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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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