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In the legend of the King and inventor of the chessboard how many grains of wheat were on the 9th square of the chessboard?
256 grains of wheat?! Quote: According to legend, Chess was invented by Grand Vizier Sissa Ben Dahir, and given as a gift to King Shirham of India. The king was so delighted that he offered him any reward he requested, provided that it sounded reasonable. The Grand Vizier requested the following:
"Just one grain of wheat on the first square of a chessboard. Then put two on the second square, four on the next, then eight, and continue, doubling the number of grains on each successive square, until every square on the chessboard is reached."
The king thought this a very modest request, promised it, and asked for a bag of wheat to be brought in. However the bag was emptied by the 20th square. The king asked for another bag, but then realized that the entire bag was needed for the next square. In fact, in 20 more squares, he would need as many bags as there were grains of wheat in the first bag!
The number of grains in the last square can be calculated by multiplying 2 times itself 63 times. (This can also be written as 2^63.) You can easily work this out on a pocket calculator. The answer is 9223372036854775808 which is approximately equal to 10^19. (It is actually closer to 0.922 x10^19 = 9.22 x10^18). If you include the grains on the first 63 squares, the sum is about twice as large (but only twice as large! Do you see why? Try it will smaller chessboards, maybe one with only 4 squares. You'll see that you always put more on the last square than on all the preceding squares.)
If all these grains were stacked into a cube, the cube would have 2,642,000 grains on each edge. (If you cube 2,642,000, you get 2 x10^19.) If each grain were 1 mm in size, then each edge would be 2,642,000 mm = 2,642 meters = 2.6 km. The cube would be 2.6 km long, 2.6 km wide, and 2.6 km high. It wouldn't fit on a chessboard.
The amazing feature of this problem is that with just 64 steps, each one quite modest (you are only doubling) you get a huge number. This type of rapid growth is called exponential growth.
What else can I help you with?
How should you position a chessboard?
A chessboard should be placed between opponents where the lower right-hand square is a 'white' square . (Rook on white.)
If you had a chessboard and on the first square you put 1 grain of rice then on the second square you doubled the amount how many would you have on the 64 square?
To solve this, observe that a chess board is an 8×8 square, containing 64 squares. If the amount of grains doubles on successive squares, then the sum of grains on all 64 squares is: This equals 18,446,744,073,709,551,615 (18.4 quintillion). hope that helped XD xx
What is the starting position of the chess king on the chessboard?
The starting position of the chess king is on the square e1 for White and e8 for Black on the chessboard.
How do you position a chessboard?
White square is on the lower right corner.
What do you call a 64 square chess board?
An intact chessboard .
How are the king and queen positioned on the chessboard in relation to each other?
The king and queen are positioned next to each other on the chessboard, with the queen placed on her own color square and the king on the opposite color square.
How do you set up the king and queen pieces on the chessboard?
To set up the king and queen pieces on the chessboard, place the king on the square of its own color (white king on white square, black king on black square) and the queen on the remaining square of the same color.
Inventor of L-square?
The inventor is not known.
How many square s are there in a normal chessboard?
In chess there are 64 squares white and black
What are the examples of square shapes?
Some examples of squares are chessboard, carom board, square rubber stamps, and tiles on the floor.
On a chessboard, what space does the queen go on?
The queen goes on the square that matches her color, typically the fourth square from the left on her side of the board.
How many ways can you place 64 pawns on a chessbord?
64 pawns upon a 64 square chessboard - one pawn per square .
