It's closer than you think

Logic Level 5

1     2     3     4  =  1000 \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 NN as the least amount of mathematical operators used. Find NN.

Details and Assumptions:

  • As an explicit example, if the equation 1÷(2+3)4!=1000 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=4N=4 .

  • You can combine the digits as well. i.e.: 12+3412 +34 .

  • You must keep the digits in order (from left to right). 1+2+3×41+2+3\times4 is valid while 1+24÷31+2-4\div3 is not valid.

  • BODMAS applied.

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

  • Exponentiation is allowed.

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