Question

459. По легенде индийский царь позволил изобретателю игры в шахматы самому себе назначить награду. Тот просил, чтобы дали ему зерен пшеницы: за первуюклетку — одно зерно, за вторуюдва зерна и так далее до последней 64-й клетки за каждуюпоследующую 2 раза больше, чем за предыдущую.а) Сколько зерен пшеницы просил он? Как прочитать это число?б) Найдите примерный вес этого зерна в тоннах, если вес одногозерна ~ 0,065 грамма.​

Answer 1

Ответ:Как правило, задача решается для стандартной 64-клеточной доски; при удвоении количества зёрен на каждой последующей клетке сумма зёрен на всех 64 клетках определяется выражением: (смотрите на фото)

Объяснение: что составляет 18 446 744 073 709 551 615.

Answer 2

Indian King and the Chessboard Legend

According to the legend, an Indian king allowed the inventor of the game of chess to choose his own reward. The inventor requested grains of wheat as his reward. He asked for one grain of wheat for the first square of the chessboard, two grains for the second square, four grains for the third square, and so on, doubling the number of grains for each subsequent square until the 64th square.

Let's answer the questions step by step:

a) How many grains of wheat did he request?

To calculate the total number of grains of wheat requested, we need to sum up the number of grains for each square on the chessboard. The formula to calculate the number of grains for each square is 2^(n-1), where n is the square number.

Using this formula, we can calculate the number of grains for each square and sum them up:

Square 1: 2^(1-1) = 1 grain Square 2: 2^(2-1) = 2 grains Square 3: 2^(3-1) = 4 grains ... Square 64: 2^(64-1) = 9,223,372,036,854,775,808 grains

Therefore, the inventor requested a total of 9,223,372,036,854,775,808 grains of wheat.

b) Approximate weight of the grains in tons

To find the approximate weight of the grains in tons, we need to know the weight of a single grain. According to the information provided, the weight of one grain is approximately 0.065 grams.

To convert the weight to tons, we need to divide the total weight in grams by 1,000,000 (since there are 1,000,000 grams in a ton).

Weight of one grain = 0.065 grams Total weight of grains = 9,223,372,036,854,775,808 grains * 0.065 grams

Converting the total weight to tons:

Total weight in grams = 9,223,372,036,854,775,808 grains * 0.065 grams = 598,631,070,650,737,360.52 grams Total weight in tons = 598,631,070,650,737,360.52 grams / 1,000,000 = 598,631,070,650.74 tons

Therefore, the approximate weight of the grains of wheat requested by the inventor is 598,631,070,650.74 tons.

Please note that the weight is an approximation and may vary depending on the actual weight of a grain of wheat.