A monkey, the shipwrecked and a whole load of coconuts

1
A monkey, the shipwrecked and a whole load of
coconuts
2
Three people, Sawyer, Kate and Hurley were
trapped on a desert island
3
The only other things on this island were a
monkey and a whole load of coconuts. With
little else to do the three shipwrecked set about
playing with the monkey and working together to
amass some coconuts to ensure they have enough to
eat. They agree that they will share them
equally in the morning. Then they all go to
sleep!
4

• In the middle of the night Sawyer wakes up and
  decides to take his share. Having made three
  equal piles there is one left over which he gives
  to the monkey. Sawyer takes his share, hides it
  away, puts the other two piles back into a single
  pile and goes back to sleep.

5

• Some time later Kate wakes up and repeats
  exactly the same process shares the remaining
  coconuts into three equal piles, finds there is
  one left over, gives it to the monkey, hides her
  pile and puts the other two piles back together.

6

• Hurley wakes up and he does the same thing with
• the now much smaller pile of coconuts.

7

• In the morning they are all feeling a bit guilty!
  So they share the pile out and find there is one
  remaining which they give to the monkey.

8

• The monkey now has four coconuts, one from each
  time a sharing took place.

9
So how many coconuts could there have been to
start off with? What is the smallest original
total? How many coconuts do each of Sawyer,
Kate and Hurley get? What different amounts of
coconuts could there have been?
10
What could the possible totals be if after each
sharing there had been 2 coconuts remaining (so
the monkey would end up with 8 coconuts) What
would be the possible totals if there had been 4
people with 1 remaining each time (and,
therefore, 5 sharings)?