20201125, 20:32  #12 
Just call me Henry
"David"
Sep 2007
Cambridge (GMT/BST)
5·19·61 Posts 
I realized the first answer could have half its 13s converted to any number. In fact, only 2 need to be 13s.
Using 2^11 was a nice solution. 9 of each using factorials ((666+666+666)/666)!^((13+13+13+13)/13)+666+13+13+13+13+((666+666+666)/666)! Hitting blank trying to use sqrt 
20201125, 21:19  #13  
Aug 2020
2×3×19 Posts 
Quote:
In saying "smooth" I was making a pun about the fact that the answer makes good use of the 7smoothness of 2016. 

20201125, 21:57  #14 
1976 Toyota Corona years forever!
"Wayne"
Nov 2006
Saskatchewan, Canada
4537_{10} Posts 

20201125, 22:00  #15 
6809 > 6502
"""""""""""""""""""
Aug 2003
101×103 Posts
23F5_{16} Posts 
2020 = 666_{13} + 666_{13}  13*13  (13+13+13+13+13+13+13)/13
2 ea 666 12 ea 13 total 14 
20201125, 22:08  #16 
6809 > 6502
"""""""""""""""""""
Aug 2003
101×103 Posts
5×7×263 Posts 
2020 = 13#/((666+666+666)/666)  (666 x 13) + 666 + (13+13)/13
6 ea 666 5 ea 13 total 11 
20201125, 22:28  #17 
1976 Toyota Corona years forever!
"Wayne"
Nov 2006
Saskatchewan, Canada
13·349 Posts 

20201125, 22:34  #18 
1976 Toyota Corona years forever!
"Wayne"
Nov 2006
Saskatchewan, Canada
13×349 Posts 
666÷6.66×(13+13)÷1.3+(666+666)÷6.66
Getting a little inventive.. but unc started it ..Nya Nya 
20201125, 22:35  #19 
6809 > 6502
"""""""""""""""""""
Aug 2003
101×103 Posts
23F5_{16} Posts 

20201125, 23:04  #20 
Feb 2017
Nowhere
10123_{8} Posts 
13*13*13  13*13  ((666+666)/666)^((666+666+666)/666)
666 + 666 + 666 + ((13+13)/13)*(13  (13+13)/13) I had checked the idea of the stated equation being valid in some base. This led to a cubic equation whose only real root was about 5.09. I concluded that the "little know fact" was an "alternative fact." 
20201126, 00:01  #21 
Apr 2020
13^{2} Posts 
Does 2020.000008 with 6 numbers count? (almost certainly beatable btw)
Code:
sqrt(sqrt(sqrt(sqrt(sqrt(sqrt(sqrt(sqrt(sqrt(666!)))))))))*sqrt(sqrt(sqrt(sqrt(sqrt(sqrt(sqrt(sqrt(sqrt(sqrt(sqrt(sqrt(sqrt(666!)))))))))))))*sqrt(sqrt(sqrt(sqrt(sqrt(sqrt(sqrt(sqrt(sqrt(sqrt(sqrt(sqrt(sqrt(sqrt(sqrt(sqrt(sqrt(sqrt(sqrt(sqrt(sqrt(sqrt(sqrt(sqrt(sqrt(sqrt(sqrt(sqrt(sqrt(666!)))))))))))))))))))))))))))))*sqrt(sqrt(sqrt(sqrt(sqrt(sqrt(sqrt(sqrt(sqrt(sqrt(sqrt(sqrt(sqrt(sqrt(sqrt(sqrt(sqrt(sqrt(sqrt(sqrt(sqrt(13)))))))))))))))))))))/sqrt(sqrt(sqrt(sqrt(sqrt(sqrt(sqrt(sqrt(sqrt(sqrt(sqrt(sqrt(sqrt(sqrt(sqrt(sqrt(sqrt(sqrt(sqrt(sqrt(sqrt(sqrt(666!))))))))))))))))))))))/sqrt(sqrt(sqrt(sqrt(sqrt(sqrt(sqrt(sqrt(sqrt(sqrt(sqrt(sqrt(sqrt(sqrt(13)))))))))))))) Last fiddled with by charybdis on 20201126 at 00:03 
20201126, 11:01  #22 
Jun 2003
Oxford, UK
2·7·137 Posts 
Certainly not the smallest, but has some symmetry and uses 5 operators, +,,^,/,()
((((((13+13)/13)^((13+13)/13)+(13/13))+(((666+666)/666)^((666+666)/666)))*(((13+13)/13)^((13+13)/13)+(13/13)))^((666+666)/666))(((13+13)/13)^((13+13)/13)+(13/13)) i.e. 2^2+1=5, 2^2=4, 5+4=9, 9*5=45, 45^2 = 2025, 20255=2020 
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