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## Operator Search

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

# Level 2

$\LARGE 9 \ \ \ \ \ 9 \ \ \ \ \ 9 \ \ \ \ \ 9 \ \ = \ \ 100$

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.)

##### Want an additional challenge? Try this harder version!

$\large 1 \; \square \; 2 \; \square \; 3 \; \square \; 4 \; \square \; 5 \; \square \; 6$

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.

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

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.

$\LARGE 8 \ \ \ \ 8 \ \ \ \ 8 \ \ \ \ 8 \ \ \ = \ \ \ 6$

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.
###### Inspiration.

$\large 3 \; \square \; 3 \; \square \; 3 \; \square \; 3$

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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