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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