The wheat and chessboard problem is a mathematical problem. If a chessboard were to have wheat 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 grains of wheat would be on the chessboard at the finish? To solve this, observe that a chess board is an 8×8 square, containing 64 squares.

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  • The wheat and chessboard problem is a mathematical problem. If a chessboard were to have wheat 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 grains of wheat would be on the chessboard at the finish? To solve this, observe that a chess board is an 8×8 square, containing 64 squares. If the amount doubles on successive squares, then the sum of grains on all 64 squares is: <math>T_{64} = 1 + 2 + 4 + \cdots + 2^{63} = \sum_{i=0}^{63} 2^i = 2^{64} - 1 \, </math> which equals 18,446,744,073,709,551,615. This problem (or a variation of it) demonstrates the quick growth of exponential sequences.
  • Задача о зёрнах на шахматной доске — математическая задача, в которой вычисляется, сколько будет зёрен на шахматной доске, если класть на каждую следующую клетку доски вдвое больше зёрен, чем на предыдущую, начиная с одного. Для её решения учтём, что доска имеет 64 клетки. При удвоении количества зёрен на каждой последующей клетке сумма зёрен на всех 64 клетках определяется выражением <math>T_{64} = 1 + 2 + 4 + \cdots + 2^{63} = \sum_{i=0}^{63} 2^i = 2^{64} - 1,</math> что составляет 18 446 744 073 709 551 615. Задача (и её вариации) демонстрирует высокую скорость роста экспоненциальных последовательностей.
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  • Wheat and Chessboard Problem
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  • WheatandChessboardProblem
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  • The wheat and chessboard problem is a mathematical problem. If a chessboard were to have wheat 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 grains of wheat would be on the chessboard at the finish? To solve this, observe that a chess board is an 8×8 square, containing 64 squares.
  • Задача о зёрнах на шахматной доске — математическая задача, в которой вычисляется, сколько будет зёрен на шахматной доске, если класть на каждую следующую клетку доски вдвое больше зёрен, чем на предыдущую, начиная с одного. Для её решения учтём, что доска имеет 64 клетки.
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  • Wheat and chessboard problem
  • Задача о зёрнах на шахматной доске
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