171 =
172 = 44 * 4 - 4
173 =
174 = 44 * 4 - √4

Yes, I took the two easy ones ... I'm still trying the other two

[quote=petrw1;100109]171 =
172 = 44 * 4 - 4
173 =
174 = 44 * 4 - √4

Yes, I took the two easy ones ... I'm still trying the other two[/quote]Back in post #10 of this thread, Wacky proposed an "interesting" rule we've followed since then:
[quote=Wacky;97581]And just to keep it "interesting", no skipping around. :)
You have to wait to post "7" until someone posts a solution for 6", etc.
Posting "better" solutions for smaller numbers is fine.[/quote]So, we need 171 before proceeding further. :-)

I did not find anything without gamma...

171 = gamma(gamma(4)) / √.4~ - 4/.4~

173 = gamma(gamma(4)) + (4! - .4~)/.4~

Edit: going further:

175 = ((4 + 4!) / .4) / .4
176 = 44 * (√4 + √4)

We move on after 177:

177 = ((√4 / .4)! - √4) / √.4~
178 = (4 * 44) + √4
179 = ((4 + √4)! - 4) / 4
180 = 4 + (4 * 44)

Some better solutions (note that I consider too many square roots to be ugly):

[QUOTE]
164 = √(√(√(4^4!)))) / .4 + 4
165 = (√4+ √(√(√(4^4!))))) / .4
170 = (√(√(√(4^4!))) + 4) / .4[/QUOTE]

164 = (√4 / .4)! + 44
165 = 44 / (.4 * √.4~)
170 = (4! + 44) / .4

Suggestion
 

I suggest you allow two additional functions, sum and subfacorial.

S4 = 4+3+2+1= 10 (I do not have a sigma on my computer)
!4= 9

These are sometimes accepable in this game.

181 = ((√4 / .4)! + √.4~)/√.4~

181 = (4 + (4 + sqrt(4))!) / 4
182 = ((4 + sqrt(4))! / 4) + sqrt(4)
183 = (sqrt(4) + (sqrt(4) / .4)!) / sqrt(.4~)
184 = 4 * (sqrt(4) + 44)

Is 185 possible?

[QUOTE=fetofs;101718]

Is 185 possible?[/QUOTE]

I didn't think 181 or 183 was possible ... but you proved me wrong.

So I won't try to guess if 185 is possible.

I did not find anything without gamma.

185 = gamma(gamma(4)) + √(√(√(4^4!))) + gamma(√4))

[QUOTE=PrimeCrazzy;101700]I suggest you allow two additional functions, sum and subfacorial.

S4 = 4+3+2+1= 10 (I do not have a sigma on my computer)
!4= 9

These are sometimes accepable in this game.[/QUOTE]

You can get the gamma function for positive integers quite easily:

gamma(n) = (n-1)!

examples:

gamma(√4) = 1! = 1
gamma(4) = 3! = 6
gamma(gamma(4)) = 5! = 120

You can also get 185 by using the sum and subfactorial functions ad follows:

(sum(sum4))*sqrt (4 subfactorial)+sum4+sum4