Question

The legend says that a peasant invented the game of chess and brought it as a gift to the king. The king liked the game so much that he offered the peasant any gift he wanted in exchange. The peasant told the king that all he wanted was 1 grain of wheat on the first square, 2 grains on the second square, 4 grains on the third square, and so on, each time doubling the amount of grains until the last square of the chessboard. The king was surprised by the modest request and called his servants to count the grains. Calculate the number of grains of rice that would fill the chessboard.

A) 2⁶³ grains
B) 2⁶⁴ grains
C) 2⁶⁵ grains
D) 2⁶⁶ grains

Answer 1

The number of grains of rice that would fill the chessboard can be calculated by doubling the amount of grains on each subsequent square. The formula to calculate this is grains = 2^(n-1), where n is the square number. Plugging in n = 64, we get grains = 2^63 grains.

Step-by-step explanation:

The number of grains of rice that would fill the chessboard can be calculated by doubling the amount of grains on each subsequent square. Since there are 64 squares on a chessboard, we can start with 1 grain on the first square and then multiply that by 2 for each subsequent square. This can be represented by the equation grains = 2^(n-1), where n is the square number. Plugging in n = 64, we get grains = 2^(64-1) = 2^63. So, the number of grains of rice that would fill the chessboard is 2^63 grains, or option A.