Sunny's Four 4's Challenge

This challenge was sent to us by SUNNY from SLOVENIA and we think it's the most extraordinary problem we've ever been sent! The question is simple enough:

HINTS

^= power
Therefore 4^SQRT4 = 42=16

! = factorial
Therefore 4!= 4x3x2x1.
 
!! = double factorial.
With an even number such as 4, you just multiply the even numbers, so
4!! = 4x2 =8 or 6!! = 6x4x2 = 48
or 8!! = 8x6x4x2=384.
With an odd number such as 7 you just multiply the odd numbers so
7!! = 7x5x3x1 =105.

We should like to apologise to any four wheel drive vehicle enthusiasts who have found this page through a search engine and are just a TINY bit disappointed.
Can you make any number from 1 to 100 using four 4's and any operators?

(See below for the TOUGH version!)

The Rules:

Here are few answers with how they work out to give you the idea:

1 = 44/44

2 = 4/4 + 4/4 = 1 + 1

6 = (4+4)/4 + 4 = 8/4 + 4 = 2 + 4

12 = 4 x 4 - SQRT4 x SQRT4 = 16 - 2x2 =16 - 4

25 = (SQRT4 + SQRT4)! + 4/4 = (2 +2)! +1 = 4! +1 = 24 +1

55 = ((4!!)!! + 4!)/ 4!! + 4 = (8!!+24)/8 +4 = (384 +24)/8 +4 = 408/8 +4 = 51 +4

75 = ((4!)^SQRT4 + 4!)/ 4!! = (24^2 + 24)/8 = (576 +24)/8 = 600/8

Let us know how you get on!

A lot of numbers have more than one solution, but if you get stuck, Sunny gave us the answers!

And now... the TOUGH version!

If you've found the challenge too easy so far, then why not do what MICHAEL JONES from England did?

Can you make any number from 101 to 200 using four 4's and any operators?

TRIPLE FACTORIAL !!!

Take your number and subtract 3, then subtract 3 again and keep subtracting 3 until you get to 0 or less. Then multiply all the answers together to get the triple factorial. Therefore:
8!!! = 8 x 5 x 2 = 80
10!!! = 10 x 7 x 4 x 1 = 280.

INT (or the INTEGER function)

If you get a number with a decimal after it, just ignore the decimal bit. Therefore:
INT(3.741) = 3
INT(19.26) = 19
We take NO RESPONSIBILITY for any damage to your brain while trying this, but we should warn you that Michael started using TRIPLE FACTORIALS and he was still stuck. However we put him in touch with Sunny who suggested using the INT function and after a lot of correspondence between England and Slovenia, he succeeded!

Here are a couple of answers to show you the sort of thing you're looking for...

131 = (((4!!)!! + 4!)/4!!) + (4!!)!!!
       = (((4x2)!! + 4x3x2x1)/(4x2)) + (4x2)!!!
       = ((8!! + 24)/8) + 8!!!
       = ((8x6x4x2 + 24)/8) + 8x5x2
       = ((384 + 24)/8) + 80
       = (408/8) + 80
       = 51 + 80
       = 131

155 = INT(SQRT((4!!)!)) - INT(SQRT((4!!)!!)) -4! -SQRT4
       = INT(SQRT((4x2)!)) - INT(SQRT((4x2)!!)) - 4x3x2x1 - 2
       = INT(SQRT(8!)) - INT(SQRT(8!!)) - 24 - 2
       = INT(SQRT(8x7x6x5x4x3x2x1)) - INT(SQRT(8x6x4x2)) - 26
       = INT(SQRT(40320)) - INT(SQRT(384)) - 26
       = INT(200.798) - INT(19.596) - 26
       = 200 - 19 - 26
       = 155

Admittedly they're not pretty, useful or even interesting, but you simply have to sit back and admire the sheer determination and brain power that produced the 101-200 answers!

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