There is a way to express 64 with only two fours and no symbols beyond +, -, *, /, ^, √, !, and parenthesis, although some may be used more than once. It isn't too hard. Can you find it?
It is asserted in a reliable source that 64 can also be expressed with a single 4 using 57 square root signs, nine factorials (no double or higher factorials), and 18 sets of parentheses. I can't figure it out. Can you?
For the second part, you actually need 8 sets of Floor(...) functions as well as the 57 square roots and 9 factorials. Let S[x]=Sqrt[x] and F[y]=Floor[y]
F[ S[ S[ S[ S[ S[ S[ S[ S[ S[ F[ S[ S[ S[ S[ S[ S[ S[ S[ S[ F[ S[ S[ S[ S[ S[ S[ S[ S[ S[ S[ S[ S[ S[ F[ S[ S[ S[ S[ S[ S[ S[ S[ F[ S[ S[ S[ S[ S[ S[ S[ S[ S[ S[ S[ F[ S[ F[ S[ F[ S[ S[ S[ S[ S[(4!)!]]]]]]!]]!]]!]]]]]]]]]]]]!]]]]]]]]]!]]]]]]]]]]]]]]!]]]]]]]]]]!]]]]]]]]]]
Second Part
