Coconuts and Monkeys

BJHorsegirl writes to ask: “Three sailors are lost at sea and all they have to eat is coconuts. That

night, they collect a lot of coconuts and split the total in to thirds.That

night, a sailor took one coconut, and threw it out. Then he split up the

coconuts

into thirds again. Later that night, another sailor woke up, and threw out

another coconut, then split the total into thirds again. Early the next


morning, the other sailor repeated the process.

What was the least amount of coconuts they could have gathered?”

Umm, this is impossible, but may have been miss worked out via blagging it from an internet site about the sailors, monkeys and coconut puzzle. What has been omited - the sailors stealing a third of the coconuts actually makes it impossible. No number in the world can you divide by three whilst the consecutively less or higher numbers being divisible by three… it’s just impossible.

If indeed this fact has been omited this is based apon iterations, if you can think linearly, but I’m actually having real trouble working out the short cut to this one. Instead I will show you the methodical version with what iterative knowledge I have.

So firstly the definition of an iteration - An equation which contains itself, ie the answer naturally falls back into the equation to give a further value. This is what fractals are based upon, and happen throughout nature.

So let’s break this question down. It states that each time the same basic rules apply, one coconut is taken out, and the pile divided into three. Now no matter how hard you think about it, it will confuse you trying to work from the whole pile downwards, so some iterative thinking comes into play.

Firstly, you start off with your minimum value x. Then there will be one coconut added three times, and the pile split into three each time, whilst a third of them disappear. This works down to be

X=3x+1

Ie - to get the next amount of coconuts, you multiply by three (the reverse of dividing), and add the missing one back on. If you do this as many times as there were sailors, you find an expression for the original amount of coconuts.

X=3(3(3x+1)+1)+1 (3 iterations.)

X=3(9x+4)+1

X=27x+13

So if each received only one coconut on the final cut, then the amount of coconuts initially would have been 40 (27+13)