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?

(In reply to better method by The riddler)

The riddler, though your "method" does indeed express 64 within the constraints given, I can not agree that it is better.

As double factorials were not disallowed for this first part of the problem, the following is also a solution:

(4!!)^SQRT(4) = 64

The square root of 4 is 2...the double factorial of 4 is 8...8 to the power of 2 is 64; or

(4!!)*(4!!) = 64

The double factorial of 4 is 8, 8 * 8 is 64.

Another alternative solution, though not as simple in expression, is:

SQRT(4)^^(SQRT(!4))! = 64

The subfactorial of 4 is 9...the square root of 9 is 3...3 factorial is 6....the square root of 4 is 2...2 to the power of 6 is 64.

I am sure other solutions are available.  Can you provide another?

Edited on April 7, 2006, 9:08 pm

Posted by Dej Mar on 2006-04-07 20:36:51