The king's impossible promise

To understand the size problem, start with an old legend about a king, a wise man, and a chessboard.

The wise man had done the king a great service. When the king offered him a reward, he asked for something that sounded tiny:

One grain of rice on the first square of a chessboard. Two on the second. Four on the third. Keep doubling until every square is filled.

The king agreed. At first, the payment looked easy. The first eight squares together held only 255 grains.

By the time every square was filled, the king owed:

18,446,744,073,709,551,615 grains

The first few steps disguised what doubling would do later. By the time the true size of the reward became visible, the promise was impossible to keep.

The king's impossible promise

To understand the size problem, start with an old legend about a king, a wise man, and a chessboard.

The wise man had done the king a great service. When the king offered him a reward, he asked for something that sounded tiny:

One grain of rice on the first square of a chessboard. Two on the second. Four on the third. Keep doubling until every square is filled.

The king agreed. At first, the payment looked easy. The first eight squares together held only 255 grains.

By the time every square was filled, the king owed:

18,446,744,073,709,551,615 grains

The first few steps disguised what doubling would do later. By the time the true size of the reward became visible, the promise was impossible to keep.