddles printed in the eighteenth century." Grandma said. "One in particular is worth reading: it is said to be the ancestor of the age-of-the-captain riddles. Let me translate it to you."

And she proceeded:

A Captain's son asks his father:

"Why Father, I've noticed that we never celebrate your birthday, and in fact I don't think I even know when you were born."

Answers the Captain:

"If you subtract four from the day I was born, then you get a non-zero
integer with several distinct prime divisors, one of which is the
month I was born. Now with that knowledge, if I tell you the day I
was born, then you shall know the year as well."

What was the Captain's date of birth? (dd/mm/yyyy)

She then closed the book and stared into my eyes with the most mischievous look I'd ever seen. She asked:

"In what language was this book written?"

First, the day, minus 4, must have at least two prime factors ("several distinct prime divisors"). Moreover, we will know his month uniquely, so one of these primes should be greater than 12 or the date greater than 28. (Checking 29 and 31 - both 29-4 and 31-4 have only one distinct prime divisor, so neither work.) So the date should be 30=2*13+4.

So his birthday is on February 30. The next larger candidate would be 2*17+4 or February 38, followed by February 42 and March 43, which are obviously not real dates.

Wait, say what?? Yes, that's a real thing! In particular, it satisfies the date requirement (we now know that his birthday was on 30/02/1712), we now know why we never celebrate his birthday (since February 30 never existed thereafter), and we also know the language it was written in, namely Swedish.

Is the answer:

02/03/1700?


Four days before that would be 26/02/1700. The month has 2 distinct prime divisors, 2 and 13, one of which is the month.


The only part of the calendar which differs from year to year is 29/02. So the 4 day stretch must span this date, if it is true that the year can be deduced by the day.


Years divisible by 100, but not 400, do not have a leap day. Of the numbers {25, 26, 27, 28, 29}, only 26 has distinct prime divisors. And 4 days ahead of 26/02 is 02/03, in a non-leap year.


The next question is the century. But the second paragraph states that the riddles were published in the 18th century (ie., the 1700s). If the Captain was alive during the 1700s then only the year 1700 makes sense.


As for the language, that has me stumped. :)