13x666=2020 - Page 2

henryzz · 2020-11-25, 20:32

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

Ensigm · 2020-11-25, 21:19

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.

petrw1 · 2020-11-25, 21:57

Quote:

Originally Posted by henryzz

Hitting blank trying to use sqrt

is SQRT(666*666) cheap?

Uncwilly · 2020-11-25, 22:00

2020 = 666₁₃ + 666₁₃ - 13*13 - (13+13+13+13+13+13+13)/13
2 ea 666
12 ea 13
total 14

Uncwilly · 2020-11-25, 22:08

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

petrw1 · 2020-11-25, 22:28

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= ???

petrw1 · 2020-11-25, 22:34

666÷6.66×(13+13)÷1.3+(666+666)÷6.66

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

Uncwilly · 2020-11-25, 22:35

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

Dr Sardonicus · 2020-11-25, 23:04

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."

charybdis · 2020-11-26, 00:01

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...

robert44444uk · 2020-11-26, 11:01

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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2020-11-25, 22:00	#15
Uncwilly 6809 > 6502 """"""""""""""""""" Aug 2003 101×103 Posts 21774₈ 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 2²·7²·47 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, 22:34	#18
petrw1 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

2020-11-25, 23:04	#20
Dr Sardonicus Feb 2017 Nowhere 3³×5×31 Posts	131313 - 1313 - ((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, 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, 95=45, 45^2 = 2025, 2025-5=2020