Friday, October 28, 2016

smallest number obtainable from 2020


If only the four basic operations, concatenation and parenthesis are allowed, the largest number which can be obtained from $2$ $0$ $2$ $0$ is... $2020$ :-) (If exponentials were allowed, $20^{20}$ would be much higher, of course). But what is the smallest number which can be obtained?


Clarifications (note that many answers were written before these were added):



  • The numbers 2, 0, 2, 0 must be used in that order.


  • None may be omitted.

  • The "four basic operations" do not include unary + (which would be a no-op in any case) or unary - (which would e.g. allow -2020 as an answer).

  • "Smallest" means "most negative", not "closest to zero".

  • Concatenation may only be applied to literal digits.

  • Exponentiation is not allowed, even though it is written without any explicit operators.

  • Inserting decimal points is not allowed.



Answer



If only addition ($+$), subtraction ($−$), multiplication ($\times$) and division ($/$), without unary minus, then




$2 \times ( 0 - 20) = -40$



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