mersenneforum.org 13x666=2020
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2020-11-25, 20:32   #12
henryzz
Just call me Henry

"David"
Sep 2007
Cambridge (GMT/BST)

2·2,897 Posts

Quote:
 Originally Posted by Ensigm The second one is really a smooth answer!
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

2020-11-25, 21:19   #13
Ensigm

Aug 2020

2·3·19 Posts

Quote:
 Originally Posted by henryzz I realized the first answer could have half its 13s converted to any number. In fact, only 2 need to be 13s.
Aha, I didn't realize the two answers are essentially the same until now.

In saying "smooth" I was making a pun about the fact that the answer makes good use of the 7-smoothness of 2016.

2020-11-25, 21:57   #14
petrw1
1976 Toyota Corona years forever!

"Wayne"
Nov 2006

23×34×7 Posts

Quote:
 Originally Posted by henryzz Hitting blank trying to use sqrt
is SQRT(666*666) cheap?

 2020-11-25, 22:00 #15 Uncwilly 6809 > 6502     """"""""""""""""""" Aug 2003 101×103 Posts 100011111010112 Posts 2020 = 66613 + 66613 - 13*13 - (13+13+13+13+13+13+13)/13 2 ea 666 12 ea 13 total 14
 2020-11-25, 22:08 #16 Uncwilly 6809 > 6502     """"""""""""""""""" Aug 2003 101×103 Posts 23EB16 Posts 2020 = 13#/((666+666+666)/666) - (666 x 13) + 666 + (13+13)/13 6 ea 666 5 ea 13 total 11
2020-11-25, 22:28   #17
petrw1
1976 Toyota Corona years forever!

"Wayne"
Nov 2006

23·34·7 Posts

Quote:
 Originally Posted by Uncwilly 2020 = 66613 + 66613 - 13*13 - (13+13+13+13+13+13+13)/13 2 ea 666 12 ea 13 total 14

3C3+3C3= ???

 2020-11-25, 22:34 #18 petrw1 1976 Toyota Corona years forever!     "Wayne" Nov 2006 Saskatchewan, Canada 23·34·7 Posts 666÷6.66×(13+13)÷1.3+(666+666)÷6.66 Getting a little inventive.. but unc started it ..Nya Nya
2020-11-25, 22:35   #19
Uncwilly
6809 > 6502

"""""""""""""""""""
Aug 2003
101×103 Posts

23EB16 Posts

Quote:
 Originally Posted by Uncwilly 2020 = 66613 + 66613 - 13*13 - (13+13+13+13+13+13+13)/13 2 ea 666 12 ea 13 total 14
66613 + 66613 - 13*13 - (13+13+13+13+13+13+13)/13
109810 + 109810 - 169 - 91/13
2196 - 169 - 7
2027 - 7
2020

 2020-11-25, 23:04 #20 Dr Sardonicus     Feb 2017 Nowhere 2×3×5×139 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."
 2020-11-26, 00:01 #21 charybdis   Apr 2020 132 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)))))))))))))) Theoretically it should be possible to get arbitrarily close to 2020 using only one number by nesting factorials as well as sqrts... Last fiddled with by charybdis on 2020-11-26 at 00:03
 2020-11-26, 11:01 #22 robert44444uk     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, 2025-5=2020

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