Square 1
The Legend
According to a well-known Indian legend, the inventor Sissa taught a king to play chess. Asked to name his reward, Sissa requested one grain of rice on the first square, then double on each subsequent square. The king agreed, thinking it modest—until he realized that by the 64th square the total would exceed any kingdom's stores. The tale illustrates how quickly exponential growth explodes from humble beginnings.
The Mathematics
Formula: Square n holds 2n−1 grains. The cumulative total through square n is the geometric series sum: Sn = 1 + 2 + 4 + … + 2n−1 = 2n − 1. For a full 64-square board, S64 = 264 − 1.
Reality Check
At 25 mg per grain, the full board's mass is on the order of billions of metric tons—far beyond any realistic supply. The exact integer is shown below with scientific notation and weight approximations.