Old Nuts
Why do this problem?
It's a well known problem but intriguing nevertheless. As the
solution shows, it can be solved by just working systematically
with the information, thinking about which numbers are divisible by
4 and 3, and testing the possibilities. Modulus arithmetic provides
an efficient way to solve the problem.
Possible extension
Solve the generalised problem with $n$ castaways, dividing the pile
into nshares, hiding one shareand throwing m coconuts to the
monkeys each time.