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Fill in the missing operations to make a true equation. See more

\[ \LARGE 9 \ \ \ \ \ 9 \ \ \ \ \ 9 \ \ \ \ \ 9 \ \ = \ \ 100 \]

What is the fewest number of operators \((+, -, \times, \div)\) needed on the left hand side of the equation to make the statement true?

**Details and Assumptions**:

For example, if the equation \( 9 + 9 + 9 \div{9}= 100 \) is true, then you have used 3 operators: one division and two additions.

You are allowed to concatenate the digits, but it does not count as an operation. (That is, you can treat 9 9 as 99.)

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\[\large 1 \; \square \; 2 \; \square \; 3 \; \square \; 4 \; \square \; 5 \; \square \; 6\]

Fill in the boxes above with any of the four mathematical operators ( \(+, -, \times , \div \) ). What is the maximum possible resultant number?

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

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

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.

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\[ \LARGE 8 \ \ \ \ 8 \ \ \ \ 8 \ \ \ \ 8 \ \ \ = \ \ \ 6 \]

How do you make this equation true by only using mathematical operators like addition, subtraction, multiplication and division and parentheses on the left hand side of the equation?

Define

\(A\) as the number of addition signs used,

\(B\) as the number of subtraction signs used,

\(C\) as the number of multiplication signs used,

\(D\) as the number of division signs used,

\(E\) as the number of pairs of parentheses used.

Submit your answer as \(\overline{ABCDE} \).

**Details and Assumptions**:

- For example, if your equation is \( -8 \times 8 \div (8 -8) = 6 \), then \(A=0,B=2,C=1,D=1,E=1\) and your answer is 02111.
- Use as few parentheses and addition signs as possible.
- Binomial coefficients don't count.
- BODMAS is applied.

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

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.

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