Here are some previous problems of the month offered by the NIU Math Club. Prizes are no longer available for them, but you're welcome to submit any solutions you might have to lharris4@niu.edu. Solutions may be posted once found.

The Skipper, Gilligan, Ginger, Mary Ann, and the Professor all go out and gather coconuts. At the end of the day they pile all of the coconuts together to be divided equally the next day.

In the middle of the night, Gilligan wakes up and decides to collect his share of the coconuts. He divides them into 5 equal piles with one coconut left over, which he gives to the monkey. He then takes one of the five piles, reassembles the others, and goes back to bed.

Next, the Skipper wakes up and decides to collect his share of the coconuts. He divides them into five equal piles with one coconut left over for the monkey. He then takes his share, reassembles the rest, and goes back to bed. Ginger, Mary Ann, and the Professor all do likewise, each time giving the extra coconut to the monkey.

In the morning, they all gather to divide the remaining coconuts. The pile is noticeably smaller, but since they are all guilty nobody says anything. The remaining coconuts divide evenly into five equal piles, which they split among themselves.

Question: What is the smallest number of coconuts they could have collected?

Bonus: How many coconuts did each person get in this case?