64

The I Ching enumerates sixty-four hexagrams, each formed from six lines that are either broken or unbroken. The structure is a complete binary enumeration, which is why Leibniz took an interest in it while developing binary arithmetic.

The I Ching (Book of Changes), an ancient Chinese text used for divination and philosophy, is organised around 64 hexagrams.

There are 64 codons in the genetic code (all known cellular life). Four bases in groups of three. Sixty-one specify amino acids and three are stop signals, so most amino acids have more than one codon.

A chessboard has sixty-four squares and the I Ching has sixty-four hexagrams, each formed from six binary lines. The two are unrelated in origin, and the second is a genuine binary enumeration rather than a coincidence of size.

64-bit is the dominant processor and operating-system architecture width in modern general-purpose computing, having superseded 32-bit systems over the 2000s and 2010s.

There are 64 squares on a chessboard (worldwide, standard chess). Eight by eight. Doubling a grain of wheat on each square in turn gives more wheat than has ever been grown, which is the point of the story usually told about it.

A standard chessboard has 64 squares, arranged in an 8×8 grid.

64 is both 8² and 4³, which makes it the smallest number above 1 that is a perfect square and a perfect cube at once (the next is 729). It is also 2⁶, so all three descriptions — square, cube and power of two — are the same fact viewed differently.