10 points to the biggest egghead?

Question

The answer is 4. Your job is come up with problem and solution. The person that uses the most unique math operations wins, for example: 2+2 counts the same as 2+2+0. 2+2-0 wins over 2+2+0.


The catch: You may not use the same number twice. You may modify your answer anytime, but if it looks like someone elses in the end, then who ever posted the answer last will be disqualified.

Good luck !!

Answer 1

A little better (without the 12-11=1 kind of cheating :):

[(from 0 to 1)∫((√20)^(5!/60)+(40-28))dx]/ [8(d/dx(x))]• [(16↑128) /(|-4| →3→2)]• ln(e)•arccos{[(0≤j≤∞) ∑{(-1)^i•1/(sec(π/3)j)!}^ {(1≤j≤p)∏[j/(p+1-j)]}

Probably not the biggest egghead, but uses:
∫
d/dx
√
^
+
-
•
/
!
ln
|a|
↑
a→b→c
(or 13 operations)
Plus new additions of:
∑
∏
arccos
sec
(thus up to 17)

Where
↑ is given by Knuth's up arrow notation (http://en.wikipedia.org/wiki/Knuth%27s_up-arrow_notation )
and
a→b→c is given by Conway chained arrow notation (http://en.wikipedia.org/wiki/Conway_chained_arrow_notation )


And to answer fcas80: "fore"

What does this equal?
(from 0 to 1)∫((√20)^(5!/60)+(40-28))dx = (√5)^(5!/60)+(10-7) =(√20)^(120/60)+12 =√20^2+12 =20+12=32
(÷)[8(d/dx(x))]=8 (=4)
(•)[(16↑128) /(|-4| →3→2)] =16^124/4^256 =4^256/4^256=1(=4)
(•)ln(e)=1 (=4)

(•)arccos{[(0≤j≤∞) ∑{(-1)^i•1/(sec(π/3)j)!}^ {(1≤j≤p)∏[j/(p+1-j)]}:
sec(π/3)=2
{(1≤j≤p)∏[j/(p+1-j)]} =(1/p)•(2/(p-1))•(3/(p-2)• . . . • ((p-2)/3)•((p-1)/2)•(p/1) =1

∑{(-1)^i•1/(2j)!}^1=cos(1)
arccos{[(0≤j≤∞) ∑{(-1)^i•1/(sec(π/3)j)!}^ {(1≤j≤p)∏[j/(p+1-j)]} =arccos(cos(1))=1 (=4)

Answer 2

4

Answer 3

5+6-7=4

Answer 4

1+3-2+7+8/4+9-16=4

Order of operations

Answer 5

90-78=12 divide by 3=4

Answer 6

3x1+2-6+5=4

Answer 7

The Answer to the Ultimate Question of Life, the Universe, and Everything / 10.5

Answer 8

[ (sin 17 + ln 28 - sqrt (4)) / (tan 59 * cost 6!) ] ^0 +3 = 4

Lets see I hit: sin, cos, tan, ln, sqrt, factorial, exponent, +, -, /, *

Everything inside the [ ] ^0 = 1 ... add 3 = 4

Answer 9

2x2=4-0+0-0+0-0+0-0+0-0+0=4

Answer 10

{52 x [465-464] - [(25^2) + 1] + [56 / 8] } / ({4678^3} - 102371873750)