Logic
# Operator Search

\[ \large 1 \, \square \, 2 \, \square \, 3 \, \square \, 4 \, \square \, 5 \, \square \, 6 \, \square \, 7 \, \square \, 8 = 9 \]

There are \( 2^7 =128 \) ways in which we can fill the squares with \( +, -\).

How many ways would make the equation true?

**Note**: You are not allowed to use parenthesis.

\[ \large 3 \; \square \; 3 \; \square \; 3 \; \square \; 3 \]

Fill in the boxes above with any of the four mathematical operators ( \(+, -, \times , \div \) ). Which of the following **cannot** be a resultant number?

**Note**: Order of operations (BODMAS) applied.

\[\large 1 \; \square \; 2 \; \square \; 3\; \square \; 4\; \square \; 5 \; \square \; 6 \; \square \; 7 \; \square \; 8 \; \square \; 9 = 33\]

Seven of the eight "\(\square\)"s above are filled with "\(+\)", and the other one with "\(-\)".

Before which integer should the "\(-\)" sign be placed to make the equation true?

\[\large 18 \ \square \ 12 \ \square \ 4 \ \square \ 5 = 59\]

Replace each \(\square\) with one of \(+,-,\times,\div\) to make the equation true.

Submit your answer as a 3 digit number, where:

- \(1\) represents \(+\)
- \(2\) represents \(-\)
- \(3\) represents \(\times\)
- \(4\) represents \(\div\)

**Example** : If your answer is \(+, -, \times \) then enter the answer as \(123\).

\[\Huge 1\ \ \ \ 4 \ \ \ \ 9 \ \ = \ \ 16 \]

Is it possible to make this equation true by inserting the appropriate operations? Any operations and functions can be used.