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?

I assume it's impossible to take the factorial of a number that's negative or not an integer, because of the domain of a factorial number. Thus, I would say that taking the square root of any number that's not a perfect square would not lead to a solution because all that is possible when taking the square root of a non-integer is a non-integer. Since you need to end up with an integer (64), that is not a possible solution.

If you take the square root of 4, you will get 2. The square root of 2 is irrational, and the factorial of 2 is 2, so that is a dead end. If you take the factorial of 4, you will keep getting numbers which are not perfect squares. Thus it seems like it is not possible.

Posted by Gamer on 2006-04-10 15:16:21