Old year – New Year


It is always hard to come up with original puzzles, let alone with a puzzle that has to do with Christmas or new year. Any way: best wishes for 2015 to all of you!

Let’s have a simple problem from the orient. Did you notice that medieval sultans always seem to have an ample supply of beautiful daughters? And that they invariably have strange ways to choose their son-in-law?

This one is no exception. His kingdom had an extensive seashore, and he said to four young men interested in the hand of his daughter: Along the coastline I own many fishing boats. But there is something very peculiar with the number of fishing boats:
when the number is divided by 2, the remainder is 1,
when the number is divided by 3, the remainder is 2,
when the number is divided by 4, the remainder is 3,
when the number is divided by 6, the remainder is 5,
when the number is divided by 7, the remainder is 6
when the number is divided by 8, the remainder is 7
when the number is divided by 12, the remainder is 11
when the number is divided by 14, the remainder is 13
when the number is divided by 18, the remainder is 17
when the number is divided by 21, the remainder is 20
when the number is divided by 24, the remainder is 23
when the number is divided by 28, the remainder is 27
when the number is divided by 32, the remainder is 31
How many fishing boats are there in my kingdom?

You can check your solution here

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