Saturday, August 31, 2002
M I N D  G A M E S


Honour among thieves

The good Christian should beware of mathematicians and all those who make empty prophecies. The danger already exists that the mathematicians have made a covenant with the devil to darken the spirit and to confine man in the bonds of Hell. — St Augustine (354-430); by mathematicians, he meant astrologers.

FIVE men - what a perfect figure - like the Pandavas, Famous Five, Hardy Boys, Horsemen of the Apocalypse - friends for life, you'd say, but let us put the group in some trouble and see if it emerges stronger. Sailors they are, in the pirate navy of Captain Nemo.

On the deck: Nemo's question: "Sailors, what keeps the navy going?" "Team spirit, sir," the group yells, keeping the pitch just below the level where the lungs would burst. "Trust makes a strong team; there is honour among thieves as well; remember that," says Nemo. Thieves being thieves, they soon forget lessons of virtue.

 


One day, high tides test the ship for its strength and it fails. The five sailors find themselves washed ashore after the shipwreck. It is a deserted island, with no treasure to offer; mutual trust is their only hope, if they have to survive. Soon, hunger comes calling and they realise that they'll need food; so, they spend all day gathering coconuts, the only food available there. Almost all coconuts on the island are plucked. Tired, they go to sleep, agreeing to divide the coconuts equally among themselves in the morning.

One of the sailors wakes up in the night, and since he doesn't quite trust the others, he thinks, for a moment, of hiding all the coconuts, so, that he may have all for himself. The others will, then, starve to death, leaving him with a huge supply of food to keep him alive for long. Then he remembers what Nemo had told them: "There is honour among thieves as well." He decides to take his share and leave the rest for the others. He divides the coconuts into five equal piles.

Finding one coconut left over, he realises that he doesn't know what to do with it, as keeping it would break the code of honour and giving it away would mean loss. He looks around and finds that a monkey had been watching him from a distance all this time. "Aha! That gives me an idea," he says to himself. He gives the coconut to this monkey, hides his pile, pushes the remaining four piles into one large pile and goes back to sleep.

Each of the other four sailors wakes up in the night and repeats the actions of the first sailor. After dividing the pile, each finds one extra coconut, which he gives to the monkey.

In the morning, horror strikes the five men when they find that the pile of coconuts is noticeably smaller, but since each is at fault, no one mentions it. They divide the remaining coconuts evenly among themselves. Nemo's submarine picks them up later in the day and the hidden coconuts remain buried. How many coconuts did the five men originally gather? Suppose that each sailor takes and hides one-fifth of the coconuts, plus one-fifth of a coconut (no monkey). In the morning, the pile is divided evenly. If no coconut is cut, how many did they originally gather? Write at The Tribune or adityarishi99@yahoo.co.in.

— Aditya Rishi