Sunday, 10 July 2011

The Chessboard: A story

Once upon a time, in a far a way kingdom, lived a king who was very greedy and taxed his people until they were almost broke and starving. The king was not a totally bad bloke - just very greedy, foolish and far too removed from his people.

Early one morning, the king decided to go for a swim in the sea. Slipping out of the palace, the king headed to the beach leaving his guards and servants unaware of his whereabouts.

After an energising swim in the bracing waters, the king turned towards the shore and began to swim towards the beach. However, the current was too strong and the king found himself fighting for his life.

"Help! Help! Help!" yelled the king, seeing his life flash before him.

Only the old hermit, who lived on in a cave on the beach, heard the king's desperate pleas.

The hermit, a very wise man, quickly found some old rope and threw the king a lifeline.

The two men sat on the beach. The old hermit panting through exertion and the king panting through exhaustion.

"I owe you my life." said the grateful king, "What would you like in return?"

The old hermit sat quietly and shook his head as the king offered him land, money and other riches.

The hermit knew the king was offering promises in the heat of the moment and would not follow through once the king had recovered from the shock of his ordeal.

Finally, the hermit went into his cave and brought out a chessboard.

"This chessboard has 64 squares. Starting today, I would like one grain of rice for the first square, tomorrow I would like two grains of rice for the second square." said the old hermit, "The day after, I would like 4 grains of rice for the third square and on the fourth day, I would like 8 grains of rice."

"So you want me to double the amount of rice each day for sixty four days?" asked the bemused king.

The old man nodded and the king readily sealed the deal with a handshake.

Walking back to the palace, the kings thoughts were racing. He was a little miffed that the old hermit had only valued his life as some rice but was pleased that he would not have to part with much of his wealth to pay off the old man. The king smiled to himself and thought no more about it.

Later that day, the hermit took his walking stick and began the long walk up the hill to the palace. Much to the hermit's surprise, the king agreed to see him. The old hermit was ushered into the packed throne room."

"My lord, ladies, gentleman and loyal subjects," began the king, pointing to the hermit, "this morning this man saved my life. I have offered him great riches but he has chosen only to take some rice."

The king outlined the deal that had been struck between the two men hours before:

Day 1 - 1 grain of rice
Day 2 - 2 grains of rice
Day 3 - 4 grains of rice
Day 4 - 8 grains of rice
Day 5 - 16 grains of rice etc until Day 64.

The gathered crowd cheered. The king beamed - he was not averse to a bit of good publicity.

Only the king's bean counter, who was standing in a corner, remained silent as he turned a fetching shade of beetroot.

With a flourish, the king held out the one grain of rice to the old hermit.

Bowing low, the old man took the grain of rice and thanked the king profusely.

"Same time , same place for the next sixty three days." declared the king.

The old man nodded and left the palace.


This story is a story about the power of doubling. The same, to a lesser extent, could be said about the power of compounding.

You can play with the numbers yourself to see what happened in this story. It is safe to say that most calculators do not have the memory to cope with the numbers involved, once you get to around the thirty day mark.