[QUOTE=Ensigm;564375]The second one is really a smooth answer![/QUOTE]

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

[QUOTE=henryzz;564386]I realized the first answer could have half its 13s converted to any number. In fact, only 2 need to be 13s. [/QUOTE]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.

[QUOTE=henryzz;564386]Hitting blank trying to use sqrt[/QUOTE]

is SQRT(666*666) cheap?

2020 = 666[SUB]13[/SUB] + 666[SUB]13[/SUB] - 13*13 - (13+13+13+13+13+13+13)/13
2 ea 666
12 ea 13
total 14

2020 = 13#/((666+666+666)/666) - (666 x 13) + 666 + (13+13)/13
6 ea 666
5 ea 13
total 11

[QUOTE=Uncwilly;564402]2020 = 666[SUB]13[/SUB] + 666[SUB]13[/SUB] - 13*13 - (13+13+13+13+13+13+13)/13
2 ea 666
12 ea 13
total 14[/QUOTE]


3C3+3C3= ???

666÷6.66×(13+13)÷1.3+(666+666)÷6.66

Getting a little inventive.. but unc started it ..Nya Nya

[QUOTE=Uncwilly;564402]2020 = 666[SUB]13[/SUB] + 666[SUB]13[/SUB] - 13*13 - (13+13+13+13+13+13+13)/13
2 ea 666
12 ea 13
total 14[/QUOTE]
666[SUB]13[/SUB] + 666[SUB]13[/SUB] - 13*13 - (13+13+13+13+13+13+13)/13
1098[SUB]10[/SUB] + 1098[SUB]10[/SUB] - 169 - 91/13
2196 - 169 - 7
2027 - 7
2020

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."

Does 2020.000008 with 6 numbers count? :razz: (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))))))))))))))[/code]

Theoretically it should be possible to get arbitrarily close to 2020 using only one number by nesting factorials as well as sqrts...

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