Anatomy Of A Puzzle

During these last few months of staying home or sheltering in place or being in lock down I have been looking at all the puzzles, riddles and such making their rounds in social media. They always show up every now and then but their frequency has definitely increased after the COVID outbreak. I am guilty of posting some myself, I confess. They do provide some diversion and are welcome in general if you like solving puzzles.

Let me get something out of the way first. I don't like certain type of problems. They involve different figures and basic arithmetic but they are just eye tests. The figures are combinations of objects, animals, and human beings - shoes, hats, glasses, coats, or whatever, and persons wearing them. In these cases, you should always consider your first answer to be wrong and go over the pictures again very carefully. Zoom in if you have to. You can easily overlook the fact that the coat has a button missing or the man is holding two batons instead of one or is/is not wearing shoes. Watch out, the girl is wearing an earring in one ear but not the other. I don't know about you but by this time, I have lost interest in it. 

Fortunately, there is a whole lot of other puzzles involving word play, logic, etc. which are more satisfying. I do enjoy solving them, but sometimes they send me off on a tangent. Take this story of the five marooned men and and a monkey and coconuts that came my way recently. It's not new. In fact, it has been around for a long time. I will state the problem for you and let you have the satisfaction of working out the answer or googling it if you prefer. I will just share the little journey which this sent me on.

Five men and a monkey were shipwrecked on an island. They spent the first day gathering coconuts. During the night, one man woke up and decided to take his share of the coconuts. He divided them into five piles. One coconut was left over so he gave it to the monkey, then hid his share, put the rest back together, and went back to sleep.

Soon a second man woke up and did the same thing. After dividing the coconuts into five piles, one coconut was left over which he gave to the monkey. He then hid his share, put the rest back together, and went back to bed. The third, fourth, and fifth man followed exactly the same procedure. The next morning, after they all woke up, they divided the remaining coconuts into five equal shares. Again there was one left which they gave to the monkey

How many coconuts were there in the original pile? To be precise, what is the smallest possible number of coconuts they would have had at the beginning (because there is no unique answer)?

Now you may have seen this problem before but if you have not do not worry. I am not going to reveal the solution here. The solution is a little involved and takes some effort to get to but the reason it set me thinking has nothing to do with the actual solution. In any case, solving it is not a requirement to read further. The real puzzle for me is the whole story which I think is a harder nut to crack (all right, I will admit that was a cheap pun).

When I realized how many coconuts were involved, I started down a proverbial rabbit hole or up on a flight of imagination. Firstly, I noted that they would have had to spend a long time collecting all those coconuts. There is no way that they could have done it all in one day. It also seemed strange that they would spend all their time on day one picking up coconuts (I am assuming that they were not climbing the trees and getting them). Not the first priority, I would think, when you find yourself cast away on a deserted island. But let us move on.   

The evident abundance of coconuts perhaps made for an easy way to pass time by collecting them. If they were all collecting them, and pooling them rather than keeping the individual shares separate shows there was a level of trust. So why try to appropriate one's share in the middle of the night without telling the others? Even in this there is a strange discipline with a robotic similarity. They wake up one at a time to do essentially the same thing. Not only that, they only take what is their share, one-fifth. Talk about honor among thieves. Well, not quite, I guess. Otherwise the piles could have been left separate.

In all seriousness, do you think any of them would have had the energy to keep awake that night (much less wake up one after another taking turns), especially after spending the day collecting an enormous cache of coconuts? Even ignoring that, I am trying hard to picture the mountain of coconuts being divided. Given their quantity, and their size and odd shape, it will take hours to count them. Maybe they were super efficient in counting and separating the piles. In passing, you will note that they would also have given their arms a fantastic workout. But the sheer number still boggles the mind. Where would you hide your share of a few thousand coconuts? The whole thing makes me wonder if the author of the riddle had even seen a coconut.

In some versions of the story, the five men were waiting to be rescued after being spotted. While waiting, one by one they divided the collected coconuts during the night in the said manner. Were they really expecting to take all the thousands of coconuts with them into the ship? Did they think that their free ride included limitless baggage allowance? Or maybe they wanted to compensate their saviours for the rescue with coconuts (if so, then why bother with counting and dividing?). But this would surely have led to 'the proverbial coconut that sank the boat'. A nice way to thank the rescuers, wouldn't you say?