# Three 4's Puzzler - Spoiler

I’m sure this is NOT the answer they are looking for:

Your use of understatement juxtaposed with hyperbolic functions creates elegant rhetorical irony. Even though we can all safely share your sureness that it isn’t the intended answer, it looks to me as if you technically followed the rules. I wouldn’t begrudge you the shopping bags should you win.

If one allows trigonometric functions to join the set of “mathematical terms that are usually used in writing mathematical expressions,” Then we can get any number from any single digit with judicious use of tangents along with the functions that tweak numbers in predictable directions (like sqrt tending to 1). Here’s an expression for 55 using one 4:

CEILING(TAN(TAN(SQRT(SQRT(SQRT(SQRT(SQRT(SQRT(SIN(SQRT(4)))))))))))

BTW, there are at least 3 solutions that use no function names at all, just non-alphabetic symbols.

Fair enough. I share your implied thought that they mean stuff like !%*/.()^ and so forth, but I was frustrated at not being able to come up with an answer just using that stuff. Possibly I’m overlooking a simple symbol or more likely just not thinking cleverly enough.

“Your expression could have any of the symbols. You could have 4 to the 4th, you could have 4 factorial, you could have 4.4. You can use anything that you’d see in a mathematical expression as fair game.”

Technically my answer is right if you rely on that final sentence, but I don’t think they’re looking for anything with trig in it. I did eschew the use of e or pi as those letters represent numbers. I guess I’ll take another run at the symbol-only solution, but I’m not optimistic about my chances.

Ok, I already felt stupid, but now I’ve proved it:

(4!-sqrt(4))/.4=55

I don’t know what the other solutions are (yet?) but I know I didn’t see a factorial sign in 10th grade, not until combinatorics in college.