Henry Ernest Dudeney/Modern Puzzles/58 - The Two Fours/Solution

by : $58$

 * The Two Fours

Solution
If you allow the $\Gamma$ function:


 * $\paren {\sqrt 4}^{\map \Gamma 4} = 2^6 = 64$

Otherwise, there is this ingenious creation that was supplied by himself, and may be original to him:


 * $\sqrt {\paren {\sqrt {\sqrt 4} }^{4 !} } = \sqrt {\paren {\sqrt 2}^{24} } = \sqrt {2^{12} } = \sqrt {4096} = 64$