The inventor of the chess board suggested a reward of 1 grain of wheat for the first square, 2 grains for the second square, 4 grains for the third square and so on, doubling the number of the grains for the subsequent squares.
How many total grains of wheat should be on the board after the the grains of wheat have been placed on square?
16,384 grains should be on square 15.
How many grains of wheat should be placed on square 16 of the chessboard?
Was the wise ruler wise after all?
| Day | Grains placed that day | Total grains placed so far |
| 16 | 32768 | 65535 |
| 17 | 65536 | 131071 |
| 18 | 131072 | 262143 |
| 19 | 262144 | 524287 |
How many grains of rice did the king have to give to the inventor?
As the story goes, when chess was presented to a great king, the king offered the inventor any reward that he wanted. The inventor asked that a single grain of rice be placed on the first square of the chessboard. Then two grains on the second square, four grains on the third, and so on. Doubling each time.
How many grains of rice would there be at the fifth squares?
On the 64th square of the chessboard alone there would be 263 = 9,223,372,036,854,775,808 grains of rice, more than two billion times as much as on the whole of the first half of the board.
Is there a pattern in the number of grain of rice after 9th Square?
All he wanted was the rice. So the king agreed and the chess game was played. He then moved onto the second row; 256 grains on the ninth square, 512 on the the tenth square, then 1024, then 2048, doubling each time until he needed to put 32 768 grains of rice on the last square of the second row.
How much wheat was put on the chessboard?
He ordered his enslaved servants to bring out the chessboard and they started putting on the wheat. Everything went well for a while, but the king was surprised to see that by the time they got halfway through the chessboard the 32nd square required more than four billion grains of wheat, or about 100,000 kilos of wheat.
What did SISSA say about wheat on the chessboard?
Finally Sissa said that he would take this reward: the king should put one grain of wheat on the first square of a chessboard, two grains of wheat on the second square, four grains on the third square, eight grains on the fourth square, and so on, doubling the number of grains of wheat with each square (an exponential rate of growth).
What is the sum of grains on a chessboard?
With 64 squares on a chessboard, if the number of grains doubles on successive squares, then the sum of grains on all 64 squares is: 1 + 2 + 4 + 8 + and so forth for the 64 squares.
Who was the inventor of chess and wheat?
Another version has the inventor of chess (in some tellings Sessa, an ancient Indian Minister) request his ruler give him wheat according to the wheat and chessboard problem.
