WOLFRAM|DEMONSTRATIONS PROJECT

Coconuts, Sailors, and a Monkey

​
number of sailors
3
number of divisions
4
m
1
1
m
2
1
m
3
1
m
4
1
m
5
1
m
6
1
m
7
1
m
8
1
m
9
1
m
10
1
Possible solutions have the form -2+81q
The solution has q = 1
​
coconutscollected
79
coconuts
share
monkey
others
79
26
1
52
52
17
1
34
34
11
1
22
22
7
1
14
Sailors, stranded on an island, collect all the coconuts they can find. They agree to divide up the coconuts in the morning. But each, in turn, gets up in the night to take his share from the pile. At each division, one is given to a monkey to keep him quiet. In the morning, none are surprised at how the pile has shrunk. They give another coconut to the monkey and divide what remains. What is the smallest number of coconuts such that all divisions come out even?
In classic examples of this problem, there are 3 sailors and 4 divisions or 5 sailors and 6 divisions. Sometimes the monkey does not get his coconut in the morning.