Four Fours/Lemmata/Two Fours/64/Solutions/1

Puzzle: Two Fours: $64$

Using exactly $2$ instances of the number $4$, the task is to write an expression for $64$, using whatever arithmetical operations you consider necessary.

Solution

$64 = \paren {\sqrt 4}^{\map \Gamma 4}$

where $\map \Gamma 4$ denotes the Gamma function of $4$.

Also presented as

This is how it appears according to Donald Ervin Knuth:

$64 = \sqrt {4^{\map \Gamma 4} }$

Sources

• 1964: Donald E. Knuth: Representing Numbers using Only One Four (Math. Mag. Vol. 37: pp. 308 – 310)  www.jstor.org/stable/2689238