[QUOTE=petrw1;564401]is SQRT(666*666) cheap?[/QUOTE]

Was trying to avoid that

(666 + (666+666+666)/666) * (13+13+13)/13 + 13

Uses 5 of each.

13 * (13*13+13-666/(13+13)) - 13

8 numbers used.

[QUOTE=petrw1;564343]
Find a formula using only 13 and 666 to get 2020.
You can only use +. -, x, /, ^, !, √

1. Find an answer with the fewest numbers (not digits).
2. Find an answer with the same number of each; and the fewest.

[/QUOTE]

For Q2 the optimal is 9 terms (using 4 pieces of 13 and 5 pieces 666):
[CODE]
13-(666-(666+666)*(666+13*(13+13)))/666
[/CODE]
and for Q1 the optimal is the above 8 terms.
Assuming that we would use "only" the +,-,*,/ operations (no other crazy . or concat) and no large (intermediate) numbers.

I've proven by brute force search that there does not exist a solution using either 7 numbers or 4 of each, if we only allow the simple operators +, -, *, /.

The closest solution with 4 of each is 13 + 13 + 666 + 666 + 666 - 666/(13*13) = 2020.05917...

2020 = 666 + 666 + 666 + sqrt(666 - 13*13 - 13)

7 numbers.

[QUOTE=swishzzz;564498]2020 = 666 + 666 + 666 + sqrt(666 - 13*13 - 13)

7 numbers.[/QUOTE]

Genius!

[QUOTE=swishzzz;564498]2020 = 666 + 666 + 666 + sqrt(666 - 13*13 - 13)

7 numbers.[/QUOTE]

Nice!

[QUOTE=swishzzz;564498]2020 = 666 + 666 + 666 + sqrt(666 - 13*13 - 13)

7 numbers.[/QUOTE]

Very impressive

Note this can be converted to 4 of each quite easily:
2020 = 666 + 666 + 666 + sqrt(666 - 13*(13+13/13))

It would surprise me if these are beaten

[QUOTE=swishzzz;564498]2020 = 666 + 666 + 666 + sqrt(666 - 13*13 - 13)

7 numbers.[/QUOTE]
[QUOTE=henryzz;564568]
Note this can be converted to 4 of each quite easily:
2020 = 666 + 666 + 666 + sqrt(666 - 13*(13+13/13))

It would surprise me if these are beaten[/QUOTE]
I can only marvel at these.

[QUOTE=henryzz;564568]Very impressive

Note this can be converted to 4 of each quite easily:
2020 = 666 + 666 + 666 + sqrt(666 - 13*(13+13/13))

It would surprise me if these are beaten[/QUOTE]

Got to love it.

The newspapers need to be told - the World needs to know :alien:

I suggest the Daily Mail or the Sun in the UK, and Fox News for the telly. And the boys and girls in QAnon, and the anti Vaxxers, and the Covid deniers, and, and....