Starting with 1, and doubling the number immediately following (as in 1 + 2 + 4 + 8 etc.) what is the total at the end of 64 such steps?

The question probes at the speed with which exponential sequences can grow. The problem is often presented in the form of a very old story (first recorded in the 13th Century) told about grains of wheat and the chessboard. How exponential powers of two were a very unpleasant surprise for a Persian King outwitted by his Grand Vizier.

Having invented the marvellous game of chess for his King, the Grand Vizier was asked to name his reward. He asked for 1 grain of wheat for the first square on the chess board, two for the second, 4 for the third, 8 for the fourth and so on...until he receives payment for all 64 squares on the board. The King argued that the reward was too modest, but agreed to pay.

When, however, the Master of the Royal Granary began to count out the grain, the King faced a staggering realisation. The number of grains starts out small enough: 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024 . . . but by the time the 64th square is approached, the number of grains becomes colossal. In fact, the total number of grains on the completed board would be 18,446,744,073,709,551,615 (18.45 quintillions).

That much grain would weigh around 75 billion metric tons, which would take today’s wheat producers about 150 years to accumulate.