The first one was asked to me by my father, the second I found in an old textbook. Both are similar in flavor.
Q1: There is a feast where several thousand people are attending (i.e. more than 1000 people). The organizers realized that if they divided the guests into tables of 5, 7, 9 people respectively, then exactly one table will have 4, 6, 8 people in the corresponding situation. If they divided them into tables of 11 people, then each table will have exactly 11 guests. What is the smallest possible number of people who attended the feast?
Q2: There are five suspicious pirates stranded on a tropical island. They worked together to gather a large amount of coconuts. During the evening, the first pirate divided the stockpile of coconuts into five equal piles with exactly one coconut left over, which he gave to the monkey. He took one of the five piles and left the remaining four piles. The next pirate then did the same thing; i.e. divided the stockpile into five equal piles with one left over, then giving the left over coconut to a monkey. The situation is exactly the same for each subsequent pirate. In the morning, all five pirates divided the remaining coconuts into five even piles (with none left over), but no one complains because each is guilty. What is the smallest number of coconuts the pirates gathered originally?