Hint to puzzle 7: Five men, a monkey, and some coconuts

Let the original pile have n coconuts.  Let a be the number of coconuts in each of the five piles made by the first man, b the number of coconuts in each of the five piles made by the second man, and so on.

Write a Diophantine equation to represent the actions of each man.  Express n + 4 in terms of e + 1, and hence deduce the smallest possible value of n + 4.