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Logic Level 5

$\LARGE 1 \ \ \ \ \ 2 \ \ \ \ \ 3 \ \ \ \ \ 4 \ \ = \ \ 1000$

Without touching the right side of the equation, find a way to make the equation above true. You are only allowed to use mathematical operators like addition, subtraction, multiplication, division and parenthesis, percentage, and factorials only.

With your answer, define $$N$$ as the least amount of mathematical operators used. Find $$N$$.

Details and Assumptions:

• As an explicit example, if the equation $$1 \div (2 + 3)^{4!}= 1000$$ is true, then you have used 4 operators: one division, one addition, one parenthesis, one factorial. In this case, $$N=4$$.

• You can combine the digits as well. i.e.: $$12 +34$$.

• You must keep the digits in order (from left to right). $$1+2+3\times4$$ is valid while $$1+2-4\div3$$ is not valid.

• BODMAS applied.

• You need a number before the percentage sign. For example. $$1234 + \%$$ is invalid while $$123 + 4\%$$ is valid.

• Exponentiation is allowed.

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