Question

If a chessboard were to have rice placed upon each square such that one grain were placed on the first square, two on the second, four on the third, and so on (doubling the number of grains on each subsequent square), how many grain of rice would be on the chessboard at the finish? (The chessboard has 64 squares)

Answer 1

Placing rice on a chessboard in the manner described would result in a total of 18,446,744,073,709,551,615 grains of rice on the board.

Step-by-step explanation:

To determine the total number of rice grains on the chessboard, we can use the formula for a geometric series:

`Sn = a(1 - r^n) / (1 - r)`

where:

* Sn is the sum of the series

* a is the first term (1 grain of rice)

* r is the common ratio (2, since the number of grains doubles each time)

* n is the number of terms (64, the number of squares on the chessboard)

Plugging in the values, we get:

Sn = 1(1 - 2⁶⁴) / (1 - 2)

Sn = 18,446,744,073,709,551,615

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Therefore, there would be 18,446,744,073,709,551,615 grains of rice on the chessboard after placing rice on each square according to the given pattern.