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Old 2020-11-25, 20:32   #12
henryzz
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Quote:
Originally Posted by Ensigm View Post
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
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Old 2020-11-25, 21:19   #13
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Quote:
Originally Posted by henryzz View Post
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.
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Old 2020-11-25, 21:57   #14
petrw1
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Quote:
Originally Posted by henryzz View Post
Hitting blank trying to use sqrt
is SQRT(666*666) cheap?
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Old 2020-11-25, 22:00   #15
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2020 = 66613 + 66613 - 13*13 - (13+13+13+13+13+13+13)/13
2 ea 666
12 ea 13
total 14
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Old 2020-11-25, 22:08   #16
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2020 = 13#/((666+666+666)/666) - (666 x 13) + 666 + (13+13)/13
6 ea 666
5 ea 13
total 11
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Old 2020-11-25, 22:28   #17
petrw1
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Quote:
Originally Posted by Uncwilly View Post
2020 = 66613 + 66613 - 13*13 - (13+13+13+13+13+13+13)/13
2 ea 666
12 ea 13
total 14

3C3+3C3= ???
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Old 2020-11-25, 22:34   #18
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666÷6.66×(13+13)÷1.3+(666+666)÷6.66

Getting a little inventive.. but unc started it ..Nya Nya
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Old 2020-11-25, 22:35   #19
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Quote:
Originally Posted by Uncwilly View Post
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
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Old 2020-11-25, 23:04   #20
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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."
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Old 2020-11-26, 00:01   #21
charybdis
 
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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
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Old 2020-11-26, 11:01   #22
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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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