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Logic Level 5

\[\begin{eqnarray} 0 &=& 2 - 3 - 4 + 5 \\ 1 &=& (2-3) \times (4-5) \\ 2 &=& 3 - 2 - 4 + 5 \\ 3 &=& 2 \times(3-4) + 5 \\ 4 &=& 2 + 3 + 4- 5 \\ 5 &=& 2 - 3\times(4-5) \\ \end{eqnarray} \]

Above shows the first 6 non-negative integers formed by using the four mathematical operators (\(+ \ - \ \times \ \div\)) from the integers 2, 3, 4, 5 (each of which is used exactly once).

What is the smallest positive integer that cannot be represented using these conditions?

Details and Assumptions:

  • You are not allowed to join digits together: \(2+34+5\).
  • You don't have to keep the digits in order. e.g.: \(2+5-3-4 \).
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