Wheat and Chessboard problem gives a lesson that knowledge and experience are the best investment that would pay for the whole life. First, learn the lessons, make use of that, and continue to turn work into an experience. Reading these lessons from wheat and chessboard is surely building curiosity to know about what is wheat and chessboard problem. After knowing the phenomenon of the problem, the attention drawn by the history of origin behind it. The story behind it just explains the success of a sage. However, there are complete logical calculations of discrete math behind it.
Keeping on reading to find wheat and chessboard story, solution for it, and the equation it’s based on. The big reason behind to tell you the story behind the problem is to keep you motivated with great lessons you learn from it.
Reality-based Wheat and Chessboard Story:
Long ago in India, there was a king who had the habit of challenging wise visitors to a game of chess. He had this habit because he himself was an enthusiastic player of chess. Similarly, once as usual when the king was traveling. He meets sage and challenged him. This sage who has been playing the game for his whole life with people from worldwide. So, without thinking for the second time he accepted the king’s challenge. The king was so confident in himself that to motivate his opponent, he offered the reward whatever sage ask for. And this was this is the actual turning point of the story.
The sage was wiser than the king. He modestly just asked for a few grains of rice. The approach was made in this way that The King has to put a single grain of rice on the first square, then double whiling placing on every consequent square. However, the king accepted the sage’s request.
As explained before, the sage was a wise player of chess. So, having lost the game. It was the turn of the king to be a man of his words. He ordered his servants to bring a sack of rice. And then as it was decided, he started placing the grains on the board of the arrangement: 1 grain on the first block of chess, 2 on the second, 4 on the third, 8 on the fourth, and so on. Continuing the exponential growth of rice payment. The king realized that he will not be able to keep his words of awarding the reward he names. As when it was the twentieth square there were 1,000,000 grains placed on it when it was to place on the sixty-fourth square it was more than 18,000,000,000,000,000,000 grains. This was approximately equal to 210 billion tons. Furthermore, this is sufficient to cover the whole territory of India with a 1-meter thick layer of rice.
And this was that point of the story that made the sage the wealthiest person of the world. However, the sage didn’t ask the king to pay the whole amount immediately. But do in its installments.
Wheat and Chessboard Solution:
It is basically a mathematical problem. In which we consider, a chessboard that 8×8 =64 square. There are wheat grains placed on by doubling the quantity. For instance, one grain on the first square, two on the second, then four on the third one and so till the 64th square. This makes the figure of 18,446,744,073,709,551,615 on the last 64th square of the chessboard.
Wheat and Chessboard Problem Equation:
To solve this wheat and chessboard there is a proper mathematical equation. First of all the number of squares on the chessboard is calculated. The is 8×8= 64.
T_ = 1 + 2 + 4 + cdots + 2^ = sum_^ 2^i = 2^ – 1 ,
There is the derivation of the too. However, it will give the result of figure 18,446,744,073,709,551,615 .
The straightforward, animal power arrangement is simply physically twofold and includes each progression of the arrangement:
T64 = 1 + 2 + 4 + …… + 9,223,372,036,854,775,808 = 18,446,744,073,709,551,615
Facts to ponder upon from Wheat and Chessboard Story:
There is not a single moral lesson that we learn from the story of wheat and chessboard. First, get to observe the proud nature of King. It teaches us that no matter how many expertise skills we have. We should never boost up in front of others. Another point is confident in yourself but never be over-confident. People are intelligent, but you have to wise and clever too. Because in many cases you should think in a clever way. Neither always be kind and soft. If you have one lesson or two, it’s not just to stuff in mind. For this, you have to be attentive and conscious to make use of lessons efficiently. Applying things, one had learned will make them experienced over time. So, you are now wise, conscious, and experienced.